Upcoming Events

Abstract: I will discuss the proof of the index formula (which generalizes an argument of Taubes), and then give applications of the formula by computing expected dimensions for moduli spaces of holomorphic curves which appear in Relative Symplectic Field Theory. A special example is provided by…

The random geometry on simply connected surfaces is a well established subject in probability. The key aspects of this theory include the scaling limit of random planar maps, Liouville quantum gravity, Schramm–Loewner evolution (SLE), and Liouville conformal field theory. For non-simply…

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…