Computer Science/Discrete Mathematics

The well-known Zig-Zag product and related graph operators, like derandomized squaring, are fundamentally combinatorial in nature. Classical bounds on their behavior often rely on a mix of combinatorics and linear algebra. However, these traditional...

The well-known Zig-Zag product and related graph operators, like derandomized squaring, are fundamentally combinatorial in nature. Classical bounds on their behavior often rely on a mix of combinatorics and linear algebra. However, these traditional...

Computational problems exhibit a diverse range of behaviors in terms of how quickly and effectively they can be solved.  What underlying mathematical structure (or lack thereof) in a computational problem leads to an efficient algorithm for solving...

I will discuss the Hanna Neumann conjecture of the 1950's and some tools in graph theory that I used to solve it.  The tools include sheaf theory on graphs, Galois theory for graphs, and the preservation of "local properties" under base change (for...