CMSA

AQFT Lecture Series
2024-03-01 11:00 - 12:00 (America/New_York) | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
AQFT Lecture Series
Speaker: Chen Wan, Rutgers Newark
Title: Some examples of the relative Langlands duality
Abstract: In this talk I will discuss some examples of the relative Langlands duality (introduced by Ben-Zvi—Sakellaridis—Venkatesh) for strongly tempered spherical varieties. In some cases, I will introduce a relative trace formula comparison for the models and prove the fundamental lemma/smooth transfer. This is a joint work with Zhengyu Mao and Lei Zhang.

AQFT Lecture Series
2024-03-01 14:00 - 15:00
AQFT Lecture Series
Speaker: Peng Shan (Tsinghua)
Title: Skein algebras and quantized Coulomb branches
Abstract: In this talk, we explain how to attach a quantized Coulomb branch in the sense of Braverman-Finkelberg-Nakajima to a compact oriented surface of genus at most one, and compare it to the Kauffman bracket Skein algebra in some special cases. This is based on a joint work with Dylan Allegretti.

AQFT Lecture Series
2024-03-07 13:30 - 14:30
AQFT Lecture Series
Speaker: An Huang (Brandeis)
Title: Tate’s thesis and p-adic strings
Abstract: I shall explain the relation between a family of deformations of genus zero p-adic string worldsheet action and Tate’s thesis, which in particular, gives rise to an attempt of physically deriving quadratic reciprocity. I shall then propose a genus one p-adic string worldsheet action, where the key is an explicit definition of a p-adic Laplacian operator on a Tate curve, and the computation of its Green’s function. I shall also mention a very recent attempt of developing a Lorentzian version of the p-adic worldsheet action.

AQFT Lecture Series
2024-03-07 15:00 - 16:00
AQFT Lecture Series
Speaker: John Francis (Northwestern)
Title: Integrating braided categories over 3-manifolds
Abstract: I’ll describe a form of factorization homology, which gives an invariant of framed 3-manifolds given as input a rigid braided-monoidal category with duals. More generally, the construction gives an invariant of framed n-manifolds from an E_{n-1}-monoidal category with duals. This construction relies on a form of the tangle hypothesis, that a dualizable object in an E_{n-1}-monoidal category uniquely determines a functor from the category of tangles in n-space. This is joint work with David Ayala.

AQFT Lecture Series
2024-03-08 13:00 - 14:00
AQFT Lecture Series
Speaker: Dihua Jiang (U Minnesota)
Title: Shalika Periods: Functoriality and Arithmetic
Abstract: Shalika periods of automorphic forms were first used by H. Jacquet and J. Shalika (1990) in their construction of global zeta integrals for exterior square L-functions of GL(2n). They were also used by S. Friedberg and H. Jacquet (1993) in their construction of global zeta integrals for the standard L-functions with connections to the linear periods. A. Ash and D. Ginzburg (1994) used them in their study of p-adic L-functions of GL(2n). In this talk, we will first review the implication of the Shalika periods to the Langlands functoriality and the connections with automorphic descents and theta correspondence. Then we turn to my recent work joint with B. Sun and F. Tian on an application of Shalika periods to algebraicity of critical L-values of cuspidal automorphic of GL(2n) of symplectic type.

AQFT Lecture Series
2024-03-15 11:45 - 12:45
AQFT Lecture Series
Speaker: Baiying Liu (Purdue)
Title: Recent progress on certain problems related to local Arthur packets of classical groups
Abstract: In this talk, I will introduce recent progress on certain problems related to local Arthur packets of classical groups. First, I will introduce a joint work with Freydoon Shahidi towards Jiang’s conjecture on the wave front sets of representations in local Arthur packets of classical groups, which is a natural generalization of Shahidi’s conjecture, confirming the relation between the structure of wave front sets and the local Arthur parameters. Then, I will introduce a joint work with Alexander Hazeltine and Chi-Heng Lo on the intersection problem of local Arthur packets for symplectic and split odd special orthogonal groups, with applications to the Enhanced Shahidi’s conjecture, the closure relation conjecture, and the conjectures of Clozel on unramified representations and on unramified components of automorphic representations. This intersection problem also has been worked out independently at the same time by Hiraku Atobe. In a recent joint work with Alexander Hazeltine, Chi-Heng Lo, and Freydoon Shahidi, we made an upper bound conjecture on wavefront sets of admissible representations of connected reductive groups. In the last part of my talk, I will introduce our recent progress towards this conjecture.

AQFT Lecture Series
2024-03-15 14:15 - 15:30
AQFT Lecture Series
Speaker: Tasho Kaletha (University of Michigan)
Title: Covers of reductive groups and functoriality
Abstract: When studying problems arising from Langlands’ functoriality principle, one often encounters groups that are extensions of complex reductive groups by Galois groups, but that do not necessarily satisfy all properties to be L-groups of reductive groups. We will show, in the case of a local base field F, that such group can be understood as L-groups of covers of reductive groups. This generalizes to the case of arbitrary local fields work of Adams–Vogan for real groups. These covers, for a fixed connected reductive group G, can be understood either as arising from a certain “universal” cover of the topological group G(F) by a certain “fundamental” group tildepi_1(G). We will present two concrete applications of this, one that gives a characterization of the local Langlands correspondence for supercuspidal L-parameters when p is sufficiently large, and one to the construction of transfer factors in the theory of endoscopy.

AQFT Lecture Series
2024-03-18 13:00 - 15:00
AQFT Lecture Series
Speaker: Xinwen Zhu (Stanford)
Title: The tame categorical local Langlands correspondence.
Abstract: I will discuss a conjectural categorical form of the local Langlands correspondence for p-adic groups and establish the tame part of such correspondence (currently for unramified groups with connected center, and for Q_l-coefficients). I will also explain how to extract a (n enhanced) discrete Langlands parameter for depth zero supercuspidal representations from the categorical equivalence.

AQFT Lecture Series
2024-03-20 11:00 - 12:15
AQFT Lecture Series
Speaker: Stephen D. Miller (Rutgers University)
Title: What 4-graviton scattering amplitudes had to say about the unitary dual
Abstract: I’ll give an update on the problem of describing all unitary representations of a Lie group, including joint work with Michael Green and Pierre Vanhove that used intuition from string theory to show the unitarity of the “next to minimal” representation of E8, and more recent work with Joe Hundley and Jeff Adams, Marc van Leeuwen, and David Vogan.

AQFT Lecture Series
2024-03-21 11:00 - 12:15
AQFT Lecture Series
Speaker: Ezra Getzler (Northwestern)
Title: Flat connections on derived stacks and the Gauss-Manin connection in derived algebraic geometry

AQFT Lecture Series
2024-03-22 13:45 - 15:00
AQFT Lecture Series
Speaker: Jayce Getz (Duke University)
Title: The Poisson summation conjecture and the fiber bundle method
Abstract: The Poisson summation conjecture of Braverman-Kazhdan, L. Lafforgue, Ngo, and Sakellaridis predicts that spherical varieties over a global field admit Schwartz spaces, Fourier transforms, and a generalized Poisson summation formula. In this talk I will state a rough form of the conjecture and explain how to deduce new cases of it from known cases using the fiber bundle method. Time permitting I will sketch an approach to proving the functional equation of triple product L-functions using this method. The approach is joint work with Pam Gu, Chun-Hsien Hsu, and Spencer Leslie.
