All Seminars
| Title: Reduced-Order Models for Parametrized PDE Models with Constraints |
|---|
| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Howard Elman of University of Maryland, College Park |
| Contact: Matthias Chung, matthias.chung@emory.edu |
| Date: 2023-10-13 at 10:00AM |
| Venue: MSC N304 |
| Download Flyer |
| Abstract: Model order reduction techniques are effective for solving parametrized models involving PDEs, including models of incompressible flow, where the constraint is the incompressibility constraint, and in optimal control, where the constraints themselves are PDEs. However, reduced models may fail to be inf-sup stable. We present a new approach for generating reduced bases in this scenario, using a so-called stacked reduced basis, which avoids some of the difficulties associated with inf-sup stability. We show that this approach is effective although in some circumstances it also requires stabilization, which can be done using either classic methods of penalization or through Petrov-Galerkin methods. Computational tests are presented for models based on PDE-constrained optimization and incompressible flow. This is joint work with Kayla Davie, Applied Mathematics Program, University of Maryland at College Park |
| Title: Regularity estimates for elliptic transmission problems |
|---|
| Seminar: Analysis and Differential Geometry |
| Speaker: Pablo Raúl Stinga of Iowa State University |
| Contact: Maja Taskovic, maja.taskovic@emory.edu |
| Date: 2023-10-13 at 2:00PM |
| Venue: MSC W301 |
| Download Flyer |
| Abstract: We present regularity estimates for solutions to transmission problems driven by second order elliptic equations with curved interfaces. First, we consider a transmission problem for harmonic functions and use the mean value theorem to prove sharp $C^{1,\alpha}$ estimates up to the transmission surface. Then, we show various up to the boundary Hölder regularity estimates for viscosity solutions to transmission problems for fully nonlinear uniformly elliptic equations depending on the regularity of the interface. Among the main tools, we introduce an ABP estimate for the problem and new constructive stability results. These are joint works with Luis A. Caffarelli (UT Austin) and María Soria-Carro (Rutgers) |
| Title: Everywhere unbalanced configurations |
|---|
| Seminar: Combinatorics |
| Speaker: Jeck Lim of Caltech |
| Contact: Liana Yepremyan, liana.yepremyan@emory.edu |
| Date: 2023-10-11 at 4:00PM |
| Venue: MSC E406 |
| Download Flyer |
| Abstract: An old problem in discrete geometry, originating with Kupitz, asks whether there is a fixed natural number $k$ such that every finite set of points in the plane has a line through at least two of its points where the number of points on either side of this line differ by at most $k$. We give a negative answer to the pseudoline variant of this problem. Joint work with David Conlon. |
| Title: Global existence for an isotropic Boltzmann-type model |
|---|
| Seminar: Analysis and Differential Geometry |
| Speaker: Stanley Snelson of Florida Institute of Technology |
| Contact: Maja Taskovic, maja.taskovic@emory.edu |
| Date: 2023-10-11 at 4:00PM |
| Venue: White Hall 111 |
| Download Flyer |
| Abstract: The Boltzmann equation is a kinetic differential equation that plays a central role in thermal and statistical physics. Global existence for this equation is a challenging open problem, and in this talk, we will discuss a new model equation—called the "isotropic Boltzmann equation"—that is more tractable than the Boltzmann equation while still encapsulating many of the key mathematical difficulties. After briefly deriving the model equation, we will discuss the proof of global existence, which features a surprising application of a fractional Hardy inequality. |
| Title: Have you Ever Meta-Conjectured? |
|---|
| Seminar: Combinatorics |
| Speaker: Ron Gould of Emory University |
| Contact: Liana Yepremyan, liana.yepremyan@emory.edu |
| Date: 2023-10-04 at 4:00PM |
| Venue: MSC E406 |
| Download Flyer |
| Abstract: 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: 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, matthias.chung@emory.edu |
| Date: 2023-10-03 at 10:00AM |
| Venue: MSC N306 |
| Download Flyer |
| Abstract: 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 |
|---|
| Seminar: Algebra |
| Speaker: Igor Rapinchuk of Michigan State University |
| Contact: Andrew Kobin, andrew.jon.kobin@emory.edu |
| Date: 2023-10-03 at 4:00PM |
| Venue: MSC N302 |
| Download Flyer |
| Abstract: 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: 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, yiran.wang@emory.edu |
| Date: 2023-09-29 at 11:00AM |
| Venue: Atwood 240 |
| Download Flyer |
| Abstract: 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: Maximising copies of H in clique-free graphs |
|---|
| Seminar: Combinatorics |
| Speaker: Natasha Morrison of University of Victoria |
| Contact: Liana Yepremyan, liana.yepremyan@emory.edu |
| Date: 2023-09-27 at 4:00PM |
| Venue: MSC E406 |
| Download Flyer |
| Abstract: Let H be a graph. We show that if r is large enough as a function of H, then the r-partite Turán graph maximizes the number of copies of H among all Kr+1-free graphs on a given number of vertices. This confirms a conjecture of Gerbner and Palmer. This is joint work with JD Nir, Sergey Norin, Pawel Rzazewski, Alexandra Wesolek. |
| Title: Convex holes and almost uniform distribution in the unit cube |
|---|
| Seminar: Atlanta Discrete Analysis |
| Speaker: Boris Bukh of Carnegie Mellon University |
| Contact: Cosmin Pohoata, cosmin.pohoata@emory.edu |
| Date: 2023-09-25 at 4:00PM |
| Venue: MSC W301 |
| Download Flyer |
| Abstract: For $P \subset \mathbb{R}^{d}$, a hole is any set of convexly independent points whose convex hull contains no other points. We will discuss constructions of large finite sets that contain no large holes. The key role will be played by subsets of $[0,1]^d$ that contain about the same number of points in every dyadic box of a fixed volume. Based on joint works with Ting-Wei Chao and Ron Holzman. |