Beijing Institute of Mathematical Sciences and Applications Beijing Institute of Mathematical Sciences and Applications

  • About
    • President
    • Governance
    • Partner Institutions
    • Visit
  • People
    • Management
    • Faculty
    • Postdocs
    • Visiting Scholars
    • Staff
  • Research
    • Research Groups
    • Courses
    • Seminars
  • Join Us
    • Faculty
    • Postdocs
    • Students
  • Events
    • Conferences
    • Workshops
    • Forum
  • Life @ BIMSA
    • Accommodation
    • Transportation
    • Facilities
    • Tour
  • News
    • News
    • Announcement
    • Downloads
About
President
Governance
Partner Institutions
Visit
People
Management
Faculty
Postdocs
Visiting Scholars
Staff
Research
Research Groups
Courses
Seminars
Join Us
Faculty
Postdocs
Students
Events
Conferences
Workshops
Forum
Life @ BIMSA
Accommodation
Transportation
Facilities
Tour
News
News
Announcement
Downloads
Qiuzhen College, Tsinghua University
Yau Mathematical Sciences Center, Tsinghua University (YMSC)
Tsinghua Sanya International  Mathematics Forum (TSIMF)
Shanghai Institute for Mathematics and  Interdisciplinary Sciences (SIMIS)
BIMSA > Burnside type results for fusion categories II \(ICBS\)
Burnside type results for fusion categories II
We extend a classical vanishing result of Burnside from the character tables of finite groups to the character tables of commutative fusion rings, or more generally to a certain class of abelian normalizable hypergroups. We also treat the dual vanishing result. We show that any nilpotent fusion categories satisfy both Burnside's property and its dual. Using Drinfeld's map, we obtain that the Grothendieck ring of any weakly-integral modular tensor category satisfies both properties. As applications, we prove new identities that hold in the Grothendieck ring of any weakly-integral fusion category satisfying the dual-Burnside's property, thus providing new categorification criteria. We also prove some new results on the perfect fusion categories.
Professor Lars Aake Andersson
Lecturer
Sébastien Palcoux
Date
10th October, 2024 ~ 3rd January, 2025
Location
Weekday Time Venue Online ID Password
Thursday,Friday 15:20 - 16:55 A3-3-301 ZOOM 02 518 868 7656 BIMSA
Prerequisite
Be a bit familiar with the finite group representation theory, and the notions of fusion categories, fusion rings and hypergroup, but the definitions will be recalled. This course serves as a continuation of the previous semester's course. Therefore, the initial sessions will be dedicated to a brief review of the material covered last semester.
Reference
- S. Burciu, S. Palcoux. Burnside type results for fusion categories, arXiv:2302.07604,
- P. Etingof, S. Gelaki, D. Nikshych, and V. Ostrik. Tensor categories, volume 205. Mathematical Surveys and Monographs, AMS, Providence, RI, 2015,
- P. Etingof, D. Nikshych, and V. Ostrik. On fusion categories. Ann. of Math. (2), 162(2):581–642, 2005,
- P. Etingof, D. Nikshych, and V. Ostrik. Weakly group-theoretical and solvable fusion categories. Adv. Math., 226(1):176–205, 2011,
- S. Gelaki and D. Nikshych. Nilpotent fusion categories. Adv. in Math., 217(3):1053–1071, 2008.
Audience
Undergraduate , Advanced Undergraduate , Graduate , Postdoc , Researcher
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
2010, obtained a doctorate from Institut de Mathématiques de Marseille (I2M); 2014-2016, Postdoc in Institute of Mathematical Sciences (IMSc); 2019, One-year visitor at Yau Mathematical Sciences Center (YMSC), Tsinghua University; 2020-2024, Assistant Professor at BIMSA; 2024-now, Associate Professor at BIMSA.
Main Research Fields include Quantum Algebra, Quantum Symmetry, Subfactor, Planar Algebra and Fusion Category.
Published papers in the journals Advances in Mathematics, Quantum Topology, IMRN, etc...
Beijing Institute of Mathematical Sciences and Applications
CONTACT

No. 544, Hefangkou Village Huaibei Town, Huairou District Beijing 101408

北京市怀柔区 河防口村544号
北京雁栖湖应用数学研究院 101408

Tel. 010-60661855
Email. administration@bimsa.cn

Copyright © Beijing Institute of Mathematical Sciences and Applications

京ICP备2022029550号-1

京公网安备11011602001060 京公网安备11011602001060