Professor Xin Li

  • Chair of Mathematical Analysis (Mathematics)

Research interests

I am working on C*-algebras and their connections to other mathematical disciplines such as topological dynamics, group theory or number theory. My research interests include semigroup C*-algebras, K-theory, Cartan subalgebras of C*-algebras, continuous orbit equivalence, and topological full groups. For more information, please see my personal website.

Research groups

Publications

List by: Type | Date

Jump to: 2024 | 2023 | 2022 | 2021 | 2020 | 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2010
Number of items: 45.

2024

Li, X. (2024) Ample groupoids, topological full groups, algebraic K-theory spectra and infinite loop spaces. Forum of Mathematics, Pi, (Accepted for Publication)

Li, X. (2024) Left regular representations of Garside categories II. Finiteness properties of topological full groups. Groups, Geometry, and Dynamics, (Accepted for Publication)

Kakariadis, E. T.A., Katsoulis, E. G. and Li, X. (2024) Stable isomorphisms of operator algebras. International Mathematics Research Notices, 2024(5), pp. 4118-4094. (doi: 10.1093/imrn/rnad146)

Bruce, C. and Li, X. (2024) Algebraic actions I. C*-algebras and groupoids. Journal of Functional Analysis, 286(4), 110263. (doi: 10.1016/j.jfa.2023.110263)

2023

Li, X. and Raad, A. I. (2023) Constructing C*-diagonals in AH-algebras. Transactions of the American Mathematical Society, (doi: 10.1090/tran/9023) (Early Online Publication)

Kakariadis, E. T.A., Katsoulis, E. G., Laca, M. and Li, X. (2023) Couniversality and controlled maps on product systems over right LCM semigroups. Analysis and PDE, 16(6), pp. 1433-1483. (doi: 10.2140/apde.2023.16.1433)

Li, X. (2023) Left regular representations of Garside categories I. C*-algebras and groupoids. Glasgow Mathematical Journal, 65(S1), S53-S86. (doi: 10.1017/S0017089522000106)

Bruce, C. and Li, X. (2023) On K-theoretic invariants of semigroup C*-algebras from actions of congruence monoids. American Journal of Mathematics, 145(1), pp. 251-285. (doi: 10.1353/ajm.2023.0005)

Chen, C. and Li, X. (2023) Semigroup C*-algebras arising from graphs of monoids. International Mathematics Research Notices, (doi: 10.1093/imrn/rnac332) (Early Online Publication)

2022

Li, X. (2022) Constructing Menger manifold C*-diagonals in classifiable C*-algebras. International Mathematics Research Notices, 2022(23), pp. 18992-19053. (doi: 10.1093/imrn/rnab199)

Kakariadis, E. T.A., Katsoulis, E. G., Laca, M. and Li, X. (2022) Boundary quotient C*-algebras of semigroups. Journal of the London Mathematical Society, 105(4), pp. 2136-2166. (doi: 10.1112/jlms.12557)

Dor-On, A., Kakariadis, E.T.A., Katsoulis, E., Laca, M. and Li, X. (2022) C*-envelopes for operator algebras with a coaction and co-universal C*-algebras for product systems. Advances in Mathematics, 400, 108286. (doi: 10.1016/j.aim.2022.108286)

Li, X. (2022) K-theory for semigroup C*-algebras and partial crossed products. Communications in Mathematical Physics, 390(1), pp. 1-32. (doi: 10.1007/s00220-021-04194-9)

2021

Li, X. , Omland, T. and Spielberg, J. (2021) C*-algebras of right LCM one-relator monoids and Artin-Tits monoids of finite type. Communications in Mathematical Physics, 381(3), pp. 1263-1308. (doi: 10.1007/s00220-020-03758-5)

2020

Barlak, S. and Li, X. (2020) Cartan subalgebras and the UCT problem, II. Mathematische Annalen, 378(1-2), pp. 255-287. (doi: 10.1007/s00208-020-02022-4)

Li, X. (2020) Every classifiable simple C*-algebra has a Cartan subalgebra. Inventiones Mathematicae, 219(2), pp. 653-699. (doi: 10.1007/s00222-019-00914-0)

2019

Li, X. (2019) K-theory for generalized Lamplighter groups. Proceedings of the American Mathematical Society, 147(10), pp. 4371-4378. (doi: 10.1090/proc/14619)

Li, X. and Renault, J. (2019) Cartan subalgebras in C*-algebras. Existence and uniqueness. Transactions of the American Mathematical Society, 372(3), pp. 1985-2010. (doi: 10.1090/tran/7654)

Cornelissen, G., Li, X. , Marcolli, M. and Smit, H. (2019) Reconstructing global fields from dynamics in the abelianized Galois group. Selecta Mathematica - New Series, 25(2), 24. (doi: 10.1007/s00029-019-0469-8)

Cornelissen, G., de Smit, B., Li, X. , Marcolli, M. and Smit, H. (2019) Characterization of global fields by Dirichlet L-series. Research in Number Theory, 5(1), 7. (doi: 10.1007/s40993-018-0143-9)

2018

Chu, C.-H. and Li, X. (2018) Amenability, Reiter's condition and Liouville property. Journal of Functional Analysis, 274(12), pp. 3291-3324. (doi: 10.1016/j.jfa.2018.03.014)

Li, X. (2018) Continuous orbit equivalence rigidity. Ergodic Theory and Dynamical Systems, 38(4), pp. 1543-1563. (doi: 10.1017/etds.2016.98)

2017

Cuntz, J., Echterhoff, S., Li, X. and Yu, G. (Eds.) (2017) K-Theory for Group C*-Algebras and Semigroup C*-Algebras. Series: Oberwolfach seminars. Birkhäuser: Cham, Switzerland. ISBN 9783319599144

Li, X. (2017) Partial transformation groupoids attached to graphs and semigroups. International Mathematics Research Notices, 2017(17), pp. 5233-5259. (doi: 10.1093/imrn/rnw166)

Barlak, S. and Li, X. (2017) Cartan subalgebras and the UCT problem. Advances in Mathematics, 316, pp. 748-769. (doi: 10.1016/j.aim.2017.06.024)

2016

Li, X. (2016) Semigroup C*-Algebras. In: Abel Symposium 2015, Coastal Express (Hurtigruten), Norway, 07-11 Aug 2015, pp. 191-202. ISBN 9783319392844 (doi: 10.1007/978-3-319-39286-8_9)

Li, X. (2016) Semigroup C*-algebras of ax + b-semigroups. Transactions of the American Mathematical Society, 368(6), pp. 4417-4437. (doi: 10.1090/tran/6469)

Li, X. (2016) On K-theoretic invariants of semigroup C*-algebras attached to number fields, Part II. Advances in Mathematics, 291, pp. 1-11. (doi: 10.1016/j.aim.2015.12.024)

Li, X. and Norling, M. D. (2016) Independent resolutions for totally disconnected dynamical systems. II. C*-algebraic case. Journal of Operator Theory, 75(1), pp. 163-193. (doi: 10.7900/jot.2014dec22.2061)

Eilers, S., Li, X. and Ruiz, E. (2016) The isomorphism problem for semigroup C*-algebras of right-angled Artin monoids. Documenta Mathematica, 21, pp. 309-343.

2015

Li, X. (2015) A new approach to recent constructions of C*-algebras from modular index theory. Journal of Functional Analysis, 269(3), pp. 841-864. (doi: 10.1016/j.jfa.2014.12.015)

Li, X. and Norling, M. D. (2015) Independent resolutions for totally disconnected dynamical systems I: algebraic case. Journal of Algebra, 424, pp. 98-125. (doi: 10.1016/j.jalgebra.2014.10.043)

Cuntz, J., Echterhoff, S. and Li, X. (2015) On the K-theory of the C*-algebra generated by the left regular representation of an Ore semigroup. Journal of the European Mathematical Society, 17(3), pp. 645-687. (doi: 10.4171/JEMS/513)

2014

Li, X. (2014) On K-theoretic invariants of semigroup C*-algebras attached to number fields. Advances in Mathematics, 264, pp. 371-395. (doi: 10.1016/j.aim.2014.07.014)

2013

Li, X. (2013) Nuclearity of semigroup C*-algebras and the connection to amenability. Advances in Mathematics, 244, pp. 626-662. (doi: 10.1016/j.aim.2013.05.016)

Cuntz, J., Echterhoff, S. and Li, X. (2013) On the k-Theory of crossed products by automorphic semigroup actions. Quarterly Journal of Mathematics, 64(3), pp. 747-784. (doi: 10.1093/qmath/hat021)

Larsen, N. S. and Li, X. (2013) Dilations of semigroup crossed products as crossed products of dilations. Proceedings of the American Mathematical Society, 141(5), pp. 1597-1603. (doi: 10.1090/S0002-9939-2013-11475-9)

2012

Li, X. and Lück, W. (2012) K-theory for ring c*-algebras: the case of number fields with higher roots of unity. Journal of Topology and Analysis, 4(4), pp. 449-479. (doi: 10.1142/S1793525312500203)

Li, X. (2012) K-theory for ring C*-algebras attached to function fields with only one infinite place. Journal of K-theory: K-theory and its Applications to Algebra, Geometry and Topology, 10(1), pp. 203-231. (doi: 10.1017/is011011023jkt177)

Li, X. (2012) Semigroup C⁎-algebras and amenability of semigroups. Journal of Functional Analysis, 262(10), pp. 4302-4340. (doi: 10.1016/j.jfa.2012.02.020)

Larsen, N. S. and Li, X. (2012) The 2-adic ring C*-algebra of the integers and its representations. Journal of Functional Analysis, 262(4), pp. 1392-1426. (doi: 10.1016/j.jfa.2011.11.008)

2011

Cuntz, J. and Li, X. (2011) C*-algebras associated with integral domains and crossed products by actions on adele spaces. Journal of Noncommutative Geometry, 5(1), pp. 1-37. (doi: 10.4171/JNCG/68)

Cuntz, J. and Li, X. (2011) K-theory for ring C-algebras attached to polynomial rings over finite fields. Journal of Noncommutative Geometry, 5(3), pp. 331-349. (doi: 10.4171/JNCG/78)

2010

Li, X. (2010) Ring C*-algebras. Mathematische Annalen, 348(4), pp. 859-898. (doi: 10.1007/s00208-010-0502-x)

Cuntz, J. and Li, X. (2010) The regular C*-algebra of an integral domain. In: Blanchard, E., Ellwood, D., Khalkhali, M., Marcolli, M., Moscovici, H. and Popa, S. (eds.) Quanta of Maths: Conference in Honor of Alain Connes, Non Commutative Geometry, Institut Henri Poincaré, Institut des Hautes Études Scientifiques, Institut de Mathématiques de Jussieu, Paris, France, March 29-April 6, 2007. Series: Clay mathematics proceedings (11). American Mathematical Society ; Clay Mathematics Institute: Providence, R.I ; Cambridge, MA, pp. 149-170. ISBN 9780821852033

This list was generated on Fri Dec 20 22:49:35 2024 GMT.
Jump to: Articles | Book Sections | Edited Books | Conference Proceedings
Number of items: 45.

Articles

Li, X. (2024) Ample groupoids, topological full groups, algebraic K-theory spectra and infinite loop spaces. Forum of Mathematics, Pi, (Accepted for Publication)

Li, X. (2024) Left regular representations of Garside categories II. Finiteness properties of topological full groups. Groups, Geometry, and Dynamics, (Accepted for Publication)

Kakariadis, E. T.A., Katsoulis, E. G. and Li, X. (2024) Stable isomorphisms of operator algebras. International Mathematics Research Notices, 2024(5), pp. 4118-4094. (doi: 10.1093/imrn/rnad146)

Bruce, C. and Li, X. (2024) Algebraic actions I. C*-algebras and groupoids. Journal of Functional Analysis, 286(4), 110263. (doi: 10.1016/j.jfa.2023.110263)

Li, X. and Raad, A. I. (2023) Constructing C*-diagonals in AH-algebras. Transactions of the American Mathematical Society, (doi: 10.1090/tran/9023) (Early Online Publication)

Kakariadis, E. T.A., Katsoulis, E. G., Laca, M. and Li, X. (2023) Couniversality and controlled maps on product systems over right LCM semigroups. Analysis and PDE, 16(6), pp. 1433-1483. (doi: 10.2140/apde.2023.16.1433)

Li, X. (2023) Left regular representations of Garside categories I. C*-algebras and groupoids. Glasgow Mathematical Journal, 65(S1), S53-S86. (doi: 10.1017/S0017089522000106)

Bruce, C. and Li, X. (2023) On K-theoretic invariants of semigroup C*-algebras from actions of congruence monoids. American Journal of Mathematics, 145(1), pp. 251-285. (doi: 10.1353/ajm.2023.0005)

Chen, C. and Li, X. (2023) Semigroup C*-algebras arising from graphs of monoids. International Mathematics Research Notices, (doi: 10.1093/imrn/rnac332) (Early Online Publication)

Li, X. (2022) Constructing Menger manifold C*-diagonals in classifiable C*-algebras. International Mathematics Research Notices, 2022(23), pp. 18992-19053. (doi: 10.1093/imrn/rnab199)

Kakariadis, E. T.A., Katsoulis, E. G., Laca, M. and Li, X. (2022) Boundary quotient C*-algebras of semigroups. Journal of the London Mathematical Society, 105(4), pp. 2136-2166. (doi: 10.1112/jlms.12557)

Dor-On, A., Kakariadis, E.T.A., Katsoulis, E., Laca, M. and Li, X. (2022) C*-envelopes for operator algebras with a coaction and co-universal C*-algebras for product systems. Advances in Mathematics, 400, 108286. (doi: 10.1016/j.aim.2022.108286)

Li, X. (2022) K-theory for semigroup C*-algebras and partial crossed products. Communications in Mathematical Physics, 390(1), pp. 1-32. (doi: 10.1007/s00220-021-04194-9)

Li, X. , Omland, T. and Spielberg, J. (2021) C*-algebras of right LCM one-relator monoids and Artin-Tits monoids of finite type. Communications in Mathematical Physics, 381(3), pp. 1263-1308. (doi: 10.1007/s00220-020-03758-5)

Barlak, S. and Li, X. (2020) Cartan subalgebras and the UCT problem, II. Mathematische Annalen, 378(1-2), pp. 255-287. (doi: 10.1007/s00208-020-02022-4)

Li, X. (2020) Every classifiable simple C*-algebra has a Cartan subalgebra. Inventiones Mathematicae, 219(2), pp. 653-699. (doi: 10.1007/s00222-019-00914-0)

Li, X. (2019) K-theory for generalized Lamplighter groups. Proceedings of the American Mathematical Society, 147(10), pp. 4371-4378. (doi: 10.1090/proc/14619)

Li, X. and Renault, J. (2019) Cartan subalgebras in C*-algebras. Existence and uniqueness. Transactions of the American Mathematical Society, 372(3), pp. 1985-2010. (doi: 10.1090/tran/7654)

Cornelissen, G., Li, X. , Marcolli, M. and Smit, H. (2019) Reconstructing global fields from dynamics in the abelianized Galois group. Selecta Mathematica - New Series, 25(2), 24. (doi: 10.1007/s00029-019-0469-8)

Cornelissen, G., de Smit, B., Li, X. , Marcolli, M. and Smit, H. (2019) Characterization of global fields by Dirichlet L-series. Research in Number Theory, 5(1), 7. (doi: 10.1007/s40993-018-0143-9)

Chu, C.-H. and Li, X. (2018) Amenability, Reiter's condition and Liouville property. Journal of Functional Analysis, 274(12), pp. 3291-3324. (doi: 10.1016/j.jfa.2018.03.014)

Li, X. (2018) Continuous orbit equivalence rigidity. Ergodic Theory and Dynamical Systems, 38(4), pp. 1543-1563. (doi: 10.1017/etds.2016.98)

Li, X. (2017) Partial transformation groupoids attached to graphs and semigroups. International Mathematics Research Notices, 2017(17), pp. 5233-5259. (doi: 10.1093/imrn/rnw166)

Barlak, S. and Li, X. (2017) Cartan subalgebras and the UCT problem. Advances in Mathematics, 316, pp. 748-769. (doi: 10.1016/j.aim.2017.06.024)

Li, X. (2016) Semigroup C*-algebras of ax + b-semigroups. Transactions of the American Mathematical Society, 368(6), pp. 4417-4437. (doi: 10.1090/tran/6469)

Li, X. (2016) On K-theoretic invariants of semigroup C*-algebras attached to number fields, Part II. Advances in Mathematics, 291, pp. 1-11. (doi: 10.1016/j.aim.2015.12.024)

Li, X. and Norling, M. D. (2016) Independent resolutions for totally disconnected dynamical systems. II. C*-algebraic case. Journal of Operator Theory, 75(1), pp. 163-193. (doi: 10.7900/jot.2014dec22.2061)

Eilers, S., Li, X. and Ruiz, E. (2016) The isomorphism problem for semigroup C*-algebras of right-angled Artin monoids. Documenta Mathematica, 21, pp. 309-343.

Li, X. (2015) A new approach to recent constructions of C*-algebras from modular index theory. Journal of Functional Analysis, 269(3), pp. 841-864. (doi: 10.1016/j.jfa.2014.12.015)

Li, X. and Norling, M. D. (2015) Independent resolutions for totally disconnected dynamical systems I: algebraic case. Journal of Algebra, 424, pp. 98-125. (doi: 10.1016/j.jalgebra.2014.10.043)

Cuntz, J., Echterhoff, S. and Li, X. (2015) On the K-theory of the C*-algebra generated by the left regular representation of an Ore semigroup. Journal of the European Mathematical Society, 17(3), pp. 645-687. (doi: 10.4171/JEMS/513)

Li, X. (2014) On K-theoretic invariants of semigroup C*-algebras attached to number fields. Advances in Mathematics, 264, pp. 371-395. (doi: 10.1016/j.aim.2014.07.014)

Li, X. (2013) Nuclearity of semigroup C*-algebras and the connection to amenability. Advances in Mathematics, 244, pp. 626-662. (doi: 10.1016/j.aim.2013.05.016)

Cuntz, J., Echterhoff, S. and Li, X. (2013) On the k-Theory of crossed products by automorphic semigroup actions. Quarterly Journal of Mathematics, 64(3), pp. 747-784. (doi: 10.1093/qmath/hat021)

Larsen, N. S. and Li, X. (2013) Dilations of semigroup crossed products as crossed products of dilations. Proceedings of the American Mathematical Society, 141(5), pp. 1597-1603. (doi: 10.1090/S0002-9939-2013-11475-9)

Li, X. and Lück, W. (2012) K-theory for ring c*-algebras: the case of number fields with higher roots of unity. Journal of Topology and Analysis, 4(4), pp. 449-479. (doi: 10.1142/S1793525312500203)

Li, X. (2012) K-theory for ring C*-algebras attached to function fields with only one infinite place. Journal of K-theory: K-theory and its Applications to Algebra, Geometry and Topology, 10(1), pp. 203-231. (doi: 10.1017/is011011023jkt177)

Li, X. (2012) Semigroup C⁎-algebras and amenability of semigroups. Journal of Functional Analysis, 262(10), pp. 4302-4340. (doi: 10.1016/j.jfa.2012.02.020)

Larsen, N. S. and Li, X. (2012) The 2-adic ring C*-algebra of the integers and its representations. Journal of Functional Analysis, 262(4), pp. 1392-1426. (doi: 10.1016/j.jfa.2011.11.008)

Cuntz, J. and Li, X. (2011) C*-algebras associated with integral domains and crossed products by actions on adele spaces. Journal of Noncommutative Geometry, 5(1), pp. 1-37. (doi: 10.4171/JNCG/68)

Cuntz, J. and Li, X. (2011) K-theory for ring C-algebras attached to polynomial rings over finite fields. Journal of Noncommutative Geometry, 5(3), pp. 331-349. (doi: 10.4171/JNCG/78)

Li, X. (2010) Ring C*-algebras. Mathematische Annalen, 348(4), pp. 859-898. (doi: 10.1007/s00208-010-0502-x)

Book Sections

Cuntz, J. and Li, X. (2010) The regular C*-algebra of an integral domain. In: Blanchard, E., Ellwood, D., Khalkhali, M., Marcolli, M., Moscovici, H. and Popa, S. (eds.) Quanta of Maths: Conference in Honor of Alain Connes, Non Commutative Geometry, Institut Henri Poincaré, Institut des Hautes Études Scientifiques, Institut de Mathématiques de Jussieu, Paris, France, March 29-April 6, 2007. Series: Clay mathematics proceedings (11). American Mathematical Society ; Clay Mathematics Institute: Providence, R.I ; Cambridge, MA, pp. 149-170. ISBN 9780821852033

Edited Books

Cuntz, J., Echterhoff, S., Li, X. and Yu, G. (Eds.) (2017) K-Theory for Group C*-Algebras and Semigroup C*-Algebras. Series: Oberwolfach seminars. Birkhäuser: Cham, Switzerland. ISBN 9783319599144

Conference Proceedings

Li, X. (2016) Semigroup C*-Algebras. In: Abel Symposium 2015, Coastal Express (Hurtigruten), Norway, 07-11 Aug 2015, pp. 191-202. ISBN 9783319392844 (doi: 10.1007/978-3-319-39286-8_9)

This list was generated on Fri Dec 20 22:49:35 2024 GMT.

Supervision

Currently, the following PhD students work with me (as their first supervisor):
Jeremy Hume and Julian Gonzales.
Moreover, the following postdocs are working with me at the moment:
Samantha Pilgrim and Sihan Wei.

Please feel free to contact me in case you are interested in working with me as a PhD student or postdoc.