Title: Gross' Canonical and Quasi-canonical Liftings
Abstract: The goal of this talk is to give an account on Gross' seminal paper on canonical and quasi-canonical liftings of formal modules. Except for basic notions on formal groups, this talk is intended to be self-contained.
Abstract: Inseparable extensions and morphisms are an important feature in positive characteristic. The study of these uses (smooth) foliations in the tangent bundle of derivations, as was first seen in a theorem of Jacobson (1944) on purely inseparable field extensions of exponent 1. In this talk we will state Jacobson's theorem and some of its generalizations: to normal domains, to regular local and non-local rings, and to morphisms of smooth varieties.
Abstract: Unipotent groups form one of the fundamental building blocks in the theory of linear algebraic groups. Over perfect fields, their behavior is very simple. But over imperfect fields, the situation is much more complicated. We will discuss various aspects of these groups, from the fundamental theory to a study of their Picard groups, which appear to play a central role in understanding their behavior.
Abstract: Iwasawa main conjecture, which is actually a theorem (Mazur & Wiles 84), fulfills the relations between arithmetic objects, p-adic L-functions and complex L-functions. In this talk we sketch how these relations arise and give some consequences.
Speaker: Spencer Leslie (Duke)
Title: The endoscopic fundamental lemma for unitary symmetric spaces
Abstract: Motivated by the study of certain cycles in locally symmetric
spaces and periods of automorphic forms on unitary groups, I propose a
theory of endoscopy for certain symmetric spaces. The main result is the
fundamental lemma for the unit function. After explaining where the
fundamental lemma fits into this broader picture, I will describe its
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Abstract. We investigate the approximation rate of a typical element of the Cantor set by dyadic rationals. This is a manifestation of the times two times three phenomenon, and is joint work with Demi Allen and Han Yu.