Click on any title to see the abstract.
| Date | Title | Speaker | Remark |
| 10/17 | Characters of p-adic groupsThis is one of the two background talks of the seminar on character sheaves on loop groups. These character sheaves are expected to be similar to and reflect properties of characters of p-adic reductive groups. Harish-Chandra had proved in the 70's that characters of a p-adic reductive groups is locally equal to the Fourier transform of a distribution supported on a nilpotent cone. While the proof is delicate, it is based on a simple idea that when we restrict an irreducible smooth representation to a sufficiently small open compact subgroup, the constituents are "degenerate/nilpotent" in a precise sense.We will explain characters of p-adic groups, the above simple idea, some heuristic of the full proof, and (if time permits) further enhancements of Moy-Prasad, Waldspurger, DeBacker and Adler-Korman. (No background on representation theory of p-adic groups will be assumed) |
Cheng-Chiang | Cheng-Chiang's note (updated after talk) |
| 10/24 | Representation theory of p-adic groupsIn this talk, I will give a brief overview of supercuspidal representations of p-adic reductive groups, which are sometimes referred to as "building blocks" of the representation theory of p-adic reductive groups. In particular, I will sketch an explicit construction of a large class of supercuspidal representations established by Adler and Yu. |
Masao | Masao's note: typed, handwritten |
| 10/31 (1-3pm) | Polar sets and character sheaves on LgI'll talk about the polar sets in a loop Lie algebra Lg and character sheaves on Lg defined by Ngô-Yun [NY25] and explain their connection with Yu's construction of supercuspidal representations. |
Wille | Lusztig's colloquium talk at 3:30pm with tea at 3pm. |
| 11/7 | No talk on 11/7 | ||
| 11/14 | [BKV, §1] Placidity and geometry in ind-infinite typeI will discuss section 1 of [BKV22]. In particular I will discuss placid presentations of schemes/ ind-schemes and attempt to motivate some of the discussions with the examples of spaces of loops and arcs into varieties. If I have time I might discuss a little Drinfeld's paper Infinite Dimensional Vector Bundles in Algerbaic Geometry, where similar considerations arise. | Emile | note |
| 11/21 | [BKV, §5] | Adeel | |
| 11/28 | No talk on 11/28 | ||
| 12/5 | [BKV, §2] | Cheng-Chiang | note |
| 12/17(Wed.), 1:20-3pm | [BKV, §3] | Wille | Ngô's lecture 3:30-4:30pm |
| 12/26 | [BKV, §6] | Adeel | |
| 1/2 | [BKV, §4&§7.1] | Cheng-Chiang |
References: [BKV22] Perverse sheaves on infinite-dimensional stacks, and affine Springer theory, A. Bouthier, D. Kazhdan, Y. Varshavsky
[BC24] Generic character sheaves on parahoric subgroups, R. Bezrukavnikov, C. Chan
[HHZ] Newton Decomposition on the Quotient Stacks of Loop Groups, X. He, A. Heleodoro, X. Zhu
[NY25] Character sheaves on loop Lie algebras: polar partition, Ngo B. C., Z. Yun
[BKV25] Perversity of coinvariants of affine Springer sheaves, A. Bouthier, D. Kazhdan, Y. Varshavsky
[INY25] An alternative construction of character sheaves on parahoric subgroups, A. B. Ivanov, S. Nie, Z. Yu
See also Seminar on character sheaves for a related seminar an year ago and Character sheaves on loop groups for another 3 years ago.