Algebra Seminar

Recent foundational work by Ben-Bassat, Kelly, and Kremnitzer describes a model for derived analytic geometry as homotopical geometry relative to the infinity category of simplicial commutative complete bornological rings. In this talk, Rhiannon Savage will discuss a representability theorem for derived stacks in these contexts and will set out some new foundations for derived smooth geometry. Rhiannon will also briefly discuss the representability of the derived moduli stack of non-linear elliptic partial differential equations by an object we call a derived C∞-bornological affine scheme.

In this talk, David Luo will use type theory to construct a family of depth $\frac{1}{N}$ minimax supercuspidal representations of $p$-adic $\text{GL}(2N, F)$ which we call \textit{middle supercuspidal representations}. These supercuspidals may be viewed as a natural generalization of simple supercuspidal representations, i.e. those supercuspidals of minimal positive depth. Via explicit computations of twisted gamma factors, David will show that middle supercuspidal representations may be uniquely determined through twisting by quasi-characters of $F^{\times}$ and simple supercuspidal representations of $\text{GL}(N, F)$. Furthermore, David poses a conjecture which refines the local converse theorem for general supercuspidal representations of $\text{GL}(n, F)$.

to follow

to follow

to follow

to follow

to follow