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Title:
Modular and mock modular generating series in arithmetic geometry
Speaker:
Abstract:
The fact that generating series constructed in many areas of geometry and number theory turn out to be modular forms or mock modular forms is a rather ubiquitous, but still striking, phenomenon. In this lecture I will describe certain examples arising from the geometry and arithmetic of Shimura curves — joint work with M. Rapoport and T. Yang. On the one hand, these examples are expected to be part of a more extensive theory of `arithmetic theta series', much of which is still only conjectural. On the other hand, they bear some resemblance to generating series that arise in string theory, and so may be of interest to people working in this area. In particular, I will describe a generating series for virtual arithmetic 0-cycles which can be identified as the central derivative of an incoherent Siegel-Eisenstein series of genus 2 and weight 3/2, which deserves to be better known.
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