Upcoming Seminars:
• 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
TBA
W. Spencer Leslie (Boston College)

• Wednesday, October 18, 2017, 3:15pm, 119 Physics, Number Theory Seminar
TBA
Michael Lipnowski (IAS)

• Wednesday, November 29, 2017, 3:15pm, 119 Physics, Number Theory Seminar
TBA
Birgit Speh (Cornell)

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