Events for 12/02/2022 from all calendars

Mathematical Physics and Harmonic Analysis Seminar

Time: 09:00AM - 10:00AM

Location: Zoom

Speaker: Hannah Kravitz, Portland State University

Title: An application of PDEs on metric graphs to epidemiology

Abstract: It has been known that a network structure enhances the spread of epidemics since the inception of the field. In the first epidemiological study John Snow (often called the father of epidemiology) determined that cholera was spreading through the 1850s London city water grid. Since then, numerous studies have supported the relationship between network structure and disease spread – parasites may be carried along fluvial networks, the colonial-era railway system in DR Congo may have contributed to the geographic spread of the first HIV outbreak, mosquitoes carrying dengue fever may be carried on trucks along highway systems, and the novel coronavirus spread from country to county first through the international air transport network.

With these examples in mind, a variation of the susceptible-infected-removed (SIR) model is developed that couples travel along a network with spatially diffusive spread in a 2D region. The model begins with a metric graph structure (a network in which a distance coordinate is defined on the edges). The classic well-mixed SIR model is implemented at the vertices of the graph (may be conceived as “cities”) which is coupled to a transport model on the edges (“roads”). This structure is embedded in a 2D region, dividing it into several subregions whose boundaries are made up of the metric graph and outer borders. A diffusive SIR model is implemented in the 2D region. This talk will discuss the development of the model and present some preliminary results.

Student/Postdoc Working Geometry Seminar

Time: 1:00PM - 2:00PM

Location: BLOC 628

Speaker: Jan Draisma, U. Bern

Title: A wonderful conjecture by Kazhdan and Ziegler

Abstract: The conjecture: if f:Z ->{nxn-matrices over the complex numbers} is a c-quasihomomorphism (this means that f(a+b)-f(a)-f(b) has rank at most c for all a,b in Z, then f(a)-a*f(1) has rank at most some C=C(c), which doesn't depend on n. I'll discuss the problem and Kazhdan-Ziegler's motivation, and our (Eggermont, Seynnaeve, Tairi, and I) solution in the diagonal case.

Mathematical Physics and Harmonic Analysis Seminar

Time: 1:50PM - 2:50PM

Location: BLOC 306

Speaker: Tal Malinovitch, Yale University

Title: Scattering for Schroedinger operators with conical decay

Abstract: In this talk, I will discuss the scattering properties of Schrodinger operators with potentials that have short-range decay along a collection of rays in \mathbb{R}^d. This generalizes the classical setting of short-range scattering in which the potential is assumed to decay along all rays. For these operators, we show that any state decomposes into an asymptotically free piece and a piece that may interact with the potential for a long time. We give a microlocal characterization of the scattering states in terms of the dynamics and a corresponding description of their complement. We also show that in certain cases these characterizations can be purely spatial. In this talk, I will state our results, sketch some of the main ideas in the proof, and briefly discuss some examples of these interacting states for different systems. This is joint work with Adam Black.

Algebra and Combinatorics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC302

Speaker: Jan Draisma, Universitat Bern, Switzerland

Title: A tensor restriction theorem over finite fields

Abstract: The theorem in the title says that tensors of a fixed format over a fixed finite field K are well-quasi-ordered by restriction: they contain no infinite anti-chains. The same holds, more generally, for "tensors" in spaces described by any finite-length functor from the category of finite-dimensional K-vector spaces to itself. I will discuss several equivalent versions and consequences of the tensor restriction theorem, and explain what their proof reveals about the coarse structure of arbitrary restriction-closed tensor properties. I will also comment on analogous results for Zariski-closed tensor properties over infinite fields, which were obtained earlier in collaborations with Bik, Eggermont, and Snowden. (Based on joint work with Andreas Blatter and Filip Rupniewski: https://urldefense.com/v3/__https://arxiv.org/abs/2211.12319__;!!KwNVnqRv!CNJ4FaC_L_qPuDq9G0SSEEvvfBB16nXYFdC5foDxs-WtoqwWfZQ_EjR6RiKm7A_-Gq1IN2ghldDEZ2BAeVyhTD0$)

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 302

Speaker: Daniel Erman, U. Wisc.

Title: The geometry of weighted syzygies

Abstract: In the 1980s, Mark Green gave a new perspective on the classical correspondence between geometry and polynomial equations. He showed that the defining equations of a curve become increasingly rigid as the degree increases, and that this rigidity could be precisely measured by syzygies. I will discuss how these ideas extend to new contexts like weighted projective spaces, and how this is a part of overarching effort to extend work on syzygies to toric varieties.