Past Events

Suppose we fix a convex domain in the plane and fix a prescribed length. What curve can we fit inside this domain so that the curve sees itself as little as possible; that is, so that it minimizes an energy functional that projects it onto itself in all directions? Using a tool…

The study of knotted surfaces in 4-manifolds is analogous to that of knotted circles in 3-manifolds. The motivations are similar: understanding cobordisms and geometric structures, but additionally motivated by the relationship between surfaces and exotic smooth structures on 4-manifolds. (Un?)…

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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…