Seminar:
Geometry, Symmetry and Physics
Event time:
Monday, October 21, 2024 - 4:30pm
Location:
KT 801
Speaker:
James Hotchkiss
Speaker affiliation:
Columbia University
Event description:
The period-index problem is a classical problem about finite-dimensional division algebras over a field. When the base field is the function field of a complex variety, there is a longstanding conjecture, which is wide open for function fields of threefolds and beyond. I will discuss recent perspectives on the conjecture from topology, Hodge theory, and moduli theory. Finally, I will explain a result showing that, roughly speaking, topological solutions to the conjecture exist for complex function fields of arbitrary dimension.
Research Area(s):
Algebraic Geometry