School of Mathematics

In this talk I will describe a real-variable method to extract long-time asymptotics for solutions of many nonlinear equations (including the Schrodinger and mKdV equations). The method has many resemblances to the classical stationary phase method...

In the talk, I will describe recent attempts to understand the mysterious and beautiful geometry of nodal lines of random spherical harmonics and of random plane waves. If time permits, I will also discuss asymptotic statistical topology of other...

The cd-index is a noncommutative polynomial which compactly encodes the flag vector data of a polytope, and more generally, of a regular cell complex. Ehrenborg and Readdy discovered the cd-index has an inherent coalgebraic structure which...

This will be an introduction to special value formulas for L-functions and especially the uses of modular forms in establishing some of them -- beginning with the values of the Riemann zeta function at negative integers and hopefully arriving at...

I will discuss the problem of determining the number of infinite-volume ground states in the Edwards-Anderson (nearest neighbor) spin glass model on $Z^D$ for $D \geq 2$. There are no complete results for this problem even in $D=2$. I will focus on...

There is a way to specify any smooth, closed oriented four-manifold using a surface decorated with simple closed curves, something I call a surface diagram. In this talk I will describe three moves on these objects, two of which are reminiscent of...

ANALYSIS/MATHEMATICAL PHYSICS SEMINAR

As originally proposed by Anderson (1958), a quantum system of many local degrees of freedom with short-range interactions and static disorder may fail to thermally equilibrate, even with strong interactions and...

In recent research it has become clear that there are fascinating connections between constructive mathematics, especially as formulated in the type theory of Martin-Löf, and homotopy theory, especially in the modern treatment in terms of Quillen...

The theory of $\varphi, \Gamma)$-modules, which was introduced by Fontaine in the early 90's, classifies local Galois representations into modules over certain power series rings carrying certain extra structures $(\varphi and \Gamma)$. In a recent...