Abstract: This will be an informal discussion of some of my favorite topics in number theory and representation theory. First, I will discuss the Deligne-Lusztig variety for GL(n) over a finite field and how its cohomology captures the representation theory of that group. Then I will discuss the local Langlands correspondence for GL(n) over a p-adic field. Finally I will relate the two topics by discussing recent work of Yoshida which shows that Deligne-Lusztig varieties are found in the reductions of stable models of modular curves and their higher-dimensional analogues.