Schedule for: 17w5097 - Automorphic Forms, Mock Modular Forms and String Theory

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Meet in the Corbett Hall Lounge for a guided tour of The Banff Centre campus.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

This is a report on arXiv:1604.02206 and arXiv:1709.06500, joint with Brubaker, Buciumas and Gray. Whittaker functions on the $n$-fold metaplectic cover of $GL(r)$ over a nonarchimedean local field were studied by Kazhdan and Patterson, who computed the scattering matrix of the intertwining integrals on the Whittaker models. It was shown in 2016 by Brubaker, Buciumas and Bump that this scattering matrix coincides with the R-matrix of a quantum group, a twist of quantum affine $U_{\sqrt{q}}(\widehat{\mathfrak{gl}}(n))$, where $q$ is the residue cardinality. Moreover, they showed that the spherical Whittaker functions could be expressed as partition functions of solvable lattice models, whose internal structure is related to the quantum affine Lie superalgebra $U_{\sqrt{q}}(\widehat{\mathfrak{gl}}(n|1))$. In recent work, Brubaker, Buciumas, Bump and Gray proved that a second solvable lattice model has the same partition function using Yang-Baxter equations. There may be analogies in mathematical physics, such as Kramers-Wannier duality for the Ising model, where the high-temperature system and the low temperature system have essentially the same partition function.

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

5-day workshop participants are welcome to use BIRS facilities (BIRS Coffee Lounge, TCPL and Reading Room) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 12 noon.