## Scientific General Events

A topological approach to orderable groups

The Hirzeburch Compactification of Hibert Modular Surfaces

Toric Varieties

Small BGK waves and Landau damping

**Ron Graham**,*University of California, San Diego*

Title: The Combinatorics of Solving Linear Equations

Abstract:One of the fundamental topics in combinatorics involves deciding whether some given linear equation has solutions with all its variables lying in some restricted set, and if so, estimating how many such solutions there are. In this talk, we will describe some of the old and new results in this area, as well as discuss a number of unsolved problems.

**Chris Godsil**,*University of Waterloo*

Title: Continuous Quantum Walks on Graphs

Abstract:If A is the adjacency matrix of a graph X, then the matrix exponential U(t)=exp(itA) determines what physicists term a continuous quantum walk. They ask questions such as: for which graphs are the vertices a and b and a t such that |U(t)a,b|=1? The basic problem is to relate the physical properties of the system with properties of the underlying graphs, and to study this we make use of results from the theory of graph spectra, number theory, ergodic theory…. My talk will present some of the progress on this topic.

**Dan Drake**,*University of Puget Sound*

Title: TBAWhy does clustered network connectivity give rise to bistable neuronal dynamics in simulations of large networks of cortical neurons, driven by Poisson spike trains?