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DTSTART:20070311T020000
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DTSTAMP:20260317T122003
DTSTART;TZID=America/Detroit:20260323T160000
DTEND;TZID=America/Detroit:20260323T170000
SUMMARY:Workshop / Seminar:GLNT: Algebraic theory of indefinite theta functions
DESCRIPTION:Abstract: Jacobi's theta function $\Theta(q) := 1 + 2q + 2q^4 + 2q^9 + \cdots $\, and more generally the theta functions associated to positive-definite quadratic forms\, have the property that they are modular forms of half-integral weight. The usual proof of this fact is completely analytic in nature\, using the Poisson summation formula. However\, $\Theta$ is also related to diffusion of heat on a uniform circle-shaped material: it is a restriction of the fundamental solution to the heat equation on a circle. By algebraically characterizing the heat equation as a specific flat connection on a certain bundle on a modular curve\, we produce a completely algebraic technique for proving modularity of theta functions. More specifically\, we produce a refinement of the algebraic theory of theta functions due to Moret-Bailly\, Faltings--Chai\, and Candelori. As a consequence of the algebraic nature of our theory and the fact that it applies to indefinite quadratic forms / non-ample line bundles (which the prior algebraic theory does not)\, we also generalize the Kudla--Millson analytic theory of theta functions for indefinite quadratic forms to the case of torsion coefficients. This is joint work in progress with Akshay Venkatesh.
UID:143322-21892901@events.umich.edu
URL:https://events.umich.edu/event/143322
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 4096
CONTACT:
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