The organizers of the seminar for 20242025 are Ovidiu Costin, Jan Lang, and Jonathan Stanfill.
The regular time for the seminar will be Thursday from 34 p.m. eastern time. For more information, to request the Zoom meeting link, or if you are interested in giving a talk at the seminar, please contact Jonathan Stanfill or Jan Lang.
Date/Time  Location  Speaker  Institution  Title (click to see abstract)  Slides 

September 5 at 3 p.m.  MW 154  Wencai Liu  Texas A&M University 
Algebraic geometry, analysis and combinatorics in the study of periodic graph operatorsIn this talk, we will discuss the crucial role that the algebraic properties of complex Bloch and Fermi varieties play in the study of periodic graph operators. I will begin with an introduction to the basics of periodic graph operators, followed by a discussion of recent discoveries, particularly focusing on the irreducibility of Bloch and Fermi varieties. 
Slides AOTS Sep 5, 24 
September 12 at 3 p.m.  Zoom  Maria Cristina Pereyra  University of New Mexico 
(Variable) Haar multipliers and weighted inequalitiesThe variable Haar multipliers are analogous to pseudodifferential operators where the trigonometric functions have been replaced by the basis of Haar functions indexed on the dyadic intervals. In the classical case the symbol of the operator depends on space and frequency variables, in the Haar case, the symbols depend on the space and the dyadic frequency variables. We study a particular class of these operators that we call signed tHaar multipliers, the symbol involves a weight w, a choice of signs \sigma, and the real parameter t. This part is joint work with Daewon Chung, Jean Moraes, Weijan Huang, and Brett Wick. 
N/A 
September 19 at 3 p.m.  MW 154  Peter D. Miller  University of Michigan 
Universality in the SmallDispersion Limit of the BenjaminOno EquationThis talk concerns the BenjaminOno (BO) equation of internal wave theory, and properties of the solution of the Cauchy initialvalue problem in the situation that the initial data is fixed but the coefficient of the nonlocal dispersive term in the equation is allowed to tend to zero (i.e., the zerodispersion limit). It is wellknown that existence of a limit requires the weak topology because highfrequency oscillations appear even though they are not present in the initial data. Physically, this phenomenon corresponds to the generation of a dispersive shock wave. In the setting of the Kortewegde Vries (KdV) equation, it has been shown that dispersive shock waves exhibit a universal form independent of initial data near the two edges of the dispersive shock wave, and also near the gradient catastrophe point for the inviscid Burgers equation from which the shock wave forms. In this talk, we will present corresponding universality results for the BO equation. These have quite a different character than in the KdV case; while for KdV one has universal wave profiles expressed in terms of solutions of Painlevétype equations, for BO one instead has expressions in terms of classical Airy functions and Pearcey integrals. These results are proved for general rational initial data using a new approach based on an explicit formula for the solution of the Cauchy problem for BO. This is joint work with Elliot Blackstone, Louise Gassot, Patrick Gérard, and Matthew Mitchell. 
N/A 
September 26 at 3 p.m.  MW 154  Jonathan Stanfill  The Ohio State University 
A finer limit circle/limit point classification for SturmLiouville operatorsWe introduce a new finer limit point/limit circle classification for SturmLiouville equations by defining the regularization index. The results rely on the integrability of the product of the principal and nonprincipal solutions near singular endpoints and constructing a spectral parameter power series (i.e., a Taylor series in the spectral parameter z) for solutions of the SturmLiouville problem. The regularization index at the singular endpoint is then defined by comparing the growth in x of the coefficients of the power series. Implications include classifying when these series are wellbehaved asymptotic series (in a precise sense), quantifying how far certain limit point endpoints are away from being Darboux transformed to a limit circle endpoint, and extending Weyl eigenvalue asymptotics to singular problems. These results will be motivated by multiple examples. This talk is based on joint work with Mateusz Piorkowski. 
Slides AOTS Sep 26, 24 
October 3 at 3 p.m.  Zoom  Tom Claeys  UCLouvain, Belgium 
Biorthogonal measures associated with polymer partition functionsI will explain how several exactly solvable polymer models are related to signed biorthogonal measures. These measures reduce to classical orthogonal polynomial ensembles in the zerotemperature limit. I will explain how asymptotic analysis of the signed biorthogonal measures provides insight in large deviations for the polymer partition functions and what the current limitations of this method are. 
Slides AOTS Oct 3, 24 
October 17 at 3 p.m.  MW 154  Chris Marx  Oberlin College 
Potential dependence of the density of states for Schrödinger operators on graphsIn this talk we will explore the dependence of the density of states for Schrödinger operators on the potential. The density of states characterizes the averaged spectral properties of a quantum system. Formally, it can be obtained as an infinite volume limit of the spectral density associated with finitevolume restrictions of a quantum system. Such a limit is known to exist for certain quantum mechanical models, most importantly for Schrödinger operators with periodic and random potentials. Following ideas by J. Bourgain and A. Klein, we will consider the density of states outer measure (DOSoM) which is well defined for all Schrödinger operators. We will explicitly quantify the parameter dependence of the DOSoM by proving a modulus of continuity with respect to the potential (in $L^\infinity$norm and weak topology). This result is obtained for all discrete Schrödinger operators on infinite graphs and captures the geometry of the graph at infinity. Applications of this result to random and ergodic operators will be presented. This talk is based on joint work with Peter Hislop (University of Kentucky). 

October 24 at 3 p.m.  MW 154  Jeffrey Schenker  Michigan State University 
TBDTBD 

October 31 at 3 p.m.  MW 154  Catalin Georgescu  University of South Dakota 
Obstructions to Frame Vectors and Group RepresentationsWe investigate obstructions to the existence of frame vectors, in particular related to group representation and we provide examples of groups having faithful representations without frame vectors. As a result of these constructions we obtain a new characterization of amenability and a weaker form of Kazhdan’s property (T). This is joint work with Gabriel Picioroaga. 

November 7 at 3 p.m.  MW 154  Chian Chuah  The Ohio State University 
TBDTBD 

†November 14 at 3 p.m.  MW 154  Armin Schikorra  University of Pittsburgh 
On CalderonZygmund theory for the pLaplacianI will discuss how to disprove a conjecture by Iwaniec from 1983 about CalderonZygmund estimates for $L^r $where $r$ is close to $p1$. 

*November 21 at 3 p.m.  MW 154  Gino Biondini  University at Buffalo, State University of New York 
TBDTBD 

December 5 at 3 p.m.  MW 154  Rodica Costin  The Ohio State University 
TBDTBD 

December 12 at 3 p.m.  MW 154  Ovidiu Costin  The Ohio State University 
TBDTBD 
* Joint PDE Seminar talk
† Joint Harmonic Analysis and Several Complex Variables Seminar talk