Past Events

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A projective variety X is called Calabi-Yau if its canonical divisor is Q-linearly equivalent to zero. The smallest positive integer m with mK_X linearly equivalent to zero is called the index of X.…

Abstract

Floer homology theories for 3-manifolds come from many sources Instantons, Seiberg-Witten Monopoles,  Heegaard Floer and Embedded Contact Floer theories.  They have proven to be a powerful tools in low dimensional topology. I’ll try to outline some of their…

Getzler Rescaling; geh harmonic oscillator; Mehler's formula

One of the striking aspects of modern  neural networks is their extreme size reaching billions or even trillions parameters.
Why are so many parameters needed? To attempt an answer to this question, I will discuss an algorithm and distribution independent non-asymptotic trade-off…

Stallings gave a group-theoretic approach to the 3-dimensional Poincaré conjecture that was later turned into a group-theoretic statement equivalent to the Poincaré conjecture by Jaco and Hempel and then proven by Perelman. Together with Blackwell, Kirby, Longo, and Ruppik, we have…

The theory of classical exponent pairs for analytic exponential sums has been extensively developed since 1920’s thanks to van der Corput, Philipps, Bombieri, Iwaniec, Bourgain, et al, motivated by various applications to analytic number theory. Recently, we were able to develop the so-called…

In 2007, Pandharipande–Thomas constructed an invariant for smooth projective Calabi–Yau 3–folds which counts stable pairs (roughly: curves with divisors).  The PT/GW conjecture predicts that their invariant is equivalent to the Gromov–Witten invariant.  It is therefore reasonably to…

Consider the time C(r) it takes a Brownian motion to come within distance r of every point in the two-dimensional torus of area one. I will discuss the key ideas in a joint work with Jay Rosen and Ofer Zeitouni, showing that as r goes to zero, the square-root of C(r), minus an explicit non-…