Past Events
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Abstract: We describe the interrelation between the exactness of Lagrangian graphs, the strong Arnol'd conjecture, and the flux conjectures. In particular we answer a question of Lalonde-McDuff-Polterovich and make new progress on the \(C^0\) flux conjecture. This is joint work in progress…
The Collatz map f(x) sends a positive integer x to x/2 if x is even, or to 3x+1 if x is odd. The well-known Collatz conjecture states that for any initial number x, the k-th iterate f^k(x) in the orbit of x under f eventually reaches 1. Motivated by this (in)famous problem, I will describe…
Floer Memorial Lecture
Abstract: Quantum cohomology is a well-known enumerative invariant of symplectic manifolds. For smooth projective varieties, quantum K-theory was defined around twenty years ago using the `virtual…
The use of deep learning has grown exponentially in the last decade, and a diverse set of architectures has been developed in computer vision, natural language processing, etc. Geometric deep learning is a method to understand the underlying and unifying symmetries and geometry between the…
Abstract: Two weeks ago, we observed that the Ising Model in Z^d exhibits discrete symmetry breaking at low temperatures in the sense that its Gibbs measures are not individually invariant under a global spin flip. In this talk, we introduce a more general framework to study models whose…
In geometric measure theory, Falconer's conjecture, named after Kenneth Falconer, is an unsolved problem concerning the sets of Euclidean distances between points in compact d-dimensional spaces. We will talk about how the basic Fourier method originated from harmonic analysis could do about the…