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A knot in the 3-sphere S3 is called “periodic” if it is preserved by a finite order, orientation preserving diffeomorphism of S3, a property that can be viewed as an internal symmetry of the knot. Many knot invariants exhibit special patterns when applied to periodic knots, patterns that reflect…

Consider map F: U --> V. Given data pairs {u_j,F(u_j)} the goal of supervised learning is to approximate F. Neural networks have shown considerable success in addressing this problem in settings where X is a finite dimensional Euclidean space and where Y is either a finite dimensional…

Abstract: Of the (2H+1)^n monic integer polynomials

The problem of counting vectors with given length in a lattice turns out to have much more structure than initially expected, and is connected with the theory of so-called automorphic forms. A geometric analogue of this problem is to count global sections of…

Abstract: We will discuss some old and new results concerning the long-time behavior of solutions to the two-dimensional incompressible Euler equations. Specifically, we discuss whether steady states can be isolated, wandering for solutions starting nearby certain steady states, singularity…

Abstract: I will introduce the notion of a flow multicategory, which
formally encodes the structure that arises when considering
holomorphic discs in Lagrangian Floer theory. Then I will indicate how to define a category of modules over a flow multicategory, as a category enriched in…