"Non UBC"@en .
"DSpace"@en .
"Julia Gordon"@en .
"2019-11-08T09:21:15Z"@en .
"2019-05-11T09:12"@en .
"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.\n\nI 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."@en .
"https://circle.library.ubc.ca/rest/handle/2429/72225?expand=metadata"@en .
"49.0 minutes"@en .
"video/mp4"@en .
""@en .
"Author affiliation: University of British Columbia"@en .
"Banff (Alta.)"@en .
"10.14288/1.0385128"@en .
"eng"@en .
"Unreviewed"@en .
"Vancouver : University of British Columbia Library"@en .
"Banff International Research Station for Mathematical Innovation and Discovery"@en .
"Attribution-NonCommercial-NoDerivatives 4.0 International"@en .
"http://creativecommons.org/licenses/by-nc-nd/4.0/"@en .
"Researcher"@en .
"BIRS Workshop Lecture Videos (Banff, Alta)"@en .
"Mathematics"@en .
"Number Theory, Combinatorics, Arithmetic Number Theory"@en .
"A product formula for isogeny classes of abelian varieties"@en .
"Moving Image"@en .
"http://hdl.handle.net/2429/72225"@en .