Number Theory Seminar
Wednesday, October 4, 2017, 3:15pm, 119 Physics
Stephen Kudla (University of Toronto)
Theta integrals and generalized error functions
Abstract:- Recently Alexandrov, Banerjee, Manschot and Pioline [ABMP] constructed generalizations of
Zwegers theta functions for lattices of signature (n-2,2). They also suggested a generalization to the case of
arbitrary signature (n-q,q) and this case was subsequently proved by Nazaroglu.
Their functions, which depend on certain collections $\CC$ of negative vectors,
are obtained by `completing' a non-modular holomorphic generating series
by means of a non-holomorphic theta type series involving generalized error functions.
In joint work with Jens Funke, we show that their completed modular series arises as integrals of the q-form valued theta functions,
defined in old joint work of the author and John Millson, over a certain singular $q$-cube determined by the data $\CC$.
This gives an alternative construction of such series and a conceptual basis for their modularity.
If time permits, I will discuss the simplicial case and a curious
`convexity' problem for Grassmannians that arises in this context. [video]
Generated at 4:10pm Monday, September 23, 2024 by Mcal. Top
* Reload
* Login