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URL:https://uwaterloo.ca/pure-mathematics/events/geometry-and-topology-semi
 nar-18
SUMMARY:Geometry and Topology Seminar
CLASS:PUBLIC
DESCRIPTION:ADAM LOGAN\, UNIVERSITY OF WATERLOO\, TIMC AND CARLETON UNIVERS
 ITY \nComputational exploration of Hilbert modular surfaces \n\nThere are 
 at least two viewpoints on the modularity of elliptic curves\nover the rat
 ionals: it can be seen either as an analytic and\nrepresentation-theoretic
  statement that the L-function of a curve is\nassociated to a modular form
 \, or as a geometric statement that the\ncurve is a quotient of a modular 
 curve. It is not clear that these\nremain equivalent for elliptic curves o
 ver number fields. For elliptic\ncurves over real quadratic fields\, analy
 tic modularity is now known\,\nand a form of geometric modularity was conj
 ectured 40 years ago by\nOda. Recent advances in the computation of rings 
 of Hilbert modular\nforms have made it possible to verify the geometric mo
 dularity\nconjecture in special cases. In this talk I will describe my wor
 k in\nthis direction\, including some interesting auxiliary algebraic\nsur
 faces that arise in the course of the computations.\n\nMC 5417
DTSTAMP:20260504T234902Z
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