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Errata

Local theta correspondence between supercuspidal representations, Ann. Sci. Éc. Norm. Supér, 2018

  1. Corollary 5.11, \Gamma+\mathfrak g_{x,r^+} should be \Gamma+\mathfrak g_{x,-r^+}. The proof was correct.

Invariants and K-spectrums of local theta lifts

  1. The condition (\dagger) (on page 180) should also include the case when (G,G') = (\mathrm{Sp}_{2n}(\mathbb C), \mathrm{O}_{4n}(\mathbb C)) and \rho is the trivial representation. In fact, in this case \Theta(\rho) has two irreducible constituents (See “Lee Soo Teck, Zhu Chenbo, Degenerate principal series and local theta correspondence III”).

2022 天元表示论讨论班

我们计划在本学期（5月-7月）的每周五下午三点邀请专家同行就约化群表示论中的一些前沿的技术做系列专题报告。
我们计划请相关领域的专家就特定专题，分2到3次，详细阐述其中的关键概念和技术，以促进同行们互相交流合作。每次报告时长约为1-1.5小时，欢迎大家参加，并在报告过程中参与讨论和提问。
报告形式：线上报告
腾讯会议ID：436 5742 3564（无密码）

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

2020 Fall Seminar on real reductive groups

This semester, 2020 Fall, we will focus on the representation theory of real reductive Lie groups.
Throughout these seminar talks, we hope to clarify the current status of the subject and stimulate collaborations. We expect the speakers to explain the technical details. The audiences are encouraged to interrupt the speaker and raise questions/make comments. Most lectures will be given in Chinese.

Click the title for the videos of the talks.

Time Conference Id Speaker Title Abstract Host
2020/09/02 NA 董超平 Towards the classification of Dirac series for real classical groups Prof. Dong will collect the math ingredients pertaining to the classification of Dirac series. In particular, he will mention its relation with unipotent representations. SJTU
2020/09/25 2pm-4pm NA 白占强 Gelfand-Kirillov dimensions and associated varieties of highest weight modules In this talk, I will give some introduction to Gelfand-Kirillov dimensions and associated varieties of highest weight modules of Lie algebras (groups). Then I will talk about our work on GKdim and Associated Varieties of highest weight (Harish-Chandra) modules. SJTU
2020/10/09 2pm-3pm 白占强 Gelfand-Kirillov dimensions and associated varieties of highest weight modules II See above SJTU
2020/10/09 3:30pm-4:30pm 余世霖 Geometric quantization I The speaker will introduce the notion of Poisson algebra and deformation quantization SJTU
2020/10/16 2:00pm-3:00pm 腾讯会议 ID：864 4848 4933 会议密码：1122 余世霖 Geometric quantization II The speaker will continue his talk last week on the notion of Poisson algebra and deformation quantization. Then he will discuss some results on the quantization of a nilpotent coadjoint orbit of a real reductive Lie group. SJTU
2020/10/16 3:30pm-4:30pm see above 马家骏 Associated character formula in Howe correspondence I I will discuss the joint works with Loke and Barbasch-Sun-Zhu on the formula of the associated character of a local theta lifting (Howe correspondence). Furthermore, I will explain its applications in the construction of unipotent representations and geometric quantization. XMU
2020/10/23 2:00pm-3:00pm see above 马家骏 Associated character formula in Howe correspondence II see above see above
2020/10/23 3:30pm-4:30pm see above Daniel Wong On NON-unitary (g,K)-modules for complex simple Lie groups I We discuss several techniques detecting non-unitarity of representations of complex Lie groups G, such as bottom layer K-types, Dirac inequality and deformation of parameters. These techniques are essential in determining the unitary spectrum of G. We will also briefly mention where the difficulties arise as one applies the same techniques for general real reductive groups. SJTU
2020/10/30 2:00pm-3:00pm Zoom: 61208845721 pass:130094 Daniel Wong On NON-unitary (g,K)-modules for complex simple Lie groups II See above SJTU
2020/10/30 3:30pm-4:30pm Zoom: 61208845721 pass:130094 Li Ning On certain invariants for constituents of degenerate principal series of Sp(2n,R) In this talk, I will describe associated cycles and wave front cycles for irreducible constituents of degenerate principal series of Sp(2n,R), and their relationship with the space of generalized Whittaker models of these representations. This can be achieved by a careful study of Loke-Ma and Gomez-Zhu’s work. SJTU

2019 春季 代数拓扑

课程信息

习题

  • 3月13日交，选做2题: Chapter 0: 4, 11, 13, 15, 23, 26
  • 3月27日交，选做2题:
    Section 1.1: 14, 15, 16 (f);
    Section 1.2: 6, 7, 8, 14, 19,20, 21;
    Section 1.3: 8, 9, 18, 26, 28, 32

    • 4月17日交, 选做3题:
      Section 2.1: 4, 9, 28, 29, 31
    • 5月29日交, 选做3题:
      Section 3.1: 5, 7, 8, 9
      Section 3.2: 2, 9, 10, 11, 15

期中题目

以下三组题中选做一组, 5月8日交

Section 1.2: 20, Section 2.1: 20, 21, Section 2.2: 26
Section 1.2: 21, Section 2.1: 17 (a), Section 2.2: 36
Section 1.3: 28, Section 2.1: 17 (b), Section 2.2: 40, 42

2019-春季 大学医科数学（A类）[MA093]

课程信息

  • 时间： 星期三 第3节–第4节（10:00 AM – 11:40AM）、星期五 第1节–第2节（8:00AM – 9:40AM）
  • 地点： 东上院201 (1-16周)
  • 课本： 李铮、咸进国（主编），高等数学（生农医药版），上海交通大学出版社，2017

分数比例

平时：10， 期中：30，期末：60

期中考试

  • 时间: 2019-04-24 (第9周星期三) 13：10－15：10
  • 地点: 东中院3-104/105

课件(ppt)

附件

一些Cocalc笔记本:
* Sage演示
* 例 5.1.5 的函数图像

习题

  • 3月8号交, 习题5: 1.2, 2.3, 3.2, 4.2, 5.3, 6, 7.3, 7.4
  • 3月15号交, 习题5: 10, 12.2, 13, 16, 18, 19.1, 20.3, 21
  • 3月22号交, 习题5: 23, 24.1, 25, 26
  • 3月29号交, 习题5: 27.1, 29.2 ,30.3, 31.2, 31.3, 33
  • 4月3号交, 习题6: 1, 5, 7, 8
  • 4月19号交, 习题6: 12, 14, 17, 19, 20, 22, 23, 24, 25
  • 4月26号交, 习题6: 29, 30, 32, 34, 36, 39
  • 5月5号， 不交作业
  • 5月10号，习题6: 40, 44, 45, 46, 47
  • 5月17号交，习题6: 48, 49, 50，习题7: 1.(2), 2.(1),(2)(4)
  • 5月24号交, 习题7: 3.(2), 4， 9，10, 11，12
  • 5月31号交, 习题7: 13, 14.(2), 15.(1), 18, 19
  • 6月12号交(第16周 周三) , 习题7: 23, 24.(2), 25.(4), 26, 27.(2)

2018-春季 大学医科数学（A类）[MA093]

课程信息

  • 时间： 星期一 第1节–第2节（8:00AM-9:40AM）、星期三 第3节–第4节（10:00AM-11:40AM）
  • 地点： 中院413 (1-16周)
  • 课本： 李铮、咸进国（主编），高等数学（生农医药版），上海交通大学出版社，2017

课件(ppt)

附件

一些Cocalc笔记本:
* Sage演示

习题

  • 3月7号交, 习题5: 1.2, 3.2, 4.2, 6, 7.4, 10, 18, 20.3, 21.
  • 3月14号交, 习题5: 25, 26, 27.1, 29,30.
  • 3月21号交, 习题5: 31, 33
  • 3月28号交, 习题6: 1, 5, 7, 8
  • 4月4号交, 习题6: 9, 10, 12, 13, 16
  • 4月11号交, 习题6: 17, 18, 19, 20, 22, 23, 24, 25
  • 4月18号交, 习题6: 26, 27, 28, 29, 30, 32, 36
  • 4月25号, 不交作业
  • 5月2号交, 习题6: 33, 34, 39, 40
  • 5月9号, 不交作业
  • 5月16号交, 习题6: 44, 45, 46, 47
  • 5月23号交, 习题6: 48, 49, 50
  • 5月30号交, 习题7: 1.(2), 2.(1),(2)(4), 3.(2), 4
  • 6月6号交, 习题7: 10, 12, 14.(2), 15.(1), 18, 19
  • 6月13号交, 习题7: 23, 24.(2), 25.(4), 26, 27.(2)

2017-Spring Springer theory

For 2017 Spring semester, from 21-Mar 2017 to 27-June 2017, the time and venue are as the following:
Time: Tuesday noon 12:00-13:30. (the time slot is updated) 
Venue: School of Mathematics SJTU, Room-1106.

TimeVenueTitle/Abstract
Mar 21, 2017,
18:30-20:00		Room-1106Introduction to Springer theory
This is the first talk of my proposed seminar on Weyl group, Springer theory, Hecke algebra and related topics. As an orientation, I will first explain the content of Springer correspondence. Then I will briefly review the basic idea of the constructions of the Springer correspondence. In the end, I will discuss some relationships of the Springer theory with other fields, such as combinatorics and representation theory of reductive groups. If time permits, I will also discuss the generalized Springer correspondence.
Mar 28, 2017Canceled
April 4, 2017Canceled due to Qingming Festival
April 11, 2017,
12:00-13:30		Room-1106A proof of Springer correspondence by Chriss-Ginzburg, (I)
I will present a proof of the Springer correspondence following Chriss-Ginzburg's book "Representation Theory and Complex Geometry" in the next two or three talks. In this talk, I plan to discuss the geometry of the flag variety and the Steinberg variety.
April 18, 2017,
12:00-13:30		Room-1106
Continue the discussion on Ghriss-Ginzburg's book.
April 25, 2017,
12:00-13:30		Room-1106
Continue the discussion on Ghriss-Ginzburg's book.
May 2 , 2017,
12:00-13:30		Canceled
May 9 , 2017,
12:00-13:30		Room-1106Discussion on Ghriss-Ginzburg's book: Borel-Moore homology
May 16 , 2017,
12:00-13:30		Room-1106Discussion on Ghriss-Ginzburg's book: Borel-Moore homology
May 23 , 2017,
12:00-13:30		Room-1106Discussion on Ghriss-Ginzburg's book.
May 30 , 2017,
12:00-13:30		Canceled due to Duanwu Festival(Dragon Boat Festival)
Jun 6 , 2017,
12:00-13:30		Discussion on Ghriss-Ginzburg's book.
Jun 13 , 2017,
12:00-13:30		Discussion on Ghriss-Ginzburg's book.
Jun 20 , 2017,
12:00-13:30		Discussion on Ghriss-Ginzburg's book. Finished Chapter 3