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11:00am - RH 306 - Harmonic Analysis Cosmin Pohoata - (Emory University) The Heilbronn triangle problem The Heilbronn triangle problem is a classical problem in discrete geometry with several old and new close connections to various topics in extremal and additive combinatorics, graph theory, incidence geometry, harmonic analysis, and number theory. In this talk, we will survey a few of these stories, and discuss some recent developments. Based on joint works with Alex Cohen and Dmitrii Zakharov. |
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4:00pm - RH 440R - Logic Set Theory Mauro Di Nasso - (University of Pisa) Ramsey's Witnesses and infinite partition regular configurations I will introduce the notion of “Ramsey partition regularity,” a generalization of partition regularity involving infinite configurations. This notion is characterized in terms of certain ultrafilters related to tensor products, and called Ramsey witnesses. We use the properties of this characterization in the nonstandard context of hypernatural numbers to determine whether various patterns involving polynomials and exponentials are Ramsey partition regular. (Joint work with L. Luperi Baglini, M. Mamino, R. Mennuni, and M. Ragosta.) |
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4:00pm to 5:00pm - RH 340N - Applied and Computational Mathematics Bhargav Karamched - (Florida State University) Dynamic Homeostasis in Relaxation and Bursting Oscillations Most physiologists and cell biologists around the world agree that homeostasis is a fundamental tenet of their disciplines. Nevertheless, a precise definition of homeostasis is hard to come by. Often times, homeostasis is simply defined as "you know it when you see it". Mathematical treatments of homeostasis involve studying equilibria of dynamical systems that are relatively invariant with respect to parameters. However, physiological processes are rarely static and often involve dynamic processes such as oscillations. In such dynamic environments, quantities such as average values may be relatively invariant with respect to parameters. This has recently been called as `homeodynamics'. In this talk, we will present a general biomolecular feedback system involving two time scales that elicits homeostasis in the average value of a relaxation oscillator. The key point is that homeostasis manifests when measuring the slow variable and is not apparent in the fast variable. We demonstrate this in the Fitzhugh-Nagumo model and then describe the pheomenon in the Chay-Keizer model-- a model for describing bursting in electrical activity and calcium oscillations in pancreatic beta cells. We briefly discuss a generalization to a system with multiple scales. |
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10:00am - RH 306 - Harmonic Analysis Haonan Zhang - (USC) On the Fourier tails of degree-two $\mathbf{F}_2$ polynomials Let $p$ be any polynomial of degree $2$ on $n$-dimensional discrete hypercubes. We prove dimension-free upper bounds for the absolute sum of all level-$k$ Fourier coefficients of Boolean functions $f(x)=(-1)^{p(x)}$. This is a joint work with L. Becker, J. Slote and A. Volberg.
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1:00pm to 2:00pm - RH 440R - Mathematical Physics Milivoje Lukic - (Rice University) Universality limits for orthogonal polynomials Fixed measure scaling limits of Christoffel--Darboux kernels encode information about orthogonal polynomials, such as the local distribution of their zeros. Different limit kernels are associated with different universality classes, e.g. sine kernel with bulk universality and locally uniform zero spacing. We will describe necessary and sufficient conditions for a class of scaling limits corresponding to homogeneous de Branges spaces; this includes bulk universality, hard edge universality, and other notable classes. The talk is based on joint work with Benjamin Eichinger and Harald Woracek. |
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9:00am to 9:50am - Zoom - Inverse Problems Tatiana Bubba - (University of Ferrara) Deeply learned regularization for sparse data tomography |
