Alex Maloney (平特五不中)
Title:听The Siegel-Weil Formula and Quantum Gravity as an Average.
Abstract:听I will explore the idea that certain theories of gravity are not traditional quantum theories, but are instead听averages over ensembles of quantum听theories.听 Remarkably, this idea can be explored quantitatively using ideas from number theory.听听I will consider the听average over听free boson conformal field theories in two dimensions, and compute the听genus g partition function using the Siegel-Weil formula.听听The result is听a real analytic Eisenstein series听which can be interpreted as the sum听over geometries in a certain exotic - but in a sense exactly solvable - theory of quantum gravity.听听The techniques used are similar to those used to study听high dimensional听sphere听packing听by听averaging over spaces of lattices, suggesting an analogy between semi-classical gravity and a theory of random lattices (or听sphere听packings) in high dimensions.听 This talk is a review of work done in collaboration with E. Witten, and is intended to be accessible to mathematicians without a specialized physics background.听
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