Non UBC
DSpace
Julia Gordon
2019-11-08T09:21:15Z
2019-05-11T09:12
There is a classical but not very well-known connection between counting objects that are in some sense `in the same class' but not isomorphic, and volume computations.
I will start by recalling the analytic class number formula, and the Minkowski-Siegel mass formula for the "number" of quadratic forms in a genus, as well as Tamagawa's reformulation of these results as a volume computation. Then I will discuss a similar formula for the number of elliptic curves in an isogeny class, and we will see that it can again appear in two versions: one is due to Gekeler (2003) and comes from probabilistic and equidistribution considerations, and the other is due to Langlands and Kottwitz and is based on a volume computation. Finally, I will talk about our recent generalization of Gekeler's result to counting principally polarized Abelian varieties, by `reverse engineering' the Langlands-Kottwitz formula.
https://circle.library.ubc.ca/rest/handle/2429/72225?expand=metadata
49.0 minutes
video/mp4
Author affiliation: University of British Columbia
Banff (Alta.)
10.14288/1.0385128
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Researcher
BIRS Workshop Lecture Videos (Banff, Alta)
Mathematics
Number Theory, Combinatorics, Arithmetic Number Theory
A product formula for isogeny classes of abelian varieties
Moving Image
http://hdl.handle.net/2429/72225