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Texas A&M University

Events for 09/22/2023 from all calendars

Mathematical Biology Seminar

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Time: 09:00AM - 10:00AM

Location: ZOOM

Speaker: Pengfei Song, Xi’an Jiaotong University, China

Title: Coupling of transmission dynamics and deep learning techniques

Abstract: Neural networks, though called as black-box uniform approximator and difficult to interpret, have an unreasonable effectiveness in learning unknown mechanisms with bless of dimensionality, and have lots of applications. In this talk, I will introduce a recent state-of-the-art universal differential equation method that embeds neural networks into differential equations. Three applications will be shown. (1) Using deep learning techniques to estimate effective reproduction number and compared with EpiEstim and EpiNow2 method. (2) Discovering unknown human behavior change mechanisms in transmission dynamics. (3) Using deep learning techniques to solve optimal control problems by representing optimal control function as neural networks, and compared with traditional direct, indirect, and dynamic programming methods.

Mathematical Physics and Harmonic Analysis Seminar

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Time: 1:50PM - 2:50PM

Location: BLOC 302

Speaker: Matthias Maier, Texas A&M University

Title: Lorentz Resonance in the Homogenization of Plasmonic Crystals

Abstract: We explain the Lorentz resonances in plasmonic crystals that consist of 2D nano dielectric inclusions as the interaction between resonant material properties and subwavelength geometric resonances of electrostatic nature. One example of such plasmonic crystals is graphene nanosheets that are periodically arranged within a non-magnetic bulk dielectric.

We identify local geometric resonances on the length scale of the small scale period. From a materials perspective, the graphene surface exhibits a dispersive surface conductance captured by the Drude model. Together these phenomena conspire to generate Lorentz resonances at frequencies controlled by the surface geometry and the surface conductance.

The Lorentz resonances found in the frequency response of the effective dielectric tensor of the bulk metamaterial is shown to be given by an explicit formula, in which material properties and geometric resonances are decoupled.

Joint work with Wei Li (DePaul University) and Robert Lipton (Louisiana State University)

Geometry Seminar

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Time: 4:00PM - 5:00PM

Location: BLOC 302

Speaker: Timothy Duff, U. Washington Seattle

Title: Geometry of two, three, or four cameras

Abstract: I will introduce a line of work that aims to characterize the set of all valid algebraic constraints that relate any number of perspective cameras, 3D points, and their 2D projections. More formally, this framework involves the study of certain multigraded vanishing ideals. This leads to several new results, as well as new proofs of old results about the well-studied multiview ideal. For example, a "folklore theorem" from geometric computer vision states: "all algebraic constraints on the 2D projections of 3D points can be obtained from those involving 2, 3, or 4 cameras." (joint w/ S. Agarwal, E. Connelly, J. Loucks-Tavitas, R. Thomas) I will also discuss a complementary line of work focused on practical estimation methods. Incremental 3D reconstruction systems usually focus on estimating the relative orientation of two cameras. This in turn requires solving systems of algebraic equations with (very) special structure. I will describe recent progress extending the domain of such solvers to problems involving three or four cameras, including non-perspective cameras with lens distortion. The key players are numerical homotopy continuation methods, and the Galois/monodromy groups that capture their inherent complexity. (joint w/ P. Hruby, K. Kohn, V. Korotynskiy, V. Larsson, A. Leykin, L. Oeding, T. Pajdla, M. Pollefeys, M. Regan)

Free Probability and Operators

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Time: 4:00PM - 5:00PM

Location: BLOC 506A

Speaker: Srivatsav Kunnawalkam Elayavalli, UCSD

Title: How to construct two non Gamma II_1 factors with non isomorphic ultrapowers

Abstract: I will describe a construction due to myself, Chifan and Ioana of a II_1 factor N such that N^omega is not isomorphic to L(F_2)^omega for any free ultrafilter omega. This is the first known such examples. The proof uses Voiculescu's free entropy theory and Popa's deformation rigidity theory.