Past Events

For a domain X with a probability measure pX, consider reconstruction of an unknown function f using discrete least squares approximation from a linear space Vm of dimension m constructed from values f(xi), where xi are randomly drawn from X w.r.t....

Basic questions in analytic number theory concern the density of one set in another (e.g. square-free integers in all integers). Motivated by Weil's number field/function field dictionary, we introduce a topological analogue measuring the...

The term ‘anomalous diffusion’ is used in the physics literature to refer to Markov processes with the property that E|X_t-X_0|^2 grows either faster or slower than linearly. In this talk I will give a survey of results in this area, including random...

We combine models and experiments to study how embryonic cells form and stabilize polarity in response to transient cues. In this talk, I will summarize our understanding of how dynamic self-stabilizing cortical polarities emerge from a system of...

Schur functions form the most interesting and important basis for the algebra of symmetric functions. They have connections to representation theory and algebraic geometry, and satisfy a multitude of beautiful combinatorial identities. We investigate...

Optimal stopping problems can be viewed as a problem to calculate the space and time dependent value function, which solves a nonlinear, possibly non-smooth and degenerate, parabolic PDE known as an Hamilton-Jacobi-Bellman (HJB) equation. These...

A packing of translates of a convex domain in the Euclidean plane is said to be totally separable if any two packing elements can be separated by a line disjoint from the interior of every packing element. This notion was introduced by G. Fejes Toth...

We introduce a class of polytopes which we call endoskeletal. The structure of an endoskeletal polytope is determined by its internal skeleton and its volume is given by a strikingly simple formula involving a single determinant. A rudimentary...

In episode 2 of the series, I will turn my attention to the setting of G-equivariant stable homotopy theory, where G is an abelian p-group. Analogous to the classical case, we can use symmetric powers of the equivariant sphere to filter H\underline{...

In this talk I will present some results on stochastic heat equations driven by a Gaussian noises. I will focus on Feynman-Kac representation of the solution and the moments of the solution. Both lower and upper bounds for the L^p moments of the...