| Talk_id | Date | Speaker | Title |
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29145
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Thursday 10/7
4:00 PM
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David Penneys, The Ohio State University
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Fusion categories in mathematics and physics
- David Penneys, The Ohio State University
- Fusion categories in mathematics and physics
- 10/07/2021
- 4:00 PM - 5:00 PM
- C304 Wells Hall
(Virtual Meeting Link)
- Brent Nelson (banelson@msu.edu)
Classically, the notion of symmetry is described by a group. In recent decades, we have seen the emergence of quantum mathematical objects whose symmetries are best described by tensor categories. Fusion categories simultaneously generalize the notion of a finite group and its category of finite dimensional complex representations, and we think of these objects as encoding quantum symmetries. We will give a basic introduction to the theory of fusion categories and describe applications to some areas of mathematics and physics, namely operator algebras and theoretical condensed matter. [Zoom passcode distributed upon request.]
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29149
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Thursday 10/14
4:00 PM
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Semyon Dyatlov, Massachusetts Institute of Technology
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What is quantum chaos?
- Semyon Dyatlov, Massachusetts Institute of Technology
- What is quantum chaos?
- 10/14/2021
- 4:00 PM - 5:00 PM
- C304 Wells Hall
(Virtual Meeting Link)
- Brent Nelson (banelson@msu.edu)
Where do eigenfunctions of the Laplacian concentrate as eigenvalues go to infinity? Do they equidistribute or do they concentrate in an uneven way? It turns out that the answer depends on the nature of the geodesic flow. I will discuss various results in the case when the flow is chaotic: the Quantum Ergodicity theorem of Shnirelman, Colin de Verdière, and Zelditch, the Quantum Unique Ergodicity conjecture of Rudnick–Sarnak, the progress on it by Lindenstrauss and Soundararajan, and the entropy bounds of Anantharaman–Nonnenmacher. I will conclude with a more recent lower bound on the mass of eigenfunctions obtained with Jin and Nonnenmacher. It relies on a new tool called "fractal uncertainty principle" developed in the works with Bourgain and Zahl.
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29146
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Thursday 10/21
4:00 PM
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Jared Bronski, University of Illinois at Urbana–Champaign
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Index Results for the Kuramoto model
- Jared Bronski, University of Illinois at Urbana–Champaign
- Index Results for the Kuramoto model
- 10/21/2021
- 4:00 PM - 5:00 PM
- C304 Wells Hall
(Virtual Meeting Link)
- Brent Nelson (banelson@msu.edu)
The Kuramoto model is a system of ordinary differential equations modeling the nonlinear interactions of a group phase oscillators. The Kuramoto and related models have been proposed as models for phenomenon like the synchronized flashing of fireflies and the dynamics of circadian rhythms and jet lag. We consider a number of problems in the stability of synchronized solutions to this model. Many of these problems involve some sort of index result, counting the dimension of some unstable manifold. We employ a number of different techniques including geometric, topological, and graph-theoretic ideas. [Zoom passcode distributed upon request.]
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29141
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Thursday 10/28
4:00 PM
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Andrei Caldararu, University of Wisconsin
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Yet another Moonshine
- Andrei Caldararu, University of Wisconsin
- Yet another Moonshine
- 10/28/2021
- 4:00 PM - 5:00 PM
- C304 Wells Hall
- Francois Greer (greerfra@msu.edu)
The j-function, introduced by Felix Klein in 1879, is an essential ingredient in the study of elliptic curves. It is Z-periodic on the complex upper half-plane, so it admits a Fourier expansion. The original Monstrous Moonshine conjecture, due to McKay and Conway/Norton in the 1980s, relates the Fourier coefficients of the j-function around the cusp to dimensions of irreducible representations of the Monster simple group. It was proved by Borcherds in 1992.
In my talk I will try to give a rudimentary introduction to modular forms, explain Monstrous Moonshine, and discuss a new version of it obtained in joint work with Yunfan He and Shengyuan Huang. Our version involves studying the j-function around CM points (so-called Landau-Ginzburg points in the physics literature) and expanding with respect to a coordinate which arises naturally in string theory.
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29144
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Thursday 11/11
4:00 PM
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Kevin Buzzard, Imperial College London
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TBA
- Kevin Buzzard, Imperial College London
- TBA
- 11/11/2021
- 4:00 PM - 5:00 PM
- Online (virtual meeting)
- Francois Greer (greerfra@msu.edu)
No abstract available.
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29142
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Thursday 11/18
4:00 PM
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Anna Seigal, University of Oxford
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TBA
- Anna Seigal, University of Oxford
- TBA
- 11/18/2021
- 4:00 PM - 5:00 PM
- Online (virtual meeting)
- Francois Greer (greerfra@msu.edu)
No abstract available.
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