Kang Li (李康)
W1 Professor for Mathematics
Workshop "Ideal Structure of C*-algebras from Dynamics and Groups"
8. April - 12. April 2024 in Erlangen
Barcelona, November 2023
Contact
Department of Mathematics
Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
Cauerstraße 11, 91058 Erlangen, Germany
Email: kang.li@fau.de
ORCID: 0000-0003-0756-0396
About Me
My name is Kang Li and I am a Danish mathematician with a Chinese migration background (I was born in Changsha but grew up in Aarhus). I went to Sølystskolen and Langkær Gymnasium & HF in Aarhus. In January 2016 I received my Ph.D. in Mathematics from University of Copenhagen under the supervision of Uffe Haagerup (passed away) and Ryszard Nest (Principal). My previous employments are University of Copenhagen, University of Münster, Polish Academy of Sciences in Warsaw and KU Leuven. Currently, I am a Junior Professor for Mathematics in Representation Theory and Operator Algebras at Department of Mathematics of Friedrich-Alexander-Universität Erlangen-Nürnberg in Germany. I am affiliated to the Lie Groups leading by Prof. Karl-Hermann Neeb.
My main research area is Operator Algebras and their interactions with Dynamical Systems, Geometric Group Theory and Representation Theory with the following topics:
Property A and coarse embedding in coarse geometry;
Approximation properties for simple Lie groups and groupoid dynamical systems;
The Baum-Connes conjecture for algebraic groups;
Rigidity, Structure and K-theory of lp uniform Roe algebras;
Structure and Dimension theories for étale groupoid C*-algebras;
Counterexamples to the coarse Baum–Connes conjecture;
Measured (asymptotic) expanders;
Regularity properties for ample groupoids and general C*-algebras in classification;
Commensurated subgroups (a.k.a. Hecke pairs) in coarse geometry and operator algebras.
Besides Mathematics, I spend my leisure time mostly on traveling, playing badminton and keyboard, watching movies, enjoying excellent beers and food, learning languages such as Chinese (Native), Danish (Fluent), English (Proficient), French (Basic), German (Conversant B2).
Research
34. (with Kevin Aguyar Brix, Chris Bruce and Eduardo Scarparo) Maximal ideals of reduced group C*-algebras and Thompson's groups, arXiv:2403.13645, (2024), Submitted
33. (with Jiawen Zhang) Tracial states on groupoid C*-algebras and essential freeness, arXiv:2401.15546, (2024), Submitted
32. (with Xin Ma) Non-free almost finite actions for locally finite-by-virtually Z groups, arXiv:2311.00649, (2023), Submitted
31. (with Christian Bönicke) Nuclear dimension of subhomogeneous twisted groupoid C*-algebras and dynamic asymptotic dimension, arXiv:2309.17178, (2023), Submitted
30. (with Hung-Chang Liao and Wilhelm Winter) The diagonal dimension of sub-C*-algebras, arXiv:2303.16762, (2023), Submitted
29. (with Eduardo Scarparo) C*-irreducibility of commensurated subgroups, arXiv:2210.00827, Pacific J. Math. 322 (2023), no. 2, 369–380
28. (with Xuanlong Fu and Huaxin Lin) Tracial approximate divisibility and stable rank one, arXiv:2108.08970, J. Lond. Math. Soc. (2) 106 (2022), no. 4, 3008–3042
27. (with Jorge Castillejos and Gabor Szabo) On tracial Z-stability of simple non-unital C*-algebras, arXiv:2108.08742, (2021), to appear in Canadian Journal of Mathematics
26. (with Ján Špakula and Jiawen Zhang) Measured expanders, arXiv:2104.06052, (2021), to appear in Journal of Topology and Analysis
25. (with Ján Špakula and Jiawen Zhang) Measured asymptotic expanders and rigidity for Roe algebras, arXiv:2010.10749, Int. Math. Res. Not. IMRN (2023), no. 17, 15102–15154
24. (with Federico Vigolo and Jiawen Zhang) A Markovian and Roe-algebraic approach to asymptotic expansion in measure, arXiv:2008.12572, Banach Journal of Mathematical Analysis, 17, no. 74, 2023
23. (with Massoud Amini, Damian Sawicki and Ali Shakibazadeh) Dynamic asymptotic dimension for actions of virtually cyclic groups, arXiv:2007.00960, Proceedings of the Edinburgh Mathematical Society 64(2), 364–372 (2021)
22. (with Piotr Nowak and Sanaz Pooya) Higher Kazhdan projections, l2-Betti numbers and Baum-Connes conjectures, arXiv:2006.09317, J. Noncommut. Geom.18(2024), no.1, 313–336
21. (with Federico Vigolo and Jiawen Zhang) Asymptotic expansion in measure and strong ergodicity, arXiv:2005.05697, J. Topol. Anal. 15 (2023), no. 2, 361–399
20. (with Bartosz K. Kwaśniewski and Adam Skalski) The Haagerup property for twisted groupoid dynamical systems, arXiv:2004.06317, Journal of Functional Analysis 283 (2022) 109484
19. (with Pere Ara, Christian Bönicke and Joan Bosa) Strict comparison for C*-algebras arising from almost finite groupoids, arXiv:2002.12221, Banach J. Math. Anal. 14, 1692–1710 (2020)
18. (with Pere Ara, Christian Bönicke and Joan Bosa) The type semigroup, comparison, and almost finiteness for ample groupoids, arXiv:2001.00376, Ergodic Theory Dynam. Systems 43 (2023), no. 2, 361–400
17. (with Ana Khukhro, Federico Vigolo and Jiawen Zhang) On the structure of asymptotic expanders, arXiv:1910.13320, Advances in Mathematics 393 (2021) 108073
16. (with Piotr Nowak, Ján Špakula and Jiawen Zhang) Quasi-local algebras and asymptotic expanders, arXiv:1908.07814, Groups Geom. Dyn. 15 (2021), 655–682
15. (with Bruno M. Braga and Yeong Chyuan Chung) Coarse Baum-Connes conjecture and rigidity for Roe algebras, arXiv:1907.10237, J. Funct. Anal. 279 (2020), no. 9, 108728
14. (with Yeong Chyuan Chung) Structure and K-theory of lp uniform Roe algebras, arXiv:1904.07050, J. Noncommut. Geom. 15 (2021), 581–614
13. (with Zhijie Wang and Jiawen Zhang) A quasi-local characterisation of Lp-Roe algebras, arXiv:1808.08593, J. Math. Anal. Appl. 474 (2019), no. 2, 1213-1237
12. (with Yeong Chyuan Chung) Rigidity of lp Roe-type algebras, arXiv:1802.08921, Bull. London Math. Soc. (6) 50 (2018), 1056–1070
11. (with Christian Bönicke) Ideal structure and pure infiniteness of ample groupoid C*-algebras, arXiv:1707.03740, Ergodic Theory Dynam. Systems 40 (2020), no. 1, 34–63
10. (with Rufus Willett) Low-dimensional properties of uniform Roe algebras, arXiv:1705.01290, J. London Math. Soc. (2) 97 (2018), 98–124
9. (with Hung-Chang Liao) Classification of uniform Roe algebras of locally finite groups, arXiv:1705.03716, J. Operator Theory 80:1(2018), 25–46
8. (with Siegfried Echterhoff and Ryszard Nest) The orbit method for the Baum-Connes conjecture for algebraic groups over local function fields, arXiv:1704.08548, J. Lie Theory 28 (2018), no. 2, 323-341
7. (with Pere Ara, Fernando Lledó and Jianchao Wu) Amenability and uniform Roe algebras, arXiv:1706.04875, J. Math. Anal. Appl. 459 (2018), no. 2, 686–716
6. (with Pere Ara, Fernando Lledó and Jianchao Wu) Amenability of coarse spaces and K-algebras, arXiv:1607.00328, Bull. Math. Sci. 8 (2018), no. 2, 257-306
5. (with Jacek Brodzki and Chris Cave) Exactness of locally compact groups, arXiv:1603.01829, Adv. Math. 312 (2017), 209-233
4. (with Søren Knudby) A Schur multiplier characterization of coarse embeddability, arXiv:1505.01364, Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 3, 403-409
3. (with Søren Knudby) Approximation properties of simple Lie groups made discrete, arXiv:1408.5238v2, J. Lie Theory 25 (2015), no. 4, 985-1001
2. (with Steven Deprez) Permanence properties of property A and coarse embeddability for locally compact groups, arXiv:1403.7111, (2014)
1. (with Steven Deprez) Property A and uniform embedding for locally compact groups, arXiv:1309.7290, J. Noncommut. Geom. 9 (2015), no. 3, 797-819
Upcoming Conference Talks
Classification of crossed product C*-algebras arising from essentially free actions, Spring Operator Algebras Program 2024, East China Normal University in Shanghai (organized by Huaxin Lin, Hang Wang and so on), April 2024
Non-commutative Dimension Theories, Math Colloquium Talk, East China Normal University in Shanghai (organized by Hang Wang), April 2024
Theses
Property A and coarse embedding for locally compact groups (Ph.D. Thesis, Advisors: Ryszard Nest and Uffe Haagerup)
Introduction to Deformation/Rigidity Theory for II1 Factors (Master Thesis, Advisors: Steven Deprez and Uffe Haagerup)
The Baum-Connes Conjecture with Coefficients (Graduate Course Project, Advisor: Ryszard Nest)
Exact C*-Algebras (Bachelor Thesis, Advisor: Mikael Rørdam)
Teaching
2008, Block 1: Introduction to Mathematics.
2008, Block 2: Linear Algebra.
2012, Block 4: Introduction to Non-commutative Geometry.
2012, Block 1: Introduction to Mathematics.
2012, Block 2: Linear Algebra.
2013, Block 1: Introduction to Mathematics.
2013, Block 2: Linear Algebra.
2014, Block 1: Introduction to Mathematics.
2014, Block 2: Linear Algebra.
2015, Block 2: Linear Algebra.
2021, Spring: Operator Algebras.
2021, Winter: Introduction to Operator Algebras.
2022, Summer: Introduction to Abstract Harmonic Analysis.
2022, Winter: Curves and surfaces.
2022, Winter: Reading Seminar "Unitary representation theory for groups and C*-algebras".
2023, Summer: Topologie.
2023, Winter: Bachelor Seminar "Topics in Topology".
2024, Summer: Querschnittsmodul "Topologie und Anwendungen".
2024, Winter: Seminar "Unitary representation theory for groups and C*-algebras".
Supervision
Bachelor Thesis Advisor for Lennard Kossmann “Mackey Machine and Unitary Duals” at FAU, 28 August 2023.
Bachelor Thesis Advisor for Luciano Melodia “Persistent Homology in Topological Data Analysis” at FAU, in progress.
Bachelor Thesis Advisor for Jonas Schindhelm “Künneth Theorem” at FAU, in progress.
Bachelor Thesis Advisor for Anghelina Manescu “Homotopy groups” at FAU, in progress.
Bachelor Thesis Advisor for Peter Langer “TBD” at FAU, in progress.
Last modified: 24-04-2024