Hongsheng Hu / 胡泓昇

A stupid math guy.

Latest update: July 07, 2024.

I am currently an assistant professor in School of Mathematics, Hunan University, Changsha, China.

CV & 中文简历.

Research Interests:

Algebra, representation theory, Lie theory, Coxeter groups and their representations, Kazhdan–Lusztig theory.

E-mail:

huhongsheng (the symbol) amss (dot) ac (dot) cn
huhongsheng (the symbol) hnu (dot) edu (dot) cn

ORCID:   0000-0002-1850-056X

Writings:

• On exterior powers of reflection representations, II.

  Preprint. 2024.
  arXiv:2401.08215

• Asymptotic log-concavity of dominant lower Bruhat intervals via the Brunn–Minkowski inequality.

  j.w. Gaston Burrull and Tao Gui (桂弢).
  Preprint. 2023.
  arXiv:2311.17980
  With an extended abstract accepted by FPSAC 2024 as a poster.

• On the dominant weight polytopes.

  j.w. Gaston Burrull and Tao Gui (桂弢).
  Preprint. 2023.
  arXiv:2311.16022

• Representations of Coxeter groups of Lusztig's a-function value 1.

  Preprint. 2023.
  arXiv:2309.00593

• On exterior powers of reflection representations.

  Published online. Bull. Aust. Math. Soc. 2023.
  DOI: 10.1017/S0004972723000965
  arXiv:2306.16946

• Reflection representations of Coxeter groups and homology of Coxeter graphs.

  Algebr. Represent. Theory 27 (2024), no. 1, 961–994.
  DOI: 10.1007/s10468-023-10242-w
  arXiv:2306.12846 / also visible at https://rdcu.be/ds3Un

• 最小二乘解与高斯消元法的注记. (A note on least squares solutions and Gaussian eliminations.)

  Preprint. Teaching paper. Written in Chinese. 2022.
  To appear in 大学数学 (College Mathematics).
  Full-text PDF

• Some infinite-dimensional representations of certain Coxeter groups.

  Published online. Ann. Comb. 2024.
  DOI: 10.1007/s00026-024-00690-6
  arXiv:2205.09294 / also visible at https://rdcu.be/dCswL

• Representations of Coxeter groups and homology of Coxeter graphs.

  Preprint. 2021.
  arXiv:2112.03771
  Note: This manuscript has been split into two revised ones, arXiv:2306.12846 and arXiv:2309.00593.

• Coxeter 群的 "反射" 表示. ("Reflection" representations of Coxeter groups.)

  Ph.D. Dissertation. Written in Chinese. 2022.
  Full-text PDF

Conferences and Talks:

• Asymptotic log-concavity of dominant lower Bruhat intervals via the Brunn–Minkowski inequality. (poster)

  July 22–26, 2024.
  The 36th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2024).
  Ruhr-Universität Bochum. Bochum, Germany.

• Exterior powers of reflection representations. (20 mins)

  Abstract. 　 Slides.
  Nov. 18, 2023.
  The 16th National Conference on Algebra.
  Huaqiao University. Quanzhou, Fujian Province, China.

• Reflection representations of Coxeter groups. (30 mins, in English)

  Abstract. 　 Slides.
  Nov. 12, 2023.
  The Fourth International Conference on Groups, Graphs and Combinatorics/
  The Fourth International Conference on Group Actions and Symmetrical Graphs.
  Southern University of Science and Technology. Shenzhen, Guangdong Province, China.

• Graphs and reflection representations, I — classifications and beyond. (60 mins)
  Graphs and reflection representations, II — exterior powers. (60 mins)

  Abstracts. 　 Notes. 　 Link I. 　 Link II.
  Sep. 14, 2023.
  Seminar on representation theory.
  Academy of Mathematics and Systems Science, Chinese Academy of Sciences. Beijing, China.

• Hecke algebras — an incomplete introduction. (120 mins)

  Abstract. 　 Notes.
  Apr. 27, 2023.
  3+X undergraduate seminar.
  School of Mathematical Sciences, Peking University. Beijing, China.

• Coxeter groups and their reflection representations. (90 mins, online)

  Abstract. 　 Slides. 　 Link.
  Nov. 28, 2022.
  Postdoc seminar.
  Beijing International Center for Mathematical Research, Peking University. Beijing, China.

Some Links:

• Beijing International Center for Mathematical Research (where I am working as a postdoc).
• Academy of Mathematics and Systems Science, Chinese Academy of Sciences (where I received my Ph.D. degree).
• Department of Mathematics, UC Riverside (where I had a visit for half a year in 2019).
• Yau Mathematical Sciences Center, Tsinghua University (where I attended some lectures during my graduate studies).
• School of Mathematical Sciences, Fudan University (where I received my B.S. degree).
• Zhangzhou No. 1 High School of Fujian/漳州一中 (my senior high school).
• Zhao'an Huai'en Middle School/诏安县怀恩中学 (my junior high school).
• Zhao'an Experimental Primary School/诏安县实验小学 (my primary school).
• Zhao'an/诏安县, Zhangzhou/漳州市, Fujian Province/福建省, China (where I burst out my first crying in May 16, 1994).
• Papers related: MathSciNet, zbMATH Open, arXiv, Google Scholar, ...
• Journals related: Clarivate JCR, MathSciNet Journals, LetPub, CAS, CMS, ...
• TeX related: Overleaf, CTAN, Detexify, ...
• MSC: MathSciNet MSC, zbMATH Open MSC, ...
• Some websites collecting conference information: MathMeetings, researchseminars, Conference Index, ...
• Some softwares: Sage, GAP, ... (who can teach me how to use them?)
• Some communities: MathOverflow, MathStackExchange, Lean Community, GitHub, ...
• Some encyclopedias: Wikipedia, EoM, WM, PlaneMath, nLab, Scientific Lib, Baidu Encyclopedia, ...
• Lievis: Lie theory visualisations.
• The On-Line Encyclopedia of Integer Sequences.
• ...

At last: 要保持数学工作者的纯粹, 纯粹得像一个小孩.

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