Workshop on Relative Langlands

General Information: This is the webpage for the workshop on relative Langlands organized at POSTECH in February 2025. It will take place in person at POSTECH in Pohang, South Korea. Feel free to contact any of the organizers if you have any questions.

News: There will be a conference and workshop on the relative Langands program organized by the National University of Singapore in January 2026.
Ruotao Yang will give a series of talks on the Gaiotto conjectures in POSTECH the week after the workshop (February 17--21).

Organizers: Valentin Buciumas, Sungmun Cho, Yeansu Kim, Qirui Li

Date and place: February 8 -- 12, 2025. All lectures will take place in Room 104 in the POSTECH math department.

Directions to the POSTECH math department: see this campus map (math building is M-10) as well as general directions to get to Pohang. Here is the math department on google maps and naver maps.

Speakers:

Zoom link: Talks will be broadcast via Zoom. Here are the Zoom link and details (one link for all talks):
Zoom ID: 898 5688 6453
password: POSTECH11


Schedule:

Time February 8 February 9 February 10 February 11 February 12
9:30-11:30 Wan Wan Wan Wan
14:00-15:30 Wan (14:00-16:00) Takeda Takeda Takeda Takeda


Titles and abstracts:

Speaker Affiliation Title
Shuichiro Takeda Osaka University Distinguished representations and dual groups
Abstract: I will give an overview of basic theory of distinguished representations of $p$-adic groups especially in the context of symmetric spaces. In particular, I will talk about how to compute the dual groups of symmetric spaces with concrete examples and how they fit into the framework of the theory of relative matrix coefficients.
Chen Wan Rutgers University An introduction to the relative Langlands program
Abstract: In these talks, I will give an overview of the relative Langlands program, with an emphasis on period integrals and local multiplicity. I will start with some basic examples, then I will move to the “classical” setting of spherical varieties. Lastly I will discuss the more general setting of the relative Langlands duality. About half of the talks will be about the local aspect and the other half will be about the global setting. I will give as many specific examples as possible.


Zoom recordings: Please find the talk recordings below. The password to all the recordings is postech12*

Speaker Lecture 1 Lecture 2 Lecture 3 Lecture 4 Lecture 5
Chen Wan Wan 1 Wan 2 Wan 3 Wan 4 Wan 5
Suichiro Takeda Takeda 1 Takeda 2 Takeda 3 Takeda 4



Lecture series on the Gaiotto conjectures: Ruotao Yang will give a lecture series on the Gaiotto conjectures (and connections to relative Langlands) as part of the POSTECH representation theory seminar.
I am copying the details of his talks here for completeness.

Date Time Speaker Affiliation Title Room Recording Recording password
February 18 2:00pm-4:30pm Ruotao Yang Chinese Academy of Sciences On the geometrization of the category O of the mixed quantum group: Iwahori fundamental local equivalence Room 404 zoom recording 1Mjbu?2w
Abstract: D.Gaitsgory introduced the mixed quantum group, whose positive part is the Lusztig quantum group and the negative part is the De Concini-Kac quantum group. It plays an important role in the study of quantum Langlands program. In this talk, we will explain how to obtain an equivalence between its category O and the twisted Whittaker category on the affine flags.
February 20 2:00pm-4:30pm Ruotao Yang Chinese Academy of Sciences On the geometrization of the category of representations of supergroup Room 404 zoom recording 0%Yr5h+*
Abstract: D. Gaiotto proposed a series of conjectures related to the geometrization of the category of representations of the quantum supergroup. In the limiting case, it says that the category of finite dimensional representations of the (degenerate) supergroup is equivalent to a certain sheaf category on the affine Grassmannian, which can be regarded as a particular case of the local relative Langlands conjecture proposed by Ben-Zvi-Sakellaridis-Venkatesh. In this talk, we will explain how to establish a geometrization of representations of the degenerate supergroup associated with GL(M|N). It is based on a joint work with R. Travkin.
February 21 10:00am-12:30pm Ruotao Yang Chinese Academy of Sciences On the geometrization of the category of representations of quantum supergroup: Gaiotto conjecture Room 404 zoom recording b*D8.$PJ
Abstract: D. Gaiotto's conjecture says that the category of finite dimensional representations (resp, category O) of the quantum supergroup is closely related to a certain twisted sheaf category on the affine Grassmannian (resp, affine flags). It is the quantum extension of (a particular case of) the relative Langlands conjecture. In this talk, we will explain recent progress on this conjecture. It is based on ongoing and in-preparation works joint with M.Finkelberg and R. Travkin.