Title:  Poisson geometry and Azumaya loci of cluster algebrasAbstract:  Roughly speaking, cluster algebra is a commutative algebra obtained from taking the intersection of Laurent polynomial rings associated a "seed". When a cluster algebra satisfies some compatibility condition, M. Gekhtman, M. Shapiro, and A. Vainshtein showed that one can connect a Poisson bracket to the cluster algebra. In […]

Title:  Spectral algebraic geometry and topological modular formsAbstract:  An important area of study in homotopy theory is the study of elliptic cohomology. In this talk we briefly review the context of elliptic cohomology and its interpretation in terms of spectral algebraic geometry. Furthermore, we construct the Deligne-Mumford compactification of the stack of oriented elliptic curves. If time […]