Back to Departmental Colloquium: Spring 2015
Departmental Colloquium
Date: Thursday, Jan 29, 2015
Time: 4:00PM
Location: LCB 219
Stefan Patrikis
Massachusetts Institute of Technology
Title |
Projective representations and motives |
Abstract |
In the theory of finite groups, there are basic but subtle differences in the behavior of ordinary representations and of projective representations. After introducing these elementary phenomena, I will discuss their ramifications in an arithmetic' setting, where abstract groups are replaced by Galois groups of field extensions of the rational numbers. Questions then naturally arise in classical’ Galois theory that seem to be impossible to understand within this framework. But an extension of classical Galois theory envisioned by Grothendieck–motivic Galois theory, an arithmeto-geometric subject in which the classical theory amounts to the study of zero-dimensional algebraic varieties–provides exactly the right language for thinking about these questions. There are many reasons for embracing this motivic Galois formalism, but I believe the one to be sketched here is among the most concrete and accessible. I will end by describing the deep problems that arise from transposing our initial question about projective representations to this motivic Galois setting. |
Number Theory
Representation Theory
Algebraic Geometry