- Wednesday, September 27, 2017, 3:15pm, 119 Physics, Number Theory Seminar
Absolute convergence of the twisted Arthur-Selberg trace formula
Abhishek Parab (Purdue University)
- We show that the distributions occurring in the geometric and spectral side of the twisted Arthur-Selberg trace formula extend to non-compactly supported test functions. The geometric assertion is modulo a hypothesis on root systems proven among other cases, when the group is split. This result extends the work of Finis-Lapid (and Muller, spectral side) in the non-twisted setting. In the end, we will give an application towards residues of Rankin-Selberg L-functions suggested by J. Getz.
- Wednesday, October 4, 2017, 3:15pm, 119 Physics, Number Theory Seminar
Theta integrals and generalized error functions
Stephen Kudla (University of Toronto)
- Recently Alexandrov, Banerjee, Manschot and Pioline constructed generalizations of
Zwegers theta functions for lattices of signature (n-2,2). Their functions, which depend on
two pairs of time like vectors, are obtained by `completing' a non-modular holomorphic generating series
by means of a non-holomorphic theta type series involving generalized error functions.
We show that their completed modular series arises as integrals of the 2-form valued theta functions,
defined in old joint work of the author and John Millson, over a surface S determined by the pairs of time like vectors.
This gives an alternative construction of such series and a conceptual basis for their modularity.
If time permits, I will discuss the generalization to the case of arbitrary signature and a curious
`convexity' problem for Grassmannians that arises in this context.
- Wednesday, October 11, 2017, 3:15pm, 119 Physics, Number Theory Seminar
W. Spencer Leslie (Boston College)
- Wednesday, October 18, 2017, 3:15pm, 119 Physics, Number Theory Seminar
Michael Lipnowski (IAS)
- Wednesday, November 29, 2017, 3:15pm, 119 Physics, Number Theory Seminar
Birgit Speh (Cornell)
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