# Combinatorial Potlatch 2012

## Topic

**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 theoryâ€¦. My talk will present some of the progress on this topic.

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

Title: TBA

## Speakers

## Additional Information

**Registration:**

The Combinatorial Potlatch has no sponsoring organization and no budget. And we like it that way. Consequently, there are no registration fees because we wouldn't know what to do with them. You are on your own for meals and lodging, speakers travel at their own expense and the host institution provides facilities and food for the breaks. So expressions of appreciation to the speakers and the hosts are preferred and especially encouraged.

**Website**: http://buzzard.ups.edu/potlatch/2012/potlatch2012.html

**Scientific, Conference**

**November 17, 2012**

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