Title: Cluster Algebras and Quiver Grassmannians

Abstract: Since their conception, cluster algebras have made appearances in different fields such as algebra, combinatorics, geometry, and topology. For example, a class of objects from representation theory called quiver Grassmannians have been useful in describing the generators of cluster algebras using the Euler characteristic. This has motivated the task of finding cell decomposition of quiver Grassmannians.

Kyungyong and I have been working on this problem for a class of quivers which we will call surface quivers.

Bio: Dr. Uly Alvarez is currently a post-doc at the University of Alabama. He received his PhD in Mathematical Sciences from Binghamton University in New York. His research interests consist of understanding combinatorial and algebraic objects, such as matroids and cluster algebras, by analyzing associated topological spaces.