董超平 教授

  本人从事基础数学研究，专业方向为李群表示，目前的主要研究兴趣是分类约化李群的狄拉克上同调非零的不可约酉表示(the classification of irreducible unitary representations with non-vanishing Dirac cohomology of reductive Lie groups). 我也在代数组合、应用数学方面做过一点研究.详细的论文目录见下方, 其中:

• 论文[A1]来自我在北京大学的硕士学位论文. 2019年Springer出版的专著《Permutation Polynomial Interleavers for Turobo Codes》的两处章节标题中称[A1]中的算法为Weng and Dong algorithm. 该专著的链接：https://doi.org/10.1007/978-981-13-2625-7

• 论文[L3]给出了处于weakly good range中的上同调诱导模的狄拉克上同调公式.

• 对任意给定的实约化李群G, 论文[L9]给出了分类G的狄拉克系列的有限性算法.

• 论文[L18]分类了复典型群的狄拉克系列，证明了自旋最低K-型只有一个且重数为一.

• 论文[L20]分类了广义实线性群的狄拉克系列.

  过往我曾在山东大学、湖南大学和上海师范大学工作. 我于2018年12月被上海师范大学聘为教授.

李群表示方面

[L21] C.-P. Dong, A non-vanishing criterion for Dirac cohomology, Transformation Groups, https://doi.org/10.1007/s00031-022-09758-0 免费链接:https://rdcu.be/cT9zr

[L20]C.-P. Dong, K.D.Wong, Dirac series of GL(n,R), International Mathematics Research Notices, https://doi.org/10.1093/imrn/rnac150

[L19] C.-P. Dong, K.D.Wong, Dirac index of some unitary representations of Sp(2n, R) and SO^*(2n),Journal of Algebra 403 (2022), 1-37.

[L18] D. Barbasch, C.-P. Dong, K.D.Wong, Dirac series for complex classical Lie groups: A multiplicity one theorem,Advances in Mathematics 403 (2022), Article Number 108370, 47pp.

[L17] C.-P. Dong, K.D.Wong, Dirac series for complex E7,Forum Mathematicum,

34 (2022), 1033-1049.

[L16] C.-P. Dong, On the Helgason-Johnson bound , Israel Journal of Mathematics, accepted.

[L15] L.-G. Ding, C.-P. Dong, H. He, Dirac series for E6(-14), Journal of Algebra, 590 (2022), 168-201. 

[L14]C.-P. Dong, K.D.Wong, Scattered representations of complex classical Lie groups, International Mathematics Research Notices 2022 (14),10431--10457.

[L13] C.-P. Dong, K.D.Wong, On the Dirac series of U(p, q), Mathematische Zeitschrift 298 (2021), 839-859.

[L12] C.-P. Dong, K.D.Wong, Scattered representations of SL(n, C), Pacific Journal of Mathematics 309 (2020), 289-312. 

[L11] J. Ding, C.-P. Dong, L. Yang, Dirac series for some real exceptional Lie groups, Journal of Algebra 559 (2020), 379-407.

[L10] J. Ding,C.-P. Dong, Unitary representations with Dirac cohomology: a finiteness result for complex Lie groups, Forum Mathematicum 32 (2020), 941-964.

[L9] C.-P. Dong, Unitary representations with Dirac cohomology: finiteness in the real case, International Mathematics Research Notices 2020 (24),10277–10316.

[L8] C.-P. Dong, Unitary representations with non-zero Dirac cohomology for complex E6, Forum Mathematicum 31 (1) (2019), 69-82.

[L7] C.-P. Dong, H. Xue, On the nonvanishing hypothesis for Rankin-Selberg convolutions for GL_n(C)×GL_n(C), Representation Theory 21 (2017), 151-171.

[L6] J. Ding, C.-P. Dong, Spin norm, K-types, and tempered representations, Journal of Lie Theory 26 (2016), 651-658.

[L5] C.-P. Dong, Spin norm, pencils, and the u-small convex hull, Proceedings of the American Mathematical Society 144 (2016), 999-1013.

[L4] C.-P. Dong, On a conjecture of Barbasch and Pandzic, Communications in Algebra 43 (2015), 3382-3388.

[L3] C.-P. Dong, J.-S. Huang, Dirac cohomology of cohomologically induced modules for reductive Lie groups, American Journal of Mathematics 137 (2015), 37-60.

[L2] C.-P. Dong, On the Dirac cohomology of complex Lie group representations, Transformation Groups 18 (2013), 61-79. Erratum: ibid, 595-597.

[L1] C.-P. Dong, J.-S. Huang, Jacquet modules and Dirac cohomology, Advances in Mathematics 226 (2011), 2911-2934.

代数组合方面

[C4] C.-P. Dong,G. Weng, Minuscule representations and Panyushev conjectures, Science China Mathematics 61 (10) (2018), 1759-1744.

[C3] C.-P. Dong, S. Wang, Orbits of antichains in certain root posets, Electronic Journal of Combinatorics 24 (4) (2017), #P4.25.

[C2] C.-P. Dong, Folded bump diagrams for partitions of classical types, Advances in Applied Mathematics 62 (2015), 141-159.

[C1] C.-P. Dong, Ad-nilpotent ideals and theShi arrangement, Journal of Combinatorial Theory, Series A 120 (2013), 2118-2136.

应用数学方面

[A3] D. Gao and C.-P. Dong, Fast diffusion inhibits disease outbreaks, Proceedings of the American Mathematical Society 148 (2020), 1709-1722.

[A2] D. Gao, T.M.Lietman, C.-P. Dong and T.C.Porco, Mass drug administration: the importance of synchrony, Mathematical Medicine and Biology 34 (2017), 241-260.

[A1] G. Weng, C.-P. Dong, A note on permutation polynomials over Z_n, IEEE Transactions on Information Theory 54(2008),4388-4390.

SUDA Lie Groups Lectures

Lecture I

Speaker: David A Vogan Jr (MIT)

Title: Lie groups and representations

Time: 2020-10-20, 20pm-21pm (Beijing Time) 

Zoom ID: 517 680 7232 Passcode: 453060

Poster for Lecture I.pdf

Slides for Lecture I.pdf

Lecture II

Speaker: Jing-Song Huang (HKUST)

Title: Segal-Shale-Weil Representations and Universal Fourier Transforms

Time: 2020-10-27, 20pm-21pm

Zoom ID: 517 680 7232 Passcode: 453060

Poster for Lecture II.pdf

Slides for Lecture II.pdf

Lecture III

Speaker: Chengbo Zhu (NUS)

Title: Classical groups and their representations

–an introduction

Time: 2020-11-3, 20pm-21pm

Zoom ID: 517 680 7232 Passcode: 453060

Poster for Lecture III.pdf

Slides for Lecture III.pdf

Lecture IV

Speaker: Pavle Pandzic (Zagreb)

Title: Representations, Harish-Chandra modules and D-modules

Time: 2021-3-31, 20pm-21pm

Zoom ID: 517 680 7232 Passcode: 453060

Poster for Lecture IV.pdf

Slides for Lecture IV.pdf

Lecture V

Speaker: Jinpeng An(Peking U)

Title: Orbits of subgroup actions on homogenuous spaces

Time: 2021-4-28, 20pm-21pm

Zoom ID: 517 680 7232 Passcode: 453060

Poster for Lecture V.pdf

Slides for Lecture V.pdf

Lecture VI

Speaker: Pavle Pandzic (Zagreb)

Title: Dirac index, translation principle and associated cycles

Time: 2022-3-9, 20pm-21pm

Zoom ID: 517 680 7232 Passcode: 453060

Slides for Lecture VI.pdf

Lecture VII

Speaker: Pavle Pandzic (Zagreb)

Title: Dirac index, translation principle and associated cycles II

Time: 2022-3-16, 20pm-21pm

Zoom ID: 517 680 7232 Passcode: 453060

Slides for Lecture VII.pdf

Lecture VIII

Speaker: Pavle Pandzic (Zagreb)

Title: Dirac index, translation principle and associated cycles III

Time: 2022-3-23, 20pm-21pm

Zoom ID: 517 680 7232 Passcode: 453060

Slides for Lecture VIII.pdf

Lecture IX

Speaker: Kei Yuen Chan (Fudan)

Title: Quotient branching law for p-adic general linear groups and affine Hecke algebras of type A

Time: 2022-4-20, 20pm-21pm

Tencent meeting: 437-586-907

Slides for Lecture IX.pdf

Lecture X

Speaker: Kayue Daniel Wong (CUHKSZ)

Title: Dirac series for complex simple Lie groups

Time: 2022-5-11, 20pm-21pm

Tencent meeting: 426-921-970

Poster for Lecture X.pdf

Slides for Lecture X.pdf

已毕业学生

2020年

丁健 (博士，工作单位：九江学院)

丁林根 (硕士，学习单位：厦门大学)

推荐过的本科生去往美国加州大学洛杉矶分校, 法国Université Grenoble Alpes, 上海数学中心等地深造.