Tuesday, 5 October 2021, 4-5pm Zoom

• Speaker: Sourav Chatterjee (Stanford University)
  
  Title: Some progress on 3D Yang-Mills
  
  Abstract: I will talk about some recent progress on the problem of constructing 3D Euclidean Yang-Mills theories. This is based on joint work with my student Sky Cao. No background in Yang-Mills is required; I will try to make the talk accessible to a general audience.

Tuesday, 2 November 2021, 4-5pm Zoom

• Speaker: Bryna Kra (Northwestern University)
  
  Title: Symmetries in symbolic dynamics
  
  Abstract: Originating in the work of Hadamard in the 1890’s on the coding of geodesic flow, symbolic dynamics has become a key tool for studying topological, smooth, and measurable dynamical systems. The automorphism group of a symbolic system capture its symmetries, reflecting the dynamical behavior and the complexity of the system. I will give an overview of relations among dynamical properties of the system, algebraic properties of the automorphism group, and measurable properties of associated systems, all of which quickly lead to open questions.

Tuesday, 7 December 2021, 4-5pm Zoom

• Speaker: Semyon Dyatlov (MIT)
  
  Title: What is quantum chaos?
  
  Abstract: 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 Verdi\`ere, 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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You'll find the old colloquium schedules here.