(Baylor Math Home Page)
The Baylor University analysis seminar meets on Wednesday afternoons from 3:30PM4:30PM in Sid Richardson 225. For questions about the analysis seminar or to be added to the seminar mailing list, please contact Paul Hagelstein, Andrei MartinezFinkelshtein, Tao Mei, Marius Mitrea, or Brian Simanek (all email addresses can be found on the Baylor math department website).
3:30 PM SDRICH 225 
Baylor University 
Graduate Prelim Exam TBA
(Contact: Blanca RadilloMurguia) 

3:30 PM Zoom 
University of Warsaw 
Painleve and QuasiPainleve Equations Painleve equations are second order nonlinear differential equations solutions of which have no movable critical points (algebraic singularities). They appear in many applications but in disguise. How to find a transformation to the canonical form? This is known as the Painleve equivalence problem. The socalled geometric approach may help in many cases. In this talk I shall present some recent results on the geometric approach for the Painleve and quasiPainleve equations.
(Contact: Andrei MartinezFinkelshtein) 

3:30 PM SDRICH 225 
University of California, Irvine 
The Area Law for XXZ Quantum Spin Systems The scaling behavior of the entanglement entropy of a state ψ contains information about the correlation structure of a quantum mechanical system when in state ψ. We present results on the XXZ model in higher dimensions, and discuss in particular which states satisfy a logarithmically corrected area law.
(Contact: Christoph Fischbacher) 

3:30 PM SDRICH 225 
Baylor University 
Boundary Problems, Herztype Hardy Spaces, and Functions of Bounded Central Mean Oscillations In this talk we present recent results in the direction of solving boundary value problems for general secondorder systems on rough domains with boundary data taken in nonstandard function spaces, thus expanding the scope of the work of B. Dahlberg, E. Fabes, and C. Kenig, among others, going back to the early 1980’s. More specifically, we study the Neumann problem with boundary data in Herztype Hardy spaces, and the Dirichlet problem with boundary data in the space of functions of bounded central mean oscillations (in the spirit of the JohnNirenberg BMO space, with a twist). We develop a comprehensive CalderónZygmund theory for the relevant class of singular integral operators acting on (and from) these brands of spaces, and succeed in employing the method of boundary layer potentials to establish solvability results for the aforementioned boundary problems. This is part of my Ph.D thesis, under the guidance of Professor Marius Mitrea.
(Contact: Pedro Da Silva) 

3:30 PM SDRICH 225 
Baylor University 
A Sharp Divergence Theorem I will discuss a version of the Divergence Theorem for vector fields which may lack any type of continuity and for which the boundary trace is taken in a strong, nontangential pointwise sense. These features of our brand of Divergence Theorem make it an effective tool in dealing with problems arising in various areas of mathematics, including Harmonic Analysis, Complex Analysis, Potential Analysis, and Partial Differential Equations.
(Contact: Dorina Mitrea) 

3:30 PM SDRICH 225 
ICMAT 
Balanced Fourier truncations and X_{p} inequalities We investigate L_{p}estimates for balanced averages of Fourier truncations in group algebras, in terms of differential operators acting on them. Our results extend a fundamental inequality of Naor for the hypercube (motivated by its consequences in metric geometry) to discrete groups. As application, we establish new forms of metric X_{p} inequalities in group von Neumann algebras. Joint work with I. CanoMarmol and J. CondeAlonso.
(Contact: Tao Mei) 

3:30 PM SDRICH 225 
Baylor University 
Continued Fractions: An Arithmetic and Analytic Study Continued fractions have a long history of use in number theory and analysis. In this honors thesis defense, we provide many of the historical theorems that made them important to mathematics, along with some more recent developments. Specifically, the results from Edward Burger’s article “A Tail of Two Palindromes” are made analogous to spectral mfunctions. The main theorem characterizes all discrete mfunctions whose Jacobi parameters are eventually doubly palindromic.
(Contact: Brian Simanek) 

3:30 PM SDRICH 225 
Baylor University 
Rank Inequality Done by Free Probability and Random Matrices Abstract (Contact: Tao Mei) 

3:30 PM SDRICH 225 
Doppler Institute for Mathematical Physics and Applied Mathematics 
Effects of a nontrivial vertex coupling in the spectra of quantum graphs Abstract (Contact: Fritz Gesztesy) 

3:30 PM SDRICH 225 
The University of Tennessee at Chattanooga 
Strict Domain Monotonicity of the Principal Eigenvalue and a Characterization of Lower Semiboundedness for the Friedrichs Extension of FourCoefficient Sturm–Liouville Operators Using the variational characterization of the smallest eigenvalue below the essential spectrum of a lower semibounded selfadjoint operator, we prove strict domain monotonicity (with respect to changing the finite interval length) of the principal eigenvalue of the Friedrichs extension T_{F} of the minimal operator for regular fourcoefficient Sturm–Liouville differential expressions. As a consequence of the strict domain monotonicity of the principal eigenvalue of the Friedrichs extension in the regular case, and on the basis of oscillation theory in the singular context, in our main result we characterize all lower bounds of T_{F} as those λ∈R for which the differential equation τu = λu has a strictly positive solution u > 0 on (a,b).
This talk is based on joint work with Fritz Gesztesy.
(Contact: Fritz Gesztesy) 

3:30 PM SDRICH 344 
Texas State University 
Thin spectra for limitperiodic Dirac and CMV operators We show that Dirac and CMV operators with limitperiodic coefficients generically have spectra that are Cantor sets of zero Lebesgue measure. The proof relies on a perturbative construction due to Avila for discrete Schr\”odinger operators together with a new argument based on analyticity and noncommutation. [Joint work with Benjamin Eichinger, Ethan Gwaltney, and Milivoje Lukic]
(Contact: Brian Simanek) 

3:30 PM SDRICH 344 
UC Irvine 
Complete NonSelfadjointness for Schrödinger Operators on the HalfLine We investigate complete nonselfadjointness for all maximally dissipative extensions of a Schröodinger operator on a halfline with dissipative bounded potential and dissipative boundary condition. We
show that all maximally dissipative extensions that preserve the differential expression are completely nonselfadjoint. However, it is possible for maximally dissipative extensions to have a onedimensional reducing subspace on which the operator is selfadjoint. We give a characterization of these extensions and the corresponding subspaces and present a specific example. (Joint work with Sergey Naboko and Ian Wood) (Contact: Fritz Gesztesy) 

3:30 PM SDRICH 344 
Georgia Southern University 
Selected problems of nonlinear science I will consider problems of stability in discrete dynamical systems. The talk will be accessible to nonexperts and graduate students.
(Contact: Paul Hagelstein) 

3:30 PM SDRICH 344 
Auburn University 
Maslov index and Spectral Flow In this talk, we will discuss a relation between the Maslov index, a topological invariant counting signed intersections of paths of Lagrangian planes with a fixed reference plane, and the spectral flow, the net number of eigenvalues of a path of Fredholm operators crossing zero in the positive direction. Applications will be given to several parameterdependent boundary value problems ranging from Rohledertype inequalities for Robin Laplacians to Hadamardtype formulas for quantum graphs. In addition, we will discuss second order Taylor expansions for reslovents, spectral projections, and eigenvalues of oneparameter families of selfadjoint extensions of symmetric operators.
(Contact: Fritz Gesztesy) 

3:30 PM SDRICH 344 
Texas A&M 
Interplay between quantum automorphism groups and nonlocal games Suppose that M is a finitedimensional C^{*}algebra, equipped with its Plancherel trace. A lot of study has gone into the “quantum automorphism group” Aut^{+}(M) of M, and what kinds of properties it has. For example, if M is abelian and with dimension n, then Aut^{+}(M)=S_{n}^{+} is the quantum permutation group on n letters. The latter object has received recent attention in quantum information, due to a specific class of two player, nonlocal games related to graphs. In this talk, we will explore this link between quantum information and quantum groups, and see some new results about Aut^{+}(M) that were inspired by a new example of a graphrelated nonlocal game. In particular, we’ll see that the von Neumann algebra L^{∞}(Aut^{+}(M)) always satisfies Connes’ embedding problem, and is not isomorphic to any free group factor when dim(M) is a perfect square. (This is based on joint work with Michael Brannan, Floris Elzinga and Makoto Yamashita.)
(Contact: Tao Mei) 

3:30 PM Zoom 
Universidad Autónoma de Santo Domingo 
Galois Theories and Orthogonal Polynomials Differential Galois Theory is the Galois Theory in the context of linear differential equations. In this talk we present some links between the theory of orthogonal polynomials and classical/differential Galois theory. Some results involve integrability of differential equations in a similar sense as for solvability of polynomials. This talk is based on my previous papers available on arxiv: arXiv:1906.09764, arXiv:1012.4796 and arXiv:1008.3445.
(Contact: Andrei MartinezFinkelshtein) 

3:30 PM SDRICH 344 
Waterloo 
ZappaSzep product, selfsimilar action, and equivalent groupoids In group theory, the ZappaSzep product generalizes the semidirect product by encoding a twoway action between two groups. Similar constructions have appeared in the context of semigroups and selfsimilar action on graphs. In this talk, I will briefly survey these constructions and their applications in operator algebras. The focus is on the selfsimilar actions on groupoids and Fell bundles, which generalizes the semidirect product constructions. This leads to a way of constructing equivalent groupoids and Fell bundles from certain symmetric actions, generalizing several imprimitivity theorems arising from semidirect products. This is a joint work with Anna Duwenig.
(Contact: Tao Mei) 

3:30 PM SDRICH 344 
IST Austria 
L_{p}L_{q} Fourier multipliers on locally compact quantum groups Let G be a locally compact quantum group with dual Ĝ. Suppose that the left Haar weight a and the dual left Haar weight â are tracial, e.g. G is a unimodular Kac algebra. We prove that for 1<p≤ 2 ≤ q<∞, the Fourier multiplier m_{x} is bounded from L_{p}(Ĝ,â) to L_{q}(Ĝ,â) whenever the symbol x lies in L_{r,∞}(G,a), where 1/r=1/p1/q. Moreover, we have
m_{x}:L_{p}(Ĝ,â)⟶ L_{q}(Ĝ,â)≤ c_{p,q} x_{Lr,∞,(G,a))}, where c_{p,q} is a constant depending only on p and q. This was first proved by Hörmander (Acta. Math. 1960) for R^{n}, and was recently extended to more general groups and quantum groups. Our work covers all these results and the proof is simpler. In particular, this also yields a family of L_{p}Fourier multipliers over discrete group von Neumann algebras. A similar result for S_{p}S_{q} Schur multipliers is also proved. The talk is based on arXiv:2201.08346. (Contact: Tao Mei) 

3:30 PM Zoom 
Kansas State University 
The Neumann problem in graph Lipschitz domains in the plane We present new aspects of the solvability of the classical Neumann boundary value problem in a graph Lipschitz domain in the plane. When the domain is the upper halfplane and the boundary data is assumed to belong to weighted Lebesgue or weighted Lorentz spaces, we show that the solvability of the Neumann problem in these settings may be characterized in terms of Muckenhoupt weights and related weights, respectively. For a general graph Lipschitz domain Ω, as proved in an unpublished work by E. Fabes and C. Kenig, there exists ε_{Ω}>0 such that the Neumann problem is solvable with data in L^{p}(∂Ω) for 1<p<2+ε_{Ω}; we show that the Neumann problem is solvable at the endpoint 2+ε_{Ω} with data in the Lorentz space L^{2+εΩ,1}(∂Ω). We present examples of the results in SchwarzChristoffel Lipschitz domains and related domains.
(Contact: Dorina Mitrea) 

3:30 PM Zoom 
University of Alabama Birmingham 
Deficiency Indices for ODEs Without the Unique Continuation Property This talk is about the spectral theory associated with the differential equation Ju’+qu=wf on the real interval (a,b) when J is an n×n constant, invertible skewHermitian matrix and q and w are n×n matrices whose entries are distributions of order zero (local measures) with q Hermitian and w nonnegative. Under these hypotheses it may not be possible to uniquely continue a solution from one point to another, thus blunting the standard tools of spectral theory. Despite this fact, we are able to show that the deficiency indices of the corresponding minimal relation are still bounded by n.
(Contact: Fritz Gesztesy) 

3:30 PM SDRICH 325 
University of Houston 
A conjecture on type I locally compact groups The notion of type I, hailing from the very origins of operator algebras and representation theory, can be seen as a rigorous way to define the class of groups for which unitary representations can be classified in any meaningful manner. By a celebrated result of Thoma, a discrete group is type I if and only if it is virtually abelian. In the nondiscrete case, the current state of the art is not nearly as complete, despite numerous results ensuring that various important families of groups (e.g. every connected semisimple Lie group) are type I. What is completely lacking, in contrast to Thoma’s theorem, is a definite structural consequence of type I. This talk is around the following conjecture: Every second countable locally compact group of type I admits a cocompact amenable subgroup. We motivate the conjecture, provide some supporting evidence for it, and prove it for type I hyperbolic locally compact groups admitting a cocompact lattice.
This is joint work with PierreEmmanuel Caprace and Nicolas Monod. **This is a joint seminar with the Baylor Quantum Information Theory seminar.** 

3:30 PM SDRICH 325 
Texas A&M University 
Index theory and Gromov’s conjectures on positive scalar curvature I will talk about my recent work on solutions to some Gromov’s conjectures and open questions on positive scalar curvature. These include positive solutions to Gromov’s cube inequality on positive scalar curvature, and Gromov’s open question on λLipschitz rigidity of positive scalar curvature metrics on hemispheres or more generally spheres with certain subsets removed. If time permits, I will also talk about my recent joint work with Jinmin Wang and Guoliang Yu on an index theoretic proof for Gromov’s (strict) cube inequality on positive scalar curvature with the optimal constant.
(Contact: Tao Mei) 

3:30 PM SDRICH 325 
University of Houston 
Complete LogSobolev inequalities Logarithmic Sobolev inequalities (LSI) were first introduced by L. Gross in 70’s, and later found rich connections to geometry, graph theory, optimal transport and information theory. In recent years, logarithmic Sobolev inequalities for quantum Markov semigroups attracted a lot of attention in quantum information theory and quantum manybody system. For a classical Markov semigroup, an important advantage of logSobolev inequalities is the tensorization property that if two semigroups each satisfy an LSI, so does their tensor product semigroup. Nevertheless, the tensorization property fails in the quantum cases. In this talk, I’ll present some recent progresses on tensor stable logSobelev inequalities for finite dimensional quantum Markov semigroups. This talk is based on joint work with Cambyse Rouze.
(Contact: Tao Mei) 

3:30 PM SDRICH 325 
Baylor University 
Boundary Value Problems in Weighted Morrey Spaces in Ahlfors Regular Domains In this talk I will report on recent progress in the direction of employing boundary layer potential operators in proving the unique solvability of boundary value problems in general rough settings, best described in the language of geometric measure theory. Using a blend of techniques from Harmonic Analysis, CalderonZygmund Theory, Functional Analysis, we succeed in proving wellposedness results in the case when the boundary data is arbitrarily prescribed in Muckenhoupt weighted Morrey spaces. This work is part of my Ph.D. thesis, carried out under the guidance of Professor Marius Mitrea.
(Contact: Marcus Laurel) 

3:30 PM Zoom 
Rice University 
Ballistic transport for limitperiodic continuum Schrodinger operators in one dimension In this talk, I will discuss recent work examining the transport properties of a subclass of uniform limitperiodic, continuum Schrodinger operators, specifically those operators whose potentials are approximated exponentially quickly by a sequence of periodic functions. Specifically, for H one of these operators and X_{H}(t) the Heisenberg evolution of the position operator, we show the limit of t^{1}X_{H}(t)ψ as t→∞ exists and is nonzero for ψ belonging to a large subspace of initial states localized in position and momentum. Since this implies these operators exhibit a particularly strong form of ballistic transport, and it is known that operators in the subclass considered have absolutely continuous spectrum, this work provides more examples of almost periodic operators for which there is absolutely continuous spectrum and ballistic transport in this sense.
(Contact: Brian Simanek) 

4:00 PM Zoom 
University of South Florida 
A free boundary problem associated with electrified droplets A droplet of perfectly conducting fluid is placed into an external electric field. If the droplet is not annihilated, the forces of pressure and surface tension will balance with the field, and the droplet will come to equilibrium, resulting in a free boundary problem. This problem was first addressed by E.B. McLeod (1955), who found a single solution to the equation describing equilibrium. The problem was readdressed by D. Khavinson, A. Solynin, and D. Vassilev (2005), where some progress was made, but no new `physical’ solutions were discovered. In this talk, I will discuss some recent work of myself and F. Wang, where we found a new 1parameter family of physical solutions, using methods of quadratic differentials.
(Contact: Andrei MartinezFinkelshtein) 

4:00 PM Zoom 
University of Delaware 
Applications of MatrixValued Clark Theory to Differential Operators
In this talk, we will utilize Clark theory to obtain spectral information about symmetric differential operators. This will begin with describing the selfadjoint extensions of a symmetric differential expression using two methods. Then, various tools of Clark Theory will be established. Lastly, we will compute (Clark) spectral measures for the selfadjoint extensions of specific examples of symmetric differential expressions.
(Contact: Fritz Gesztesy) 

4:00 PM Zoom 
Auburn University 
Asymptotic perturbation theory for extensions of symmetric operators This talk concerns asymptotic perturbation theory for varying selfadjoint extensions of symmetric operators. First, we will discuss a symplectic version of the celebrated Krein formula for resolvent difference. Then we will switch to an asymptotic analysis of resolvent operators via first order expansion for the path of Lagrangian planes associated with perturbed operators. This asymptotic perturbation theory yields an Hadamard–Rellichtype variational formula for multiple eigenvalue curves bifurcating from an eigenvalue of the unperturbed operator. Applications will be given to quantum graphs, periodic Kronig–Penney model, elliptic second order partial differential operators with Robin boundary conditions, and heat equations with thermal conductivity. This talk is based on various joint projects with G. Berkolaiko (Texas A&M) and Y. Latushkin (Missouri/NYU).
(Contact: Fritz Gesztesy) 

4:00 PM Zoom 
University of Illinois 
Decay estimates of open quantum systems The generators of finite dimensional selfadjoint quantum systems are fully characterized as Lindblad operators. I will use the geometric approach to prove the entropy decay for semigroups generated by such Lindblad operators. I will also mention some related open problems (classical and quantum) that I am currently working on. This is joint work with Marius Junge and Li Gao.
(Contact: Tao Mei) 

4:00 PM Zoom 
Louisiana State University 
Besov classes and Sobolev inequalities in Dirichlet spaces In this talk, I will introduce a theory of heat semigroup based Besov spaces in abstract Dirichlet spaces which include Riemannian manifolds, subRiemannian manifolds and some fractals like Sierpinski gasket. I will then discuss its applications on Sobolev and isoperimetric inequalities with sharp exponents. The talk is based on joint works with Patricia AlonsoRuiz, Fabrice Baudoin, Luke Rogers, Nageswari Shanmugalingam and Alexander Teplyaev.
(Contact: Tao Mei) 

3:30 PM CANCELLED 
Texas A&M 
TBA TBA
(Contact: Tao Mei) 

SDRICH 324 
NAM 
TBA TBA


3:30 PM WEBEX 
Baylor 
Paley inequality on ordered group The classical Khintchine inequality implies that the L^{1} norm of the function Σ_{k} a_{k} z^{2^k} on the torus is equivalent to the l^{2} norm of its Fourier coefficients. Paley’s inequality is an improvement of the classical Khintchine inequality, which says that the Fourier coefficients of the the function in the Hardy space on torus is square summmable on the support of the lacunary set. We will introduce a similar result for the countable ordered nonabelian group, e.g. free group.


SDRICH 324

TU Graz 
Schrödinger operators with prescribed spectral properties The main objective of this talk is to illustrate how one can construct Schrödinger operators on a bounded interval with predefined essential and discrete spectra. The required structure of the spectrum is realized by a special choice of a sequence of δinteractions. Our construction is inspired by a celebrated paper [R. Hempel, L. Seco, B. Simon, J. Funct. Anal. 102 (1991), 448483] and its sequel [R. Hempel, T. Kriecherbauer, P. Plankensteiner, Math. Nachr. 188 (1997), 141168], where a similar problem was treated for Neumann Laplacians on bounded domains.
This is joint work with Jussi Behrndt (TU Graz). 

3:30 PM Video Seminar 
Texas A&M 
Quantum Markov semigroup, logarithmic Sobolev inequality and nonnegative Ricci curvature Quantum Markov semigroups models the time evolution of dissipative open quantum systems. Mathematically, they are noncommutative version of Markov semigroups where the underlying function space is replaced by matrix or operator algebras. For a Markov semigroup, the modified logarithmic Sobolev inequality (MLSI) describes the convergence property in terms of relative entropy. It was a famous result by Bakry and Emery that the heat semigroup on a compact Riemannian manifold satisfies MLSI if the Ricci curvature admits a strictly positive lower bound. Recently Carlen and Maas introduce the notation of Ricci curvature lower bound for quantum Markov semigroup and show that a positive Ricci lower bound implies MLSI in the noncommutative setting. In this talk, I will present an approach to MLSI for quantum Markov semigroup via Ricci curvature bounded below but not necessarily positive. We will show that “central” semigroups on groups and quantum groups admits nonnegative curvature and MLSI. This approach gives new examples of MLSI in both operator algebras and quantum information theory. This talk is based on joint work with Michael Brannan and Marius Junge.
(Contact: Tao Mei) 

3:30 PM SDRICH 324 
Texas A&M 
A complex analytic approach to mixed spectral problems We consider the Schroedinger operator on a finite interval with an L^{1}potential. Borg’s two spectra theorem says that the potential can be uniquely recovered from two spectra. By another classical result of Marchenko, the potential can be uniquely recovered from the spectral measure or Weyl mfunction. After a brief review of inverse spectral theory of one dimensional Schroedinger operators, we will discuss a complex analytic approach to the following problem: Can one spectrum together with subsets of another spectrum and norming constants recover the potential?
(Contact: Fritz Gesztesy) 

3:30 PM SDRICH 207 
University of New Mexico 
Bounds on Extremal Polynomials In this talk I will discuss upper and lower bounds on the norms of monic Lpextremal polynomials. In particular, I will present a sharp universal lower bound for the extremal polynomials with respect to a probability measure on a compact subset of the complex plane and its improvement for the orthogonal polynomials with respect to the equilibrium measure of a compact subset of the real line.
(Contact: Fritz Gesztesy) 

3:30 PM SDRICH 324 
Temple University 
Singular Integral Operators of Layer Potential Type One of the most efficient approaches to solving boundary value problems for elliptic partial differential equations is the method of boundary layer potentials.
In this talk I will survey some of the recent progress made in understanding the nature of integral operators of boundary layer type in optimal geometrical settings. (Contact: Dorina Mitrea, Marius Mitrea) 

2:50 PM SDRICH 324 
University of Delaware 
Singular parts of matrixvalued Aleksandrov—Clark Measures To obtain matrixvalued Aleksandrov–Clark (AC) measures, fix a matrixvalued pure contraction b on the unit disk D. Here b may be noninner and/or nonextreme. For each unitary matrix α, the linear fractional transformation (I+b(z))α^{*})(Ib(z))α^{*})^{1} has nonnegative real part. So, Herglotz’s representation theorem associates a matrixvalued measure μ^{α*}. The collection {μ^{α}: α unitary} forms the family of matrixvalued AC measures, which stand in bijection with matrixvalued pure contractions. A description of the measures’ absolutely continuous parts is easily obtained in terms of nontangential boundary values of b.
The singular parts μ^{αs} are harder. We present a matrixvalued version of Nevanlinna’s result relating nontangential boundary limits with the measures’ point masses. The connection to Carathéodory angular derivatives is more subtle than in the scalar setting. Aleksandrov spectral averaging yields restrictions on the singular parts. We have a directional version of the mutual singularity of μ^{αs} and μ^{βs}, α≠β both unitary. This presentation is based on joint work with R.T.W. Martin and S. Treil. 

3:30 PM SDRICH 325 
Baylor University 
Summary of Spring 2019 Research Leave
This will be a summary of my research activities undertaken during my research leave in Spring 2019.


3:30 PM SDRICH 325 
Baylor University 
Spectral Zeta Functions, Conformal Transformations, and Gluing Formulas Let M_{1} and M_{2} be two Riemannian manifolds each of which have theboundary N. Consider the Laplacian on M_{1} and M_{2} augmented with Dirichlet boundary conditions on N. A natural question to ask is if there is any relation between spectral properties of the Laplacian on M_{1}, M_{2}, and the Laplacian on the manifold M (without boundary) obtained gluing together M_{1} and M_{2}, namely M=M_{1}∪M_{2}. Using spectral zeta functions, a partial answer is given by the BurgheleaFriedlanderKappelergluing formula for zetadeterminants. This formula contains an (in general) unknown polynomial which is completely determined by some data on a collar neighborhood of the hypersurface N. I will use conformal transformations to understand the geometric content of this polynomial. The understanding obtained will pave theway for a fairly straightforward computation of the polynomial (at least for low dimensions of M). Furthermore it leads to a partial understanding of the heat invariant for the DirichlettoNeumann map, that is for the Steklov problem.


3:30 PM SDRICH 325 
University of South Florida 
Stahl’s theorem on a Riemann surface H.Stahl’s theorem on convergence of Pade approximats for analytic functions with branch points [St861] [St861] is one of the fundamental results in the theory of rational approximations of analytic functions. It is also one of the basic facts in the theory of orthogonal pokynomilas. Denominators of Pade approximats are complex (nonhermittian) orthogonal polynomilas and Stahl’s created an original method of investigating asymptotics of complex orthogonal polynomials based directly on complex orthogonality.
The method has been further developed by A. Gonchar and E. Rakhmanov in [GR87] for the case of orthogonality with varying weight which is equivalnt to introduction of external field in associated equilibrium problem. Incorporation of the external field in the method makes circle of its application essentially larger. The GRSmethod may be applied to general rational interpolation, Hermite – Pade approximants (systems of interpolation conditions) and other constructions of freepole approximation by rational functions. Also the geometry of the problem in the presence of the external field becomes much more sophisticated. We generalize the method for the case of interpolation by meromorphic functions on a closed Riemann surface R which are, hence, algebraic functions. It turns out that basic results on zero distribution of poles of interpolating functions remain valid in essentially the same form. (Contact: Andrei MartinezFinkelshtein) 

3:30 PM SDRICH 325 
University of Vienna 
Discrete and continuous Diractype systems on the semiaxis: spectral and scattering problems Both discrete and continuous Diractype systems play an important role in several domains of mathematics. We discuss Weyl theory, the corresponding direct and inverse spectral problems, and their explicit and general solutions. There is also a close connection between spectral and scattering problems.
(Contact: Fritz Gesztesy) 

2:30 PM SDRICH 325 
University of Michigan 
A nonlocalnonlinear PDE for the limiting distribution of the periodic TASEP Many interacting random particle systems, in a suitable limit, can be described in terms of integrable systems. For instance, it is now a classical result that the onepoint fluctuations of the height function in the TASEP (with step initial data) converge, in a suitable scaling, to the TracyWidom distribution F_{2}. In addition to remarkable universality features of F_{2}, appearing in dozens of different models that are seemingly unrelated, this distribution also enjoys several nice different characterizations, for instance it can be given interms of a somewhat simple Fredholm determinant for an integral operator, or yet in terms of a solution to the Painléve II differential equation.
If, on one hand, one can learn about the particle systems by studying the corresponding integrable system,on the other hand these different characterizations have intrinsict operatortheoretic value on their own, and a large class of integral operators can actually be connected to integrable systems in a nice systematic and, somehow, easy way via RiemannHilbert problems. In this talk, we plan to discuss how this general methodology recently produced a nice connection between the limiting distribution for the periodic TASEP and a nonlocalnonlinear PDE. This is based on work in progress with Jinho Baik (University of Michigan) and Zhipeng Liu (Universityof Kansas). (Contact: Andrei MartinezFinkelshtein) 

3:30 PM SDRICH 213 
Lund University 
Chebyshev polynomials A classical problem that goes back to Chebyshev and his study of mechanisms is to find the best uniform approximation of a continuous function f: [a,b]→R by algebraic polynomials of degree ≤n. It is well known that the monic degree n polynomial that deviates the least from zero on [1, 1] is given by
T_{n}(x)=2^{n+1}cos(nθ) with x=cos(θ). This polynomial oscillates for x between 1 and 1 and grows faster than any other monic polynomial of the same degree outside [1, 1]. But how can we describe the monic polynomials of least deviation from zero on E⊆R when E is the union of, say, k intervals or a Cantortype set?
In the talk, I shall discuss the theory for these polynomials that also bear the name of Chebyshev. Since explicit representations are rare, I’ll focus on their asymptotic behavior and the asymptotics of the approximation error. One may ask how this depends on the size and geometry of E. As we shall see, potential theory enters the field and part of the analysis relies on studying the zeros in gaps of E. Towards the end, I shall also explain how relatively little is known when E is a closed region in the complex plane and discuss some open problems in the field. The talk is based on joint work with B. Simon (Caltech), P. Yuditskii (JKU Linz), and M. Zinchenko (UNM). 

3:30 PM SDRICH 213 
Baylor University 
Selfadjoint boundary conditions for singular SturmLiouville problems and the computation of mfunctions for Bessel, Legendre, and Laguerre operators We extend the classical boundary values for (general, threecoefficient) regular SturmLiouville operators on compact intervals to the singular case as long as the associated minimal operator is bounded from below, utilizing principal and nonprincipal solutions of the underlying differential equation.
We derive the singular WeylTitchmarshKodaira mfunction and illustrate the theory with the examples of the Bessel, Legendre, and Laguerre (resp., Kummer) operators. This is based on joint work with Lance Littlejohn and Roger Nichols. 

3:30 PM SDRICH 213 
University of Cape Town 
Zeros of Laguerre Polynomials
The sequence of Laguerre polynomials {L_{n}^{(α)}(x)}_{n=0}^{∞} is orthogonal on (0,∞) with respect to the weight function e^{x} x^{α} provided α > 1. The classical result that for each natural number n, the zeros of L_{n1}^{(α)}(x) interlace with the zeros of L_{n}^{(α)}(x) can (and has) been extended by several authors in various ways. In 2014, we proved that for each natural number n, the zeros of L_{n}^{(α)}(x) and L_{nk}^{(α+t)}(x) are interlacing for each t with 0 < t ≤ 2k and the tinterval 0 < t ≤ 2k is sharp in order for interlacing to hold for every k in {1,2,…, n1} and each natural number n. Recently, this was extended to zeros of Laguerre polynomials of equal degree, namely, for each natural number n, the zeros of L_{n}^{(α)}(x) and L_{n}^{(α+t)}(x) are interlacing for each t with 0 < t ≤ 2 and the t interval 0 < t ≤ 2 is sharp in order for interlacing to hold for every natural number n. For α in the parameter range 2 < α < 1, the polynomial L_{n}^{(α)}(x) has n real zeros with n1 positive zeros and 1 negative zero. However, for α lying in this range 2 < α < 1, the sequence {L_{n}^{(α)}(x)}_{n=0}^{∞} is NOT orthogonal with respect to any positive measure and, for each natural number n, the zeros of L_{n1}^{(α)}(x) DO NOT interlace with the zeros of L_{n}^{(α)}(x) for any natural number n. However, for each natural number n, the zeros of xL_{n1}^{(α)}(x) interlace with the zeros of L_{n}^{(α)}(x). The aim of the talk is to give some background to these results and raise open problems and questions that arise naturally.
(Contact: Lance Littlejohn) 

3:30 PM SDRICH 
Williams College 
Random Unitary Matrices and Matrix Models for the Circular Beta Ensemble We consider various families of random unitary band matrices (CMV and Joye) and study their spectral properties. In particular, we investigate the distribution of the eigenvalues of these matrices and use them to construct matrix models for the circular beta ensemble. We also study spectral properties of these matrix models for beta approaching zero and infinity.
(Contact: Brian Simanek) 

3:30 PM SDRICH 
Louisiana State University 
Nodal sets of Robin and Neumann eigenfunctions We investigate the measure of nodal sets for Robin and Neumann eigenfunctions in the domain and on the boundary of the domain. A polynomial upper bound for the nodal sets is obtained for the Robin eigenfunctions. For the analytic domains, we show a sharp upper bound for the nodal sets on the boundary of the Robin and Neumann eigenfunctions. Furthermore, the sharp doubling inequality and vanishing order are obtained.


3:30 PM SDRICH 
Universidad Carlos III Madrid 
On a construction of some rational approximants to ζ(n), n=2,3,… An approach based on a RiemannHilbert problem associated to a simultaneous rational approximation problem involving the Riemann zeta function will be discussed. As a consequence of the proposed approach infinitely many rational approximants (Diophantine approximations) to ζ(3) proving its irrationality can be generated. Moreover, this approach unifies the most famous “independent” proofs of the irrationality of ζ(3). In addition, rational approximants for ζ(5), ζ(7),…, ζ(41),… will be presented.
(Contact: Lance Littlejohn) 

3:30 PM SDRICH 
Baylor University 
Numerical Ranges, Blaschke Products, and Zeros of Orthogonal Polynomials This talk will focus on the location of zeros of orthogonal polynomials on the unit circle. We will begin with an introduction of some basic results and then briefly review some more recent results of NevaiTotik and MhaskarSaff. We will conclude with new results connecting the zeros of orthogonal polynomials to the zeros of paraorthogonal polynomials and highlight some interesting connections with complex function theory and even algebraic geometry. Some open problems will be discussed along the way. This talk is based on joint work with Barry Simon and Andrei MartinezFinkelshtein.


3:30 PM SDRICH 
University of New Mexico 
A tourist in the land of Hardy spaces (Equivalent definitions of Hardy spaces on product spaces of homogeneous type) In this talk I would like to give you a glimpse into the history of the H^{p} Hardy spaces starting from its origins in complex analysis, moving into the realm of real analysis first on Euclidean space, then into oneparameter spaces of homogeneous type, and finally into twoparameter spaces of homogeneous type. The tools we will need are “dyadic cubes” and orthonormal “wavelets” in these exotic settings that will allow us to introduce appropriate square functions used in the definition of the Hardy spaces. To show independence of these Hardy spaces on the reference wavelets and dyadic grids, we will introduce atomic Hardy spaces (defined independently of wavelets and their reference grids) and use a crucial tool in the multiparameter world, a Journétype lemma adapted to this setting. We are following in the foot steps of R. Coifman, G. Weiss, R. Fefferman, and J. Pipher to mention just a few. This is work in progress joint with Yongsheng Hahn, Ji Li, and Lesley Ward.
(Contact: Paul Hagelstein) 

3:30 PM SDRICH 
University of Michigan 
Products of Coupled Random Matrices Products of random matrices have been introduced in the literature a long while ago, but only in the past few years they received attention from the mathematical physics’ community, much in virtue of the development of new techniques that can be applied to their study.
In this talk we plan to briefly explain some motivations on why we should care about these products, discuss some recent developments when the matrices in the product are independent, and share some of the most recent findings, amongst others by the speaker together with Lun Zhang (Fudan University), in a model when the matrices being multiplied are not independent, but instead coupled in a useful way. We will focus on asymptotic results obtained when the size of the matrices involved gets large, discussing both universal and nonuniversal features of the model, and in particular the emergence of the recently found MeijerG kernel. Some key elements in our analysis are a family of mixed type multiple orthogonal polynomials with respect to Bessel weights, and their zero asymptotic distribution which is described in terms of a constrained vector equilibrium problem. (Contact: Andrei MartinezFinkelshtein) 

3:30 PM SDRICH 
Baylor University 
Fourier Multipliers on Free Groups along a Geodesic Path The topic of Fourier multipliers has been studied for many years since the late 19th century in order to understand the convergence of Fourier series. Following the success in this field, the study of harmonic analysis has been expanded to the class of abelian groups. Recently, there has been a lot of new progress in the area of noncommutative harmonic analysis. As a result, much effort has been made to generalize all the theory into the realm of noncommutative groups. In this talk, we will discuss about noncommutative version of Fourier multipliers on free groups and some results and questions regarding it.


3:30 PM SDRICH 207 
Texas A&M and IITP, Moscow 
Virtual levels, zeroenergy resonances, properties of virtual states, and the limiting absorption principle near thresholds The virtual levels, also known as the threshold resonances and zero energy resonances, admit several equivalent definitions:
(1) there are corresponding virtual states from the space slightly larger than L2; (2) absence of the limiting absorption principle in the vicinity of the threshold point; (3) bifurcation of eigenvalues from thresholds under a small perturbation. We prove the equivalence of these definitions and study properties of corresponding virtual states. Once there is no virtual level, we study the limiting absorption principle near the threshold points, proving that, in the vicinity of a threshold, the resolvent is uniformly bounded in particular weighted spaces. We apply the theory to the Schroedinger operators, although the approach works for general nonselfadjoint operators (and in arbitrary dimension).
This is a joint work with Nabile Boussaid (Besançon) and Fritz Gesztesy (Baylor). (Contact: Fritz Gesztesy) 

2:30 PM SDRICH 207 
University of Kent 
Embedding eigenvalues for periodic Jacobi operators using Wignervon Neumanntype perturbations We consider a method of embedding eigenvalues in a band of absolutely continuous spectrum of a periodic Jacobi operator by adding a potential. We first discuss embedding a single eigenvalue and then show that the method can be extended to allow embedding infinitely many eigenvalues into the band.


4:30 PM SDRICH 
Cardiff University 
Spectral problems on star graphs In this talk we report on a twostep reduction method for spectral problems on a star graph with n+1 edges and a selfadjoint matching condition at the central vertex.
The first step is a reduction to the problem on a single edge, but with an energy depending boundary condition at the vertex. In the second step, by means of an abstract inverse result for mfunctions, a reduction to a problem on a path graph with two edges, joined by continuity and Kirchhoff conditions, is given. All results are proved for symmetric linear relations in an orthogonal sum of Hilbert spaces. This ensures wide applicability to various different realisations, in particular, to canonical systems and Krein strings which include, as special cases, Dirac systems and Stieltjes strings. Employing two other key inverse results by de Branges and M. Krein, we answer the following question: If all differential operators are of one type, when can the reduced system be chosen to consist of two differential operators of the same type? This is joint work with Heinz Langer and Christiane Tretter. (Contact: Lance Littlejohn) 

3:30 PM SDRICH 
University of Houston 
On the isomorphisms of Fourier algebras of finite abelian groups Can one distinguish groups by their group algebras? In this talk, I will try to convince you that the answer is yes, for infinite Vilenkin groups of bounded exponents.
We prove that if G_{1} and G_{2} are two infinite Vielenkin groups of bounded exponents such that G_{1} is not a subgroup of G_{2} then there are finite dimensional invariant convolution subalgebras of L^{1}(G_{1}) distant from any invariant convolution subalgebras of L^{1}(G_{2}). We show that the norm of certain class of algebraic isomorphims between them grows to infinity with the dimension. (Contact: Tao Mei) 

3:30 PM SDRICH 
Cambridge Center for Analysis 
The Kissing Polynomials
Motivated by the numerical analysis of highly oscillatory integrals, we discuss a family of polynomials known as the Kissing Polynomials, which satisfy a nonHermitian orthogonality condition on the interval [1,1]. We first discuss how these polynomials can be used to bridge the gap between traditional numerical methods, such as Gaussian quadrature, and the asymptotic methods that are commonly used to handle oscillatory integrals. Next, we discuss various types of asymptotics of these polynomials, where the connection with the asymptotic theory of highly oscillatory integrals becomes apparent. We will end with numerics of the zeros (part of an ongoing work with Guilherme Silva at the University of Michigan) and some open problems concerning the Kissing Polynomials.
(Contact: Andrei MartinezFinkelshtein) 

3:30 PM SDRICH 
University of Strathclyde 
On a theory for nonlocal homogenisation problems The theory of nonperiodic homogenisation problems for elliptic type equations in divergence form has been conveniently described by the notion of (local) Hconvergence for multiplication operators as coefficients. In this talk, we introduce the notion of “nonlocal Hconvergence”, which serves as an abstract description of divergence form homogenisation problems, where the coefficients are allowed to be nonlocal. This new notion is a direct generalisation of local Hconvergence. The topology induced by nonlocal Hconvergence is both compact and Hausdorff. It turns out that this topology is weaker than the strong operator topology and cannot be compared with the weak operator topology. Time permitting, we shall sketch an application to electromagnetic theory. This will lead to new homogenisation results for nonperiodic, nonlocal, fully 3D timedependent Maxwell’s equations. The talk is based in arXiv:1804.02026.
(Contact: Lance Littlejohn) 

3:300 PM SDRICH 
St. Petersburg State 
Operator error estimates for homogenization of elliptic and parabolic systems We consider a matrix strongly elliptic second order differential operator acting in a bounded domain with the Dirichlet boundary condition. The operator is selfadjoint. Coefficients are periodic and oscillate rapidly. We study the behavior of solutions of the corresponding elliptic and parabolic systems in the small period limit. The results can be written as approximations of the resolvent and the semigroup in L^{2}→L^{2} and L^{2}→H^{1} operator norms. So, the estimates of this type are called operator error estimates in homogenization theory. The talk is based on a joint work with T. A. Suslina.
(Contact: Fritz Gesztesy) 

3:30 PM SDRICH 
University of Kentucky 
Alternation points, orthogonal polynomials and cubature We say that m+1 decreasing numbers h_{0}, h_{1}, …, h_{m} are alternation points for a finite sequence p_{0}, p_{1}, …, p_{m} of orthogonal polynomials if
p_{mn}(h_{j})=(1)^{j}p_{n}(h_{j}) for all j,n=0,…,m. For example, the Chebyshev points h_{j}=cos(jπ/m), for j=0,…,m are alternation points for the Chebyshev polynomials T_{0}, T_{1},…,T_{m}.
In this talk, we show that every finite decreasing sequence is a set of alternation points for some finite sequence of orthogonal polynomials and apply this to construct Lagrange polynomials and cubature formulas for the even and odd nodes of the Cartesian product of the points. (Contact: Brian Simanek) 

3:30 PM SDRICH 
University of Houston 
Introduction to Quantum Information I will give a general introduction to quantum information science and, in particular, to quantum information theory (which are not the same!). No prior knowledge of quantum mechanics, computer science, information theory is necessary, although the enthusiasm to hear about them is needed. The talk will be accessible to a graduate student and will be aimed at a general audience. Three main questions will be discussed: “What is a quantum computer?” “Why don’t we yet have one? Or do we?” and “How does one build a quantum computer?”. Everyone who is eager to glimpse into the future of science and our society is welcome to attend.
(Contact: Tao Mei) 

3:30 PM SDRICH 
University of Illinois 
Uncertainty Relation via Noncommutative L^{p}Space The Heisenberg uncertainty principle states that it is impossible to prepare a quantum particle for which both position and momentum are sharply defined. A natural measure of uncertainty is entropy. The first entropic formulation of uncertainty principle was proved by Hirschman in 1957 and since then entropic uncertainty relations have been obtained for many scenarios, including some recent advances with quantum memory. In this talk, I will present an approach to entropic uncertainty relations using noncommutative L^{p} norms. We prove a general entropic uncertainty relations for two quantum channels (completely positive trace preserving maps). We will also discuss the connection between noncommutative L^{p} Spaces and Renyi information measure sand show how this gives a quantum information approach to von Neumann algebra index. This talk is based on joint works with Marius Junge and Nicholas LaRacuente.
(Contact: Tao Mei) 

3:30 PM SDRICH 
University of Tennessee Chattanooga 
The Limiting Absorption Principle for the Massless Dirac Operator In 1999, Iftimovici and Mantoiu proved a global limiting absorption principle for massive Dirac operators in three dimensions. The first limiting absorption principle for the threedimensional massless Dirac operator was given by Saito and Umeda in 2008. In this talk, we establish a global limiting absorption principle for the ndimensional massless Dirac operator based on Kato’s inequality. The spectral theoretic consequences of the global limiting absorption principle for the Dirac operator will be explored.
(Contact: Fritz Gesztesy) 

3:30 PM SDRICH 
Texas A&M 
Random Waves and Remainder Estimates in the Weyl Law on a Compact Manifold Let (M,g) be a compact smooth Riemannian manifold. I will discuss some recent offdiagonal estimates for the remainder in the Weyl Law and their applications to the study of random waves, a popular Gaussian model for eigenfunctions of the Laplacian. This is joint work with Y. Canzani.
(Contact: Brian Simanek) 

3:30 PM SDRICH 
Baylor University 
Constructing probabilistically compatible conditionals A binary operator c on an algebra of sets can be considered “a conditional” provided that it satisfies a number of plausible “logical” axioms, such as that A ∩ c(A,B) ⊆ B (if A and A–>B), then B) and c(A,B∩ C)=c(A,B)∩ c(A,C) (A–> BC iff A–> B and A–> C).
If the algebra of sets has a probability measure, a plausible further axiom on conditionals is the Adams Thesis connecting conditionals and conditional probabilities: P(c(A,B)) = P(BA). There are a number of simple theorems showing that in the presence of various auxiliary assumptions, the Adams Thesis can only hold in trivial cases. I show, however, that there is a natural collection of logical axioms on conditionals such that any probability space can be extended to a probability space on which there is a conditional satisfying the axioms and the Adams Thesis. The proof uses deep results in measure theory from the middle of the last century: the Maharam classification theorem and the von NeumannMaharam lifting theorem. (Contact: Alexander Pruss) 

3:30 PM SDRICH 
Baylor University 
What are noncommutative L^{p} spaces? This talk is a brief introduction on the socalled noncommutative L^{p} spaces. Two main examples will be those associated with matrices and discrete groups.
(Contact: Tao Mei) 

3:30 PM SDRICH 
University of Delaware 
Rank d Perturbations The KatoRosenblum theorem and AronszajnDonoghue theory provide us with reasonably good understanding of the subtle theory of rank one d=1 perturbations. We will briefly discuss these statements. When d>1, the situation is different. While the KatoRosenblum theorem still ensures the stability of the absolutely continuous part of the spectrum, the singular parts can behave more complicated. We demonstrate this using simple examples. Nonetheless, some positive results prevail in the finite rank setting.
(Contact: Fritz Gesztesy) 

3:30 PM SDRICH 
University of Alabama 
A similarity criteria for CowenDouglas operators There are operators such as the backward shift operator on various analytic function spaces that cannot be understood by spectral theory. M. J. Cowen and R. G. Douglas, in 1978, defined an important class of operators to study these kinds of operators. They introduced concepts from complex geometry to classify operators up to unitary equivalence. I will discuss some recent progress on the similarity problem of CowenDouglas operators. A wellknown method of solving various versions of the corona problem is used to come up with a similarity characterization.
(Contact: Tao Mei) 

3:30 PM SDRICH 
Washington University in St. Louis 
A new index theorem for monomial ideals by resolutions We will explain an index theorem for the quotient module of a monomial ideal. We obtain this result by resolving the monomial ideal by a sequence of Bergman space like essentially normal Hilbert modules. This is joint work with R. Douglas, M. Jabbari, and G. Yu.
(Contact: Tao Mei) 

3:30 PM SDRICH 
University of Missouri, Columbia 
A Sharp Lower Bound for the First Eigenvalue of the Vibrating Clamped Plate under Compression We give a sharp lower bound to the fundamental frequency of a vibrating clamped plate under compression in the context of plates of different shapes of fixed area. Mathematically, the problem is that of bounding the first eigenvalue of a certain 4thorder partial differential operator with leading term the biLaplacian from below by a positive constant over the square of the area of the domain. We give a RayleighFaberKrahntype result for this problem for small compressions. Thus, our lower bound is saturated for a disk, and the constant appearing in the inequality is that for the disk under the given compression. Our results apply only in two dimensions. Time permitting, possibilities and impediments for the analogs of our results in higher dimensions will be discussed.
This is joint work with Rafael Benguria (P. Universidad Catolica de Chile, Santiago) and Rajesh Mahadevan (Universidad de Concepcion, Chile). (Contact: Fritz Gesztesy) 

3:30 PM SDRICH 
Baylor University 
Birman’s Sequence of Inequalities and Their Relation to Generalized Continuous Cesaro Operators In 1961, Birman proved a sequence of inequalities I_{n}, for n∈N, valid for functions in C_{0}^{n}((0,∞))⊆ L^{2}((0,∞)). In particular, I_{1} is the classical (integral) Hardy inequality and I_{2} is the wellknown Rellich inequality.
In this talk, we give a proof of this sequence of inequalities valid on a certain Hilbert space H_{n}([0,∞)) of functions defined on [0,∞). Moreover, f∈H_{n}([0,∞)) implies f^{‘}∈H_{n1}([0,∞)); as a consequence of this inclusion, we see that the classical Hardy inequality implies each of the inequalities in Birman’s sequence. We also show that for any finite b>0, these inequalities hold on the standard Sobolev space H^{n}((0,b)). Furthermore, the Birman constants ((2n1)!!)^{2}/2^{2n} in these inequalities are sharp and the only function that gives equality in any of these inequalities is the trivial function in L^{2}((0,∞)). We also show that these Birman constants are related to the norm of a generalized continuous Cesaro averaging operator. (Contact: Fritz Gesztesy & Lance Littlejohn) 

3:30 PM SDRICH 
Norwegian University of Science and Technology 
What are the compact sets in Lebesgue spaces? We show an improvement of the classical KolomogorovRiesz theorem. This is joint work with Harald HancheOlsen and Eugenia Malinnikova (both at NTNU).
(Contact: Fritz Gesztesy) 

3:30 PM SDRICH 
Texas Tech University 
Image recognition, lemniscates, and quadratic differentials We will discuss several aspects of mathematical theory designed for recognition of twodimensional images or “shapes.” An idea to use the socalled “fingerprints” to study twodimensional ”shapes” goes back to a paper Kahler structure on the Korbits of a group of diffeomorphisms of the circle of Alexander Kirillov published in 1987. But it was Eiten Sharon and David Mumford who turned this idea (in their 2004 paper 2dshape analysis using conformal mapping) into a tool, which can be applied for recognition of planar shapes, such as shapes on TV screens and in pictures. After that this theory became quite a popular topic in recent publications on applications of complex analysis to problems in pattern recognition.
An interesting approach to fingerprint problem was suggested by Peter Ebenfelt, Dima Khavinson and Harold Shapiro in their paper Twodimensional shapes and lemniscates published in 2011. In this paper, the authors have shown, in particular, that fingerprints of polynomial lemniscates (which, by a classical result due to David Hilbert, are dense in the space of all twodimensional shapes) are generated by solutions of functional equations, which involve Blaschke products. A simpler proof of the main result of Ebenfelt, Khavinson and Shapiro and its generalization to the case of rational lemniscates was presented in a nice short paper Shapes, fingerprints and rational lemniscates by Malik Younsi published in 2016. The first goal of this talk is to discuss how methods of Complex Analysis can be applied to the problems of pattern recognition. In particular, I will discuss the main results on fingerprints obtained by Ebenfelt, Khavinson and Shapiro and by Younsi. In addition, I will also mention a different approach to fingerprints via circle packing which was used by Brock Williams. My second goal here is to present my recent results, which include as special cases the EbenfeltKhavinsonShapiro characterization of fingerprints of polynomial lemniscates as well as Younsi’s characterization of rational lemniscates. My main intention here is to emphasize the role of quadratic differentials in this developing theory. (Contact: Brian Simanek) 

3:30 PM SDRICH 
Baylor University 
Hyponormal Toeplitz operators acting on the Bergman space In 1988 Carl Cowen completely characterized hyponormal Toeplitz operators acting on the Hardy space. In the Bergman space setting, similar studies have mostly focused on Toeplitz operators with harmonic symbols. In this talk, we will examine these results and give some new results on the hyponormality of Toeplitz operators acting on the Bergman space with nonharmonic symbols. This is joint work with Conni Liaw.
(Contact: Matthew Fleeman) 

3:30 PM SDRICH 
Baylor University 
Fourier multipliers on L^{p} spaces — the Mikhlin conditions The boundedness of Fourier multipliers is a central topic in analysis. I will review the socalled Mikhlin condition for Fourier multipliers to be bounded on Euclidean L^{p} spaces in the first half of the seminar. In the second half, I will explain an extension of the classical Mikhlin multiplier theorem to Free groups (recent joint work with Q. Xu).
(Contact: Tao Mei) 

August 30 September 6 3:30 PM SDRICH 
Baylor University 
A Short Course on A^{p}weights This is a threepart series. The goal of the lecture series is to show that the HardyLittlewood maximal operator is bounded on L^{p}(w) if and only if w lies in the Muckenhoupt A_{p} class, via the reverseHolder inequality.
(Contact: Paul Hagelstein) 

2:30 PM SDRICH 
Odessa Polytechnical University 
Stabilization of Dynamical Systems and the Ranges of Complex Polynomials on the Unit Disk TBA.
(Contact: Paul Hagelstein) 

3:30 PM SDRICH 
University of Houston 
Stationary C^{*}dynamical systems We introduce the notion of stationary actions in the context of C^{*}algebras. As an application of this concept we prove a new characterization of C^{*}simplicity in terms of unique stationarity. This ergodic theoretical characterization provides an intrinsic and conceptual understanding of why C^{*}simplicity is stronger than the unique trace property. In addition it allows us to conclude C^{*}simplicity of new classes of examples, including recurrent subgroups of C^{*}simple groups. This is joint work with Yair Hartman.
(Contact: Tao Mei) 

3:30 PM SDRICH 
University of Caen 
Hilbert transforms – old and new stories None
(Contact: Tao Mei) 

3:30 PM SDRICH 
Baylor University 
A Probabilistic Proof of the Vitali Covering Lemma The Vitali Covering Lemma states that, given a finite collection of balls in ℝ^{n}, there exists a disjoint subcollection that fills at least 3^{−n} of the measure of the union of the original collection. We present classical proofs of this lemma due to Banach and Garnett. Subsequently, we provide a new proof of this lemma that utilizes probabilistic “Erdös” type techniques and Padovan numbers.
(Contact: Paul Hagelstein) 

4:00 PM SDRICH 
University of Missouri 
The Maslov index and the spectra of second order elliptic operators In this talk I will discuss a formula relating the spectral flow of the oneparameter families of second order elliptic operators to the Maslov index, the topological invariant counting the signed number of conjugate points of certain paths of Lagrangian planes. In addition, I will present formulas expressing the Morse index, the number of negative eigenvalues, in terms of the Maslov index for several classes of second order differential operators. The talk is based on joint work with Yuri Latushkin.
(Contact: Fritz Gesztesy) 

3:00 PM SDRICH 
Rice University 
Higherorder Szego theorems and related problems We study relations between probability measures μ on the unit circle and their sequences of Verblunsky coefficients (coefficients in the recurrence relation obeyed by orthogonal polynomials with respect to μ). The Szego theorem is a celebrated result proving that the logarithm of the absolutely continuous part of μ is integrable if and only if the sequence of Verblunsky coefficients is squaresummable. We will discuss some recent results on higherorder Szego theorems, which are similar equivalence statements relating weaker integrability conditions on the measure to weaker decay, and bounded variation, conditions on the coefficients. We will also discuss a related problem of determining the asymptotic behavior of the weight at the critical point for powerlaw decaying coefficients.
(Contact: Brian Simanek) 

3:30 PM SDRICH 
University of Missouri 
On (Conditional) Positive Semidefiniteness in the Matrix Valued Context We extend Schoenberg’s classical theorem, which relates conditionally positive definite functions F:R^{n} → C, n ∈ N, to their positive semidefinite exponentials exp(tF), t>0, to matrixvalued conditionally positive semidefinite functions F:R^{n} → C^{mxm}, m ∈ N. Moreover, we study the closely related property that the multiplier operators exp(tF)(i∇), t>0, is positivity preserving and its failure to extend directly to the matrixvalued context. If time permits, we will discuss some of the main tools used in the proofs. (Joint work with Fritz Gesztesy.)
(Contact: Fritz Gesztesy) 

3:30 PM SDRICH 
Baylor University 
Boundary Conditions associated with the LeftDefinite Theory for Differential Operators In the early 2000’s, Littlejohn and Wellman developed a general leftdefinite theory for certain selfadjoint operators which explicitly determined their domains. However, the description of these domains do not contain boundary conditions. We present characterizations of these domains given by the leftdefinite theory for all operators which possess a complete system of orthogonal eigenfunctions, in terms of classical boundary conditions.
(Contact: Conni Liaw) 

3:30 PM SDRICH 
University of Tennessee Chattanooga 
Krein’s Resolvent Identity and Boundary Data Maps for Regular Sturm–Liouville Operators This talk centers on Kreintype resolvent identities and boundary data maps associated to selfadjoint extensions of minimal threecoefficient Sturm–Liouville operators on a finite interval. We consider various parameterizations of the selfadjoint extensions, give the explicit form of Krein’s resolvent identity in terms of boundary conditions, and identify the Kreinvon Neumann extension in the special case when the underlying minimal operator is strictly positive. Boundary data maps for general selfadjoint extensions, and their application to Krein’s resolvent identity, trace formulas, and symmetrized perturbation determinants, are discussed. This talk is based on joint work with Stephen Clark, Fritz Gesztesy, and Maxim Zinchenko.
(Contact: Fritz Gesztesy) 

3:30 PM SDRICH 
Texas A&M 
Radial multipliers and approximation properties for qArakiWoods algebras I will discuss a class of von Neumann algebras introduced by Hiai, called the qArakiWoods algebras. These operator algebras are constructed by combining two wellknown deformations of free group von Neumann algebras: the qGaussian deformations of Bożejko and Speicher, and the type III deformations of Shlyakhtenko. The main focus of this talk will be on the problem of characterizing (and computing norms of) of a simple class of linear maps on these algebras, called completely bounded radial multipliers. I will describe some joint work with Steve Avsec and Mateusz Wasilewski in this direction. Although we are still very far from any sort of full classification of the cb radial multipliers on qArakiWoods algebras, our work on this problem allow us to establish an extremely useful finiterank approximation property for these algebras: they always have the complete metric approximation property.
(Contact: Tao Mei) 

3:30 PM SDRICH 
Northern Illinois 
Eigenvalues of SturmLiouville Problems with Periodic Coefficients For hperiodic coefficients and any integer k>2 it is well known that the eigenvalues of some selfadjoint complex boundary condition on the interval [a,a+h] are the same as the periodic eigenvalues on the interval [a,a+kh]. For each k we identify explicitly which of the uncountable number of complex conditions generates these periodic eigenvalues. In addition, we prove an analogous result for semiperiodic eigenvalues.
(Contact: Lance Littlejohn) 

3:30 PM SDRICH 
Baylor University 
Completely monotone functions, Markov semigroup generators, and functional calculus The story will be on a joint work with Brian Simanek and Tim Ferguson. I will review the meaning and connections between the three objects in the title and will explain the main result that every Markov semigroup generator satisfying Γ_{2} criterion has a bound H\infty calculus on BMO with an optimal angle.
(Contact: Tao Mei) 

3:30 PM SDRICH 
University of the Basque Country 
Asymptotic Estimates for Halo Sets and Applications (Contact: Paul Hagelstein) 

3:30 PM SDRICH 
University of Mississippi 
Asymptotics for polynomials orthogonal over a planar domain with holes Let D be a bounded domain of the complex plane and let {P_{n}} be the sequence of orthonormal polynomials over D, that is, for each n=0,1,2,… P_{n} has degree n and positive leading coefficient, and
∫_{D} P_{n}(z)P_{m}(z)dA(z)=δ_{n,m.} The asymptotic behavior of P_{n}(z) as n→∞ has been investigated to a considerable extent, particularly when the region D is a simply connected domain bounded by a Jordan curve. In this work we investigate the situation when the domain of orthogonality is no longer simply connected but a multiply connected domain, trying to understand how the holes in the domain influence the asymptotic behavior of P_{n} inside D. Of particular interest is the canonical case of a circular multiply connected domain (CMCD) consisting of a disk with a finite number of mutually disjoint subdisks removed. We will also consider domains D that are conformally equivalent in a strong sense to a CMCD. This is a joint work with James Henegan. (Contact: Brian Simanek) 

3:30 PM SDRICH 
Korean National University, visiting Texas A&M 
HardyLittlewood inequality in compact quantum groups Hardy and Littlewood studied L^{p}l^{p} multiplier on circle and there have been some progress in this direction. In particular, the inequality was studied on compact homogeneous spaces recently. In this seminar, I will talk about such inequalities on compact quantum groups, mainly on reduced group C^{*} algebras and free quantum groups.
(Contact: Tao Mei) 

3:30 PM SDRICH 
Dalhousie University 
PseudoWronskians of Hermite polynomials In this talk we consider a certain class of identities involving determinants of Hermite polynomials. The prototypical example of such a determinant is the Wronskian of a finite set of Hermite polynomials. Remarkably, all such Wronskians may be reexpressed as an infinity of other determinants of a certain structure, determinants that we refer to as “pseudoWronskians”. The entire theory can be easily understood in terms of Maya diagrams and partitions. This approach allows us to find the optimal determinantal representation of any given Hermite Wronskian. Time permitting, we will also discuss applications to exceptional Hermite polynomials and to rational solutions of the Painleve IV equation.
(Contact: Lance Littlejohn) 

3:30 PM SDRICH 
Westminster College 
Differential Operators in Discrete Sobolev Spaces At the Fifth International Symposium on Orthogonal Polynomials, Special Functions and their Applications, held in Patras, Greece, 1999, W.N. Everitt, K.H. Kwon, and L.L. Littlejohn presented ten open problems. Problem 10 called for a GKNtype theory for identifying selfadjoint operator representations of a Lagrangian symmetric differential expression in a Hilbert space L^{2}([a,b];dμ) where dμ is a discrete Sobolev measure of the form
dμ = w + Σ_{j=0}^{n}(α_{j}δ_{a}^{(j)}+β_{j}δ_{b}^{(j)}) α_{j},β_{j}≥ 0; n ∈ N_{0}. In particular Problem 10 asked for a ‘recipe’ for finding selfadjoint differential operators generated by a BochnerKrall spectral differential expression having the associated orthogonal polynomial sequence as eigenfunctions.
In this lecture we will discuss the history and motivation of this question and present a new GKNEM type theory that resolves this longstanding problem. (Contact: Lance Littlejohn) 

3:30 PM SDRICH 
Oklahoma State University 
Equidistribution of Zeros of Random Orthogonal Polynomials We study the asymptotic distribution of zeros for the random polynomials P_{n}=Σξ_{k}B_{k}(z), where {ξ_{k}}_{k=0}^{∞} are nontrivial i.i.d. complex random variables. The polynomials {B_{k}}_{k=0}^{∞} are deterministic, and are selected from a standard basis such as Bergman or Szego polynomials associated with a Jordan domain G bounded by an analytic curve. We show that the zero counting measures of P_{n} converge almost surely to the equilibrium measure on the boundary of G if and only if the expected value of log^{+}ξ_{0} is finite. This talk is based on joint work with Igor Pritsker.
(Contact: Brian Simanek) 

3:30 PM SDRICH 
Baylor University 
Monotone operators and nonlinear semigroups Many PDEs can be usefully rewritten as abstract ODEs of the form u’ = Au, where A is a typically unbounded operator on a Banach space. In the linear case, the HilleYosida theorem allows us to determine precisely when A generates a strongly continuous semigroup of operators, from which one can deduce that the PDE is wellposed. In the nonlinear case, an analogy to HilleYosida can be found for socalled “maximal monotone” operators. In this talk I will outline the theory of monotone operators and nonlinear semigroups, give important examples, and briefly describe how to apply the theory to certain nonlinear PDEs.
(Contact: Jameson Graber) 

3:30 PM SDRICH 
Baylor University 
A brief survey of Hardy and Bergman Spaces Two of the most important spaces in modern function theory are the Hardy and Bergman spaces. In this talk, I will give a brief survey of some of the similar differences in the structure of these spaces, as well as the flavor of solving problems in these different settings. In particular we will look at the differences between the zeros of Hardy and Bergman functions, and look at the differences in the Invariant Subspace Problem in both Hardy and Bergman settings.
(Contact: Matthew Fleeman) 

3:30 PM SDRICH 
Baylor University 
Extremal Problems for Analytic Functions and Their Connections to Other Topics In this talk, I will discuss extremal problems in spaces of analytic functions and connections between such problems and other areas of analysis. The main focus will be the problem of maximizing linear functionals on Bergman spaces, which are spaces of analytic functions of finite L^{p} norm. I will speak about the connections of this problem to topics in analysis such as partial differential equations, quasiconformal mappings, and uniform convexity.
(Contact: Brian Simanek) 

3:30 PM SDRICH 
TCU 
Topological invariants of groups obtained by deformations An old problem that goes back to Halmos asked whether a pair of unitary matrices U and V that almost commute (in the sense that the operator norm of the commutator UV – VU is small) can always be slightly perturbed to obtain a pair of commuting unitary matrices. Voiculescu produced examples in the 80s that gave a negative answer, and commented that they seemed to depend on the cohomology of the twotorus. Later, Exel and Loring provided a direct link by giving a formula that related the Ktheory of the twotorus to these almost commuting unitaries.
We will discuss previous and ongoing work with Marius Dadarlat that elucidates this connection further. In fact, regarded in the right light, the answer comes from an index theory calculation that relates deformations of the fundamental group Z^{2} of the twotorus with “almost flat” bundles over the twotorus. In this context, the theory generalizes to other surface groups, and beyond. (Contact: Tao Mei) 

3:30 PM SDRICH 
Bucknell University 
Compressions of the shift on twovariable model spaces There are many classical results about operatortheoretic properties of the compressed shift on onevariable model spaces, especially spaces associated to finite Blaschke products. In this talk, we will discuss generalizations of such results to the setting of twovariable model spaces associated to rational inner functions on the bidisk. Among other things, we will discuss characterizations and properties of the numerical range and radius of compressed shifts on two variable model spaces as well as when the commutator of a compressed shift with its adjoint has finite rank. This is joint work with Constanze Liaw and Pam Gorkin.
(Contact: Constanze Liaw) 

3:300 PM SDRICH 
University de Franche Comte 
Maximal Inequalities in Noncommutative Analysis (Contact: Tao Mei) 

4:00 PM SDRICH 
Universidad Carlos III de Madrid 
Applications of finite dynamic asymptotic dimension to algebraic Ktheory The n^{th} root asymptotic behavior of some discrete multiple orthogonal polynomials is presented. Two main ingredients of the proposed approach for the study of the aforementioned asymptotic behavior are discussed; namely, an algebraic function formulation for the solution of the equilibrium problem with constraint to describe their zero distribution and the limiting behavior of the coefficients of the recurrence relations for multiple orthogonal polynomials.


3:30 PM SDRICH 
Texas A&M University 
Applications of finite dynamic asymptotic dimension to algebraic Ktheory I will give a brief introduction of the notion of finite dynamic asymptotic dimension and its applications to algebraic Ktheory. In particular, for a large class of groups, we prove the FarrellJones conjecture with coefficients in the algebra of Schatten class operators. It is based on joint work with Guoliang Yu.
(Contact: Tao Mei) 

3:30 PM SDRICH 
Baylor University 
Solyanik Estimates in Harmonic Analysis Let B be a collection of open sets in ℝ^{n}. Associated to B is the geometric maximal operator M_{B} defined by
M_{B}f(x) = sup_{x ∈ R ∈ B}∫_{R}f. For 0 <α< 1, the associated Tauberian constant C_{B}(α) is given by C_{B}(α) = sup_{E ⊆ ℝn : 0 <E< ∞}{x ∈ ℝ^{n} : M_{B}χ_{E}(x)>α}/E. A maximal operator M_{B} such that lim_{α → 1–}C_{B}(α) = 1 is said to satisfy a Solyanik estimate. In this talk we will prove that the uncentered HardyLittlewood maximal operator satisfies a Solyanik estimate. Moreover, we will indicate applications of Solyanik estimates to smoothness properties of Tauberian constants and to weighted norm inequalities. We will also discuss several fascinating open problems regarding Solyanik estimates. This research is joint with Ioannis Parissis. 

3:30 PM SDRICH 207 
Cardiff University 
Uniqueness for an inverse problem in electromagnetism with partial data A uniqueness result for the recovery of the electric and magnetic coefficients in the timeharmonic Maxwell equations from local boundary measurements is showen. No special geometrical condition are imposed on the inaccessible part of the boundary of the domain, apart from that that the boundary of the domain is C1,1. The coefficients are assumed to coincide on a neighbourhood of the boundary: a natural property in many applications.
(Contact: Lance Littlejohn) 

3:30 PM SDRICH 
University of Utah 
Dirichlet graph partitions I’ll discuss a geometric approach to graph partitioning where the optimality criterion is given by the sum of the first DirichletLaplacian eigenvalues of the partition components. This eigenvalue optimization problem can be solved by a rearrangement algorithm, which we show to converge in a finite number of iterations to a local minimum of a relaxed objective. I’ll give a consistency result for geometric graphs, stating convergence of graph partitions to an appropriate continuum partition. The model has a semisupervised extension, provides natural representatives for the clusters, and is related to an interesting random process.
(Contact: Brian Simanek) 

3:30 PM SDRICH 
Baylor University 
Cyclic vectors in Dirichlet type spaces and optimal approximants Dirichlet types spaces D_{α}, α∈R, are a wellstudied range of spaces; each consisting of analytic functions f on the unit disk D with the property that a certain weighted sum of Fourier coefficients of f is bounded. These weights depend on α. The classical Hardy space furnishes the most prominent example.
A function f(z) is said to be cyclic in D_{α} if the sequence of forward orbits z^{k} f(z), k∈{0,1,2,…}, has a dense span in D_{α}. Since the constant function g=1 is cyclic, we set out on an endeavor to learn about the approximation of the function 1 by functions of the form p_{n} f for fixed f∈ D_{α} and polynomials p_{n} of varying degrees n. 

3:30 PM SDRICH 
University of Caen 
Hypercontractivity for Free Groups We look for hypercontractivity results for the Poisson semigroup associated to free groups. We rely mainly on probabilistic methods combined with a noncommutative twopoints inequality.
(Contact: Tao Mei) 

3:30 PM SDRICH 
University of Mississippi 
Spectral transformations in the theory of orthogonal polynomials One of the basic spectral transformations of orthogonal polynomials on the real line corresponds to the multiplication of the orthogonality measure dµ(t) by t provided that all orthogonal polynomials for the original and resulting measures exist. This transformation is called Christoffel transformation. Intuitively, the inverse transformation to Christoffel transformation can be gotten by dividing the measure by t and this is another basic spectral transformation. The latter one is known as Geronimus transformation. In fact, both of them are discrete versions of the famous Darboux transformations and it turns out that the consistency of Christoffel and Geronimus transformations leads to the discretetime Toda equation, which is basically the qdalgorithm, one of the most important tools in numerical analysis.
In my talk I’m going to discuss some nonclassical situations in regard to spectral transformations of orthogonal polynomials on the real line. Namely, I’ll start with showing how spectral transformations help to deal with signed measures with one sign change and with the corresponding nonsymmetric tridiagonal matrices. In particular, the theory of such matrices brings us to the context of Padé approximation and, more importantly, the behavior of spurious poles of Padé approximants at infinity for Cauchy transforms of signed measures with one sign change is fully characterized. Then, we’ll see that to get such results for signed measures with several sign changes and other singularities one needs to consider multiple Christoffel and Geronimus transformations. Finally, it’ll be demonstrated that multiple Geronimus transformations could lead to Sobolev orthogonal polynomials. (Contact: Brian Simanek) 

3:30 PM SDRICH 
Baylor University 
Iterated RankOne Perturbations and Absence of Extended States We construct an Anderson–type Hamiltonian in its spectral representation via the iterative introduction of rank one perturbations. We remain in control of the expected value for the total mass of the resulting operators’ absolutely continuous part.


3:30 PM SDRICH 
University of Utah 
Random Geometry in the Spectral Measure of the Circular Beta Ensemble The Circular Beta Ensemble is a family of random unitary matrices whose eigenvalue distribution plays an important role in statistical physics. The spectral measure is a canonical way of describing the unitary matrix that takes into account the full operator, not just its eigenvalues. When the matrix is infinitely large (i.e. an operator on some infinitedimensional Hilbert space) the spectral measure is supported on a fractal set and has a rough geometry on all scales. This talk will describe the analysis of these fractal properties. Joint work with Raoul Normand and Balint Virag.
(Contact: Brian Simanek) 

3:30 PM SDRICH 
University of Albany and Texas A&M 
Joint spectrum for noncommuting operators In multivariable operator theory, joint spectra are defined to gauge the interaction of operators. If a tuple of operators is commuting, then the Taylor spectrum, which is defined through a Koszul complex, played a fundamental role in the theory. However, for noncommuting tuples spectral theory remains a mystery. In 2008, the notion of projective joint spectrum was introduced by the speaker. It appears to be the simplest kind of spectrum one can define for noncommuting tuples. Yet, this simplicity turns out to be the very source of its richness.
(Contact: Tao Mei) 

3:30 PM SDRICH 
University of Texas at Austin 
Inequalities in Fourier Analysis and Measures for Fractional Smoothing Geometric inequalities provide insight into the structure of manifolds. Our objective is to develop deeper understanding for how sharp constants for functionspace inequalities encode information about the geometric structure of the manifold. Functional forms that characterize smoothness lie at the heart of understanding and rigorously describing the manybody interactions that determine the behavior of dynamical phenomena. Smoothing estimates provide new structural understanding for density functional theory, the Coulomb interaction energy and quantum mechanics of phase space.
(Contact: Tao Mei) 

3:30 PM SDRICH 
University of Houston 
Generalizing positivity techniques in Banach and operator algebras With Charles Read we have introduced and studied a new notion of (real) positivity in operator algebras, with an eye to extending certain C^{*}algebraic results and theories to more general algebras. We have continued this work together with Read, and also with Matthew Neal, and with Narutaka Ozawa we have investigated the parts of the theory that generalize further to Banach algebras. We describe some of this work, and the ideas behind it.
(Contact: Tao Mei) 

3:30 PM SDRICH 
Baylor University 
Riesz transforms associated with cocycles and Hormander Fourier multipliers on OUMD spaces Riesz transforms and Hormander Fourier multipliers are central objects in the classical Fourier analysis. I will explain recent work on Riesz transforms associated with group 1cocycles. It is a new point of view of P. A. Meyer and D. Bakry’s Riesz transforms associated with Markov semigroups. From this viewpoint, all classical Hormonder Fourier multipliers are essentially Riesz transforms. The talk is based on a joint work with Junge and Parcet.


3:30 PM SDRICH 
Baylor University 
GlazmanKreinNaimark Theory, LeftDefinite Theory and the Square of the Legendre Polynomials Differential Operator As an application of a general leftdefinite spectral theory, Everitt, Littlejohn and Wellman, in 2002, developed the leftdefinite theory associated with the classical Legendre selfadjoint secondorder differential
operator A in L^{2}(1,1) having the Legendre polynomials {P_{n}}_{n=0}^{∞} as eigenfunctions. As a particular consequence, they explicitly determine the domain D(A^{2}) of the selfadjoint operator A^{2}. However, this domain, in their characterization, does not contain boundary conditions. In fact, this is a general feature of the leftdefinite approach developed by Littlejohn and Wellman. Yet, the square of the secondorder Legendre expression is in the limit4 case at each end point x = ± 1 in L^{2}(1,1) meaning that D(A^{2}) should exhibit four boundary conditions. In this talk, after a gentle ‘crash course’ on leftdefinite theory and the classical GlazmanKreinNaimark (GKN) theory, we show that D(A^{2}) can, in fact, be expressed using four (separated) boundary conditions. In addition, we determine a new characterization of D(A^{2}) that involves four nonGKN boundary conditions. These new boundary conditions are surprisingly simple – and natural – and are equivalent to the boundary conditions obtained from the GKN theory. 

3:30 PM SDRICH 
Baylor University 
Thick distributions, asymptotic expansion of distributions, and spectral asymptotics I will briefly introduce the theory of thick distributions. I will also introduce the asymptotic expansions of distributions and of thick distributions. As an example, I will show how recent observations of Kolomeisky et al. fit into the established framework of the distributional asymptotics of spectral functions. A common tool in Casimir physics (and many other areas) is the asymptotic (highfrequency) expansion of eigenvalue densities, employed as either input or output of calculations of the asymptotic behavior of various Green functions.


3:30 PM SDRICH 
Baylor University 
Extremal Polarization Configurations for Integrable Kernels We will use Smale’s 7th problem to motivate the polarization problem. This is a classic problem in potential theory that provides the crudest bounds on the effectiveness of a greedy algorithm for finding optimal energy configurations. I will mention some of my own recent work on this problem along with some directions for future research. Many open problems will be provided throughout this talk.


3:30 PM SDRICH 
Baylor University 
An Introduction to Minimum Energy Problems This will be an introduction to the research field of minimum energy problems. We will start by motivating the topic with some big open problems like sphere packing problems and Smale’s 7th problem for the 21st century. A large portion of the talk will focus on equilibrium measures and leading order asymptotic of minimal energies. This talk will be accessible to nonspecialists and serve as a primer for the higherlevel research talk on September 23.

