Kang Li (李康)

Junior Professor for Mathematics

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

My ResearchGate

About Me

My name is Kang Li and I received my Ph.D. in Mathematics from University of Copenhagen in January 2016 under the supervision of Uffe Haagerup and Ryszard Nest (Principal). 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. Dr. Karl-Hermann Neeb.


My research areas are operator algebras, topological/measurable dynamical systems, and coarse geometry as well as representation theory of Lie/algebraic groups 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.


Besides Mathematics, I spend my leisure time mostly on traveling, learning languages, playing badminton and keyboard, watching movies and UFC, and enjoying excellent beers and food.

Research

  • 28. (with Xuanlong Fu and Huaxin Lin) Tracial approximate divisibility and stable rank one, arXiv:2108.08970, (2021), to appear in Journal of the London Mathematical Society

  • 27. (with Jorge Castillejos and Gabor Szabo) On tracial Z-stability of simple non-unital C*-algebras, arXiv:2108.08742, (2021), Submitted

  • 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, (2020), Submitted

  • 24. (with Federico Vigolo and Jiawen Zhang) A Markovian and Roe-algebraic approach to asymptotic expansion in measure, arXiv:2008.12572, (2020), Submitted

  • 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, (2020), Submitted

  • 21. (with Federico Vigolo and Jiawen Zhang) Asymptotic expansion in measure and strong ergodicity, arXiv:2005.05697, (2020), to appear in Journal of Topology and Analysis

  • 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, (2020), to appear in Ergodic Theory and Dynamical Systems

  • 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 Talks

  • Kirillov's orbit method to the Baum-Connes conjecture for algebraic groups, C*-algebras and geometry of groups and semigroups at the University of Oslo (organized by Nadia Larsen, Sven Raum, Martijn Caspers), May 2022

  • Diagonal dimension for C*-pairs, C*-algebras: Structure and Dynamics at the Ben-Gurion University, Israel (organized by George Elliott, N. Christopher Phillips, Ilan Hirshberg), May 2022

  • Kirillov's orbit method to the Baum-Connes conjecture for algebraic groups, Conference on Nest Celebration at the University of Copenhagen, Denmark (organized by Elmar Schrohe, David Kyed, Jens Kaad and Boris Tsygan), June 2022

  • Kirillov's orbit method to the Baum-Connes conjecture for algebraic groups, Special Week on Operator Algebras 2022 at East China Normal University, Shanghai (organized by Huaxin Lin, Hang Wang, Qin Wang, and Jianchao Wu), August 2022

  • Rigidity for Roe algebras and measured asymptotic expanders, Special Session "Operator Algebra and Noncommutative Geometry" in 28th Nordic Congress of Mathematicians at Aalto University, Finland (organized by Sven Raum, Jens Kaad, Magnus Goffeng, and David Kyed), August 2022

Theses

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: Unitary Representation Theory.

  • 2023, Summer: Introduction to Operator Algebras.

Last modified: 21-05-2022