Scholarship and Biography
I am Professor of Mathematics and Chair of the Brandeis Department of Mathematics.
My main research interests are in combinatorics (a.k.a. discrete mathematics). I study problems coming from probability, mathematical physics, computer science and algebra.
I have a particular interest for bijective methods, where one aims at encoding some complex mathematical structures (often geometric objects) by simpler ones (lattice paths, trees, permutations). These encodings help reveal hidden patterns and structures in the objects of interest and can be used to solve mathematical questions about them.
One of my favorite topics is the combinatorics of maps (graphs embedded in surfaces). Maps are important mathematical structures which appear in a wide variety of contexts: graph theory, statistical mechanics, random surface theory, random matrix theory, representation theory, and computer science.