| Date | Title | Speaker | Video | Remark |
| 8/25 | Overview of the seminar goals | Tsao-Hsien | See below | Followed by Cheng-Chiang's talk. |
| 8/25 | Introduction to [W1]-[W6], I | Cheng-Chiang | video(8/25) | C.C.'s note for the series. |
| 9/1 | Introduction to [W1]-[W6], II | Cheng-Chiang | video(9/1) | |
| 9/8 | Introduction to [W1]-[W6], III | Cheng-Chiang | Planned for 30 minutes, then Harrison's talk. | |
| 9/8 | Categorical centers and traces, IAbstract: We will introduce a few notions of categorical centers and traces, and give some examples. | Harrison | video(9/8) | Harrison's note for the series. |
| 9/15 | seminar cancelled | |||
| 9/22 | Categorical centers and traces, IIAbstract: We will discuss 1- and 2-categorical traces and compute examples, with special attention to finite, spherical and affine Hecke categories. | Harrison | [3] | |
| 9/29 | Introduction to [BKV1] and [BV], part 1Abstract: I will give an introduction to the work of Bezrukavnikov-Kazhdan-Varshavsky and Bezrukavnikov-Varshavsky on stable center conjecture, affine Springer fibers, and depth zero L-packets. | Tsao-Hsien | video(9/29)[4] | |
| 10/6 | Categorical centers and traces, IIIAbstract: We will discuss 1- and 2-categorical traces and compute examples, with special attention to finite, spherical and affine Hecke categories. | Harrison | video(10/6)[5] | |
| 10/13 | Depth filtration on character sheaves and affine Harish--Chandra bimodulesAbstract: We will explain how to define a depth filtration on the category of affine character sheaves, i.e. adjoint equivariant D-modules on the loop group, and describe some basic properties. We will then specialize to depth zero, and explain a relation to the center of the affine Hecke category and certain categories of affine Harish--Chandra bimodules. | Gurbir | video(10/13) | Gurbir's note for the first talk. |
| 10/17(Mon.) 4-5pm | Depth filtration on character sheaves and affine Harish--Chandra bimodules, IIAbstract: We will explain how to define a depth filtration on the category of affine character sheaves, i.e. adjoint equivariant D-modules on the loop group, and describe some basic properties. We will then specialize to depth zero, and explain a relation to the center of the affine Hecke category and certain categories of affine Harish--Chandra bimodules. | Gurbir | video(10/17) | |
| 10/20 | Gluing character sheavesAbstract: I will talk about joint work with David Nadler, where we describe the dg category of character sheaves on a complex reductive group as gluing (limit) of sheaves on various nilpotent cones. Then we will discuss some applications, including a classification result for the dg category of character sheaves. | Penghui | video(10/20) | |
| 10/27 | The fundamental lemma implies the transferAbstract: We attempt to give a short report on Waldspurger's seminal paper with the same name en francais. In this paper, Waldspurger used a different global method - not Hitchin fibrations, but Poisson summation formula and trace formula - to prove smooth transfer for Langlands-Shelstad endoscopy assuming the fundamental lemma. As a corollary Waldspurger showed that the space of stable distributions is invariant under Fourier transform. | Cheng-Chiang | video(10/27) | |
| 11/3 | Categorical centers and traces, IVAbstract: We will discuss 1- and 2-categorical traces and compute examples, with special attention to finite, spherical and affine Hecke categories. | Harrison | video(11/3) | |
| 11/10 | Unipotent almost characters for p-adic groupsAbstract: I will give an introduction to Lusztig's work on a conjectural definition of unipotent "almost characters" for p-adic groups. In the finite group case, these are essentially the characteristic functions of irreducible unipotent character sheaves, and hopefully the definition in the affine case can serve as a guiding principle for understanding constructible character sheaves for loop groups. | Oscar | video(11/10) | Oscar's note |
| 11/17 | Introduction to [BKV1] and [BV], part 2Abstract: I will give an introduction to the work of Bezrukavnikov-Kazhdan-Varshavsky and Bezrukavnikov-Varshavsky on stable center conjecture, affine Springer fibers, and depth zero L-packets. | Tsao-Hsien | video(11/17) | |
| 11/24 | Introduction to [BKV1] and [BV], part 3Abstract: I will give an introduction to the work of Bezrukavnikov-Kazhdan-Varshavsky and Bezrukavnikov-Varshavsky on stable center conjecture, affine Springer fibers, and depth zero L-packets. | Tsao-Hsien | video(11/24) | |
| 12/1(1:30-2:30) | On the Bernstein center of Hecke algebras at deeper levelAbstract: This talk is based on joint work with Reda Boumasmoud. We will discuss results that describe the Bernstein center of the Hecke algebra H(G(F), K) via the theory of types, where G is a connected, reductive group over a nonarchimedean local field F (that satisfies some additional hypothesis), and K belongs to a nice family of compact open subgroups of G(F). Along the way, we will also describe the center of the Hecke algebra of a type attached to a Bernstein block. | Radhika | video(12/1) | Radhika's note |
This is a research-oriented seminar. The starting plan is to study these references.