|Title: Weighted X-ray mapping properties on the Euclidean and Hyperbolic Disks|
|Seminar: Analysis and Differential Geometry|
|Speaker: Joey Zou of Northwestern University|
|Contact: Yiran Wang, email@example.com|
|Date: 2023-09-29 at 11:00AM|
|Venue: Atwood 240|
We discuss recent works studying the sharp mapping properties of weighted X-ray transforms and weighted normal operators. These include a C^\infty isomorphism result for certain weighted normal operators on the Euclidean disk, whose proof involves studying the spectrum of a distinguished Keldysh-type degenerate elliptic differential operator; we also describe mapping properties for the weighted normal operator in terms of Sobolev-type spaces adapted to this distinguished differential operator. In addition, we discuss ongoing work which applies these results to the X-ray transform on the hyperbolic disk by using a projective equivalence between the Euclidean and hyperbolic disks. Joint works with N. Eptaminitakis, R. K. Mishra, and F. Monard.
|Title: Bayesian Filtering Methods for Dynamic Parameter Estimation in Differential Equations|
|Seminar: Numerical Analysis and Scientific Computing|
|Speaker: Andrea Arnold of Worcester Polytechnic Institute|
|Contact: Matthias Chung, firstname.lastname@example.org|
|Date: 2023-10-03 at 10:00AM|
|Venue: MSC N306|
Estimating and quantifying uncertainty in unknown system parameters from partial, noisy system measurements remains a challenging inverse problem. In addition to constant parameters, a variety of systems stemming from real-world applications include unobservable parameters that change with time but have unknown evolution models. In this talk, we present several approaches using Bayesian filtering techniques to estimate time-varying parameters in deterministic dynamical systems governed by differential equations.
|Title: Local-global principles for reductive groups over finitely generated fields|
|Speaker: Igor Rapinchuk of Michigan State University|
|Contact: Andrew Kobin, email@example.com|
|Date: 2023-10-03 at 4:00PM|
|Venue: MSC N302|
One of the major results in the arithmetic theory of algebraic groups is the validity of the cohomological local-global (or Hasse) principle for simply-connected and adjoint semisimple groups over number fields. Over the last several years, there has been growing interest in studying Hasse principles for reductive groups over arbitrary finitely generated fields with respect to suitable sets of discrete valuations. In particular, we have conjectured that for divisorial sets, the corresponding Tate-Shafarevich set, which measures the deviation from the local-global principle, should be finite for all reductive groups. I will report on recent progress on this conjecture, focusing in particular on the case of algebraic tori as well as on connections to groups with good reduction. This talk is based on joint work with V. Chernousov and A. Rapinchuk.
|Title: Have you Ever Meta-Conjectured?|
|Speaker: Ron Gould of Emory University|
|Contact: Liana Yepremyan, firstname.lastname@example.org|
|Date: 2023-10-04 at 4:00PM|
|Venue: MSC E406|
The study of cycles in graphs has a long history. In 1971 A. Bondy noted a tie linking hamiltonian graphs and pancyclic graphs. He stated his famous meta-conjecture: Almost any nontrivial condition on a graph which implies the graph is hamiltonian also implies the graph is pancyclic. There may be some simple family of exceptional graphs. A cycle contains a chord if there exists an edge between two vertices of the cycle that is not an edge of the cycle. A cycle is said to be chorded if it has one or more chords. In this talk I will extend Bondy's meta-conjecture in several ways to a broader class of cycle problems in graphs, namely to finding conditions that imply the existence of chorded cycles in graphs. I will offer supporting evidence to these meta-conjectures.
|Title: Nonlocal PDEs and Quantum Optics|
|Colloquium: Analysis and Differential Geometry|
|Speaker: John Schotland of Yale University|
|Contact: Yiran Wang, email@example.com|
|Date: 2023-10-20 at 2:00PM|
|Venue: MSC W301|
Quantum optics is the quantum theory of the interaction of light and matter. In this talk, I will describe a real-space formulation of quantum electrodynamics with applications to many body problems. The goal is to understand the transport of nonclassical states of light in random media. In this setting, there is a close relation to kinetic equations for nonlocal PDEs with random coefficients.