Abstract:
Representation theory of $GL_n$ over a $p$-adic field was developed in the 1970s in the seminal work of Bernstein and Zelevinsky. Over the years, deep connections with other areas of representation theory and cluster algebras were discovered. I will discuss some known and open combinatorial problems resulting from the theory and their connection to geometry. No prior familiarity with the subject will be assumed. Based in part on joint works with Avraham Aizenbud, Max Gurevich and Alberto Minguez.