本页为 2022 年 5–7 月天元表示论讨论班的历史存档。报告以约化群表示论的前沿技术为主题，采用线上系列专题报告形式；下表保留原报告摘要、海报与录像链接。
| Date | Time | Speaker | Title | Abstract | Host |
|---|---|---|---|---|---|
| 2022/05/06 | 15:00-16:30 | 陈阳洋 | Schwartz homologies of Nash groups, part I | In this talk, we will give a brief introduction to the Schwartz induction theory of almost linear Nash groups. | Poster@XMU |
| 2022/05/13 | 15:00-16:30 | 陈阳洋 | Schwartz homologies of Nash groups, part II | Same as the above. | Poster@XMU |
| 2022/05/20 | 15:00-16:30 | 陈阳洋 | Schwartz homologies of Nash groups, part III | Same as the above. | XMU |
| 2022/05/27 | 15:00-16:30 | 陈哲 | Higher Deligne-Lusztig theory I | (I) In the first talk I would like to give an introduction to Deligne–Lusztig theory of reductive groups over finite fields, with a focus on the case of SL_2(F_q). Time permitting, I will also discuss some basics of the generalisation for reductive groups over discrete valuation rings (called higher Deligne–Lusztig theory). | XMU |
| 2022/06/03 | 15:00-16:30 | 陈哲 | Higher Deligne-Lusztig theory II | (II) In the second talk, I would like to discuss the algebraisation problem of higher Deligne–Lusztig representations raised by Lusztig, which seeks algebraic realisations (via, say, Clifford theory) of these geometrically constructed representations. I will discuss our resolution of this problem at even levels in a joint work with Stasinski in 2017, as well as our recent progress towards the odd level case. | XMU |
| 2022/06/10 | 15:00-16:30 | 陈哲 | Higher Deligne-Lusztig theory III | (III) In the third talk, I plan to discuss a curious restriction-to-torus formula of Deligne–Lusztig characters, which is motivated by a phenomenon appeared in the algebraisation problem and by a work of Reeder. | XMU |
| 2022/06/17 | 15:00-16:30 | 聂思安 | Lusztig’s map from conjugacy classes of the Weyl group to the unipotent classes | For a connected reductive group over an algebraically closed field, Lusztig constructed a miraculous map from the conjugacy classes of the Weyl group to the unipotent conjugacy classes. We will discuss various interesting properties and applications of the map. Part of the talk is based on joint work with Jeffrey Adams and Xuhua He. | XMU |
| 2022/06/24 | 15:00-16:30 | 聂思安 | Counting points on Newton strata and a multiplicity-one phenomenon | Affine Deligne-Lusztig varieties play an important role in the theory of Shimura varieties. Their geometries are controlled by the Newton strata in Iwahori double cosets. In this talk, I will report a multiplicity-one phenomenon on the Newton strata of a large class of Iwahori double cosets, namely, these strata form a stratification and each of them is nonempty and irreducible. We prove it by counting rational points on the Newton strata. As a consequence, we show the corresponding affine Deligne-Lusztig varieties are explicit unions of classical Deligne-Lusztig varieties of Coxeter type. This is based on joint work in progress with X. He and Q. Yu. | XMU |