Professor Christian Voigt
- Professor of Mathematics (Mathematics)
telephone:
0141 330 2221
email:
Christian.Voigt@glasgow.ac.uk
pronouns:
He/him/his
School of Mathematics, and Statistics, Mathematics building, Room 328
https://orcid.org/0000-0003-3225-5633Research interests
My research area is noncommutative geometry, a modern part of mathematics with connections to classical disciplines like number theory, topology and mathematical physics. I work in particular on problems in operator K-theory, cyclic cohomology and the theory of quantum groups.
For more information see my personal webpage.
Research groups
Publications
2025
Daws, M., Krajczok, J. and Voigt, C. (2025) Averaging multipliers on locally compact quantum groups. Journal of the London Mathematical Society, 111(3), e70104. (doi: 10.1112/jlms.70104)
2024
Lee, H. and Voigt, C. (2024) Beurling-Fourier algebras of q-deformations of compact semisimple Lie groups and complexification. International Mathematics Research Notices, (Accepted for Publication)
Daws, M., Krajczok, J. and Voigt, C. (2024) The approximation property for locally compact quantum groups. Advances in Mathematics, 438, 109452. (doi: 10.1016/j.aim.2023.109452)
2023
Skalski, A., Vergnioux, R. and Voigt, C. (2023) Hecke algebras and the Schlichting completion for discrete quantum groups. Journal of the London Mathematical Society, 107(3), pp. 843-885. (doi: 10.1112/jlms.12701)
Voigt, C. (2023) Infinite quantum permutations. Advances in Mathematics, 415, 108887. (doi: 10.1016/j.aim.2023.108887)
Voigt, C. and Yuncken, R. (2023) The Plancherel formula for complex semisimple quantum groups. Annales Scientifiques de l'École Normale Supérieure, 56(1), pp. 299-322. (doi: 10.24033/asens.2535)
2022
Voigt, C. (2022) On the assembly map for complex semisimple quantum groups. International Mathematics Research Notices, 2022(13), pp. 9603-9632. (doi: 10.1093/imrn/rnaa370)
Brannan, M., Eifler, K., Voigt, C. and Weber, M. (2022) Quantum Cuntz-Krieger algebras. Transactions of the American Mathematical Society, 9, pp. 782-826. (doi: 10.1090/btran/88)
2020
Antoun, J. and Voigt, C. (2020) On bicolimits of C*-categories. Theory and Applications of Categories, 35(46), pp. 1683-1725.
Voigt, C. and Yuncken, R. (2020) Complex Semisimple Quantum Groups and Representation Theory. Series: Lecture notes in mathematics, 2264. Springer: Cham. ISBN 9783030524623 (doi: 10.1007/978-3-030-52463-0)
2019
Monk, A. and Voigt, C. (2019) Complex quantum groups and a deformation of the Baum-Connes assembly map. Transactions of the American Mathematical Society, 371, pp. 8849-8877. (doi: 10.1090/tran/7774)
2017
Voigt, C. (2017) On the structure of quantum automorphism groups. Journal für die Reine und Angewandte Mathematik (Crelles Journal), 732, pp. 255-273. (doi: 10.1515/crelle-2014-0141)
Barlak, S., Szabo, G. and Voigt, C. (2017) The spatial Rokhlin property for actions of compact quantum groups. Journal of Functional Analysis, 272(6), pp. 2308-2360. (doi: 10.1016/j.jfa.2016.09.023)
2015
Bhowmick, J., Voigt, C. and Zacharias, J. (2015) Compact quantum metric spaces from quantum groups of rapid decay. Journal of Noncommutative Geometry, 9(4), pp. 1175-1200. (doi: 10.4171/JNCG/220)
Voigt, C. and Yuncken, R. (2015) Equivariant Fredholm modules for the full quantum flag manifold of SUq(3). Documenta Mathematica, 20, pp. 433-490.
2014
Voigt, C. (2014) Cyclic cohomology and Baaj-Skandalis duality. Journal of K-theory: K-theory and its Applications to Algebra, Geometry and Topology, 13(1), pp. 115-145. (doi: 10.1017/is013012001jkt248)
2013
Vergnioux, R. and Voigt, C. (2013) The K-theory of free quantum groups. Mathematische Annalen, 357(1), pp. 355-400. (doi: 10.1007/s00208-013-0902-9)
2012
Voigt, C. (2012) Quantum SU(2) and the Baum-Connes conjecture. Banach Centre Publications, 98, pp. 417-432. (doi: 10.4064/bc98-0-17)
2011
Voigt, C. (2011) The Baum-Connes conjecture for free orthogonal quantum groups. Advances in Mathematics, 227(5), pp. 1873-1913. (doi: 10.1016/j.aim.2011.04.008)
2010
Nest, R. and Voigt, C. (2010) Equivariant Poincaré duality for quantum group actions. Journal of Functional Analysis, 258(5), pp. 1466-1503. (doi: 10.1016/j.jfa.2009.10.015)
2009
Voigt, C. (2009) Chern character for totally disconnected groups. Mathematische Annalen, 343(3), pp. 507-540. (doi: 10.1007/s00208-008-0281-9)
2008
Voigt, C. (2008) Bornological quantum groups. Pacific Journal of Mathematics, 235(1), pp. 93-135. (doi: 10.2140/pjm.2008.235.93)
Voigt, C. (2008) A new description of equivariant cohomology for totally disconnected groups. Journal of K-theory: K-theory and its Applications to Algebra, Geometry and Topology, 1(3), pp. 431-472. (doi: 10.1017/is007011019jkt020)
Voigt, C. (2008) Equivariant cyclic homology for quantum groups. In: ICM Satellite Conference on K-theory and Noncommutative Geometry, Valladolid, pp. 151-179.
2007
Voigt, C. (2007) Equivariant local cyclic homology and the equivariant Chern-Connes character. Documenta Mathematica, 12, 313-359 (electronic).
Voigt, C. (2007) Equivariant periodic cyclic homology. Journal of the Institute of Mathematics of Jussieu, 6(4), pp. 689-763. (doi: 10.1017/S1474748007000102)
Articles
Daws, M., Krajczok, J. and Voigt, C. (2025) Averaging multipliers on locally compact quantum groups. Journal of the London Mathematical Society, 111(3), e70104. (doi: 10.1112/jlms.70104)
Lee, H. and Voigt, C. (2024) Beurling-Fourier algebras of q-deformations of compact semisimple Lie groups and complexification. International Mathematics Research Notices, (Accepted for Publication)
Daws, M., Krajczok, J. and Voigt, C. (2024) The approximation property for locally compact quantum groups. Advances in Mathematics, 438, 109452. (doi: 10.1016/j.aim.2023.109452)
Skalski, A., Vergnioux, R. and Voigt, C. (2023) Hecke algebras and the Schlichting completion for discrete quantum groups. Journal of the London Mathematical Society, 107(3), pp. 843-885. (doi: 10.1112/jlms.12701)
Voigt, C. (2023) Infinite quantum permutations. Advances in Mathematics, 415, 108887. (doi: 10.1016/j.aim.2023.108887)
Voigt, C. and Yuncken, R. (2023) The Plancherel formula for complex semisimple quantum groups. Annales Scientifiques de l'École Normale Supérieure, 56(1), pp. 299-322. (doi: 10.24033/asens.2535)
Voigt, C. (2022) On the assembly map for complex semisimple quantum groups. International Mathematics Research Notices, 2022(13), pp. 9603-9632. (doi: 10.1093/imrn/rnaa370)
Brannan, M., Eifler, K., Voigt, C. and Weber, M. (2022) Quantum Cuntz-Krieger algebras. Transactions of the American Mathematical Society, 9, pp. 782-826. (doi: 10.1090/btran/88)
Antoun, J. and Voigt, C. (2020) On bicolimits of C*-categories. Theory and Applications of Categories, 35(46), pp. 1683-1725.
Monk, A. and Voigt, C. (2019) Complex quantum groups and a deformation of the Baum-Connes assembly map. Transactions of the American Mathematical Society, 371, pp. 8849-8877. (doi: 10.1090/tran/7774)
Voigt, C. (2017) On the structure of quantum automorphism groups. Journal für die Reine und Angewandte Mathematik (Crelles Journal), 732, pp. 255-273. (doi: 10.1515/crelle-2014-0141)
Barlak, S., Szabo, G. and Voigt, C. (2017) The spatial Rokhlin property for actions of compact quantum groups. Journal of Functional Analysis, 272(6), pp. 2308-2360. (doi: 10.1016/j.jfa.2016.09.023)
Bhowmick, J., Voigt, C. and Zacharias, J. (2015) Compact quantum metric spaces from quantum groups of rapid decay. Journal of Noncommutative Geometry, 9(4), pp. 1175-1200. (doi: 10.4171/JNCG/220)
Voigt, C. and Yuncken, R. (2015) Equivariant Fredholm modules for the full quantum flag manifold of SUq(3). Documenta Mathematica, 20, pp. 433-490.
Voigt, C. (2014) Cyclic cohomology and Baaj-Skandalis duality. Journal of K-theory: K-theory and its Applications to Algebra, Geometry and Topology, 13(1), pp. 115-145. (doi: 10.1017/is013012001jkt248)
Vergnioux, R. and Voigt, C. (2013) The K-theory of free quantum groups. Mathematische Annalen, 357(1), pp. 355-400. (doi: 10.1007/s00208-013-0902-9)
Voigt, C. (2012) Quantum SU(2) and the Baum-Connes conjecture. Banach Centre Publications, 98, pp. 417-432. (doi: 10.4064/bc98-0-17)
Voigt, C. (2011) The Baum-Connes conjecture for free orthogonal quantum groups. Advances in Mathematics, 227(5), pp. 1873-1913. (doi: 10.1016/j.aim.2011.04.008)
Nest, R. and Voigt, C. (2010) Equivariant Poincaré duality for quantum group actions. Journal of Functional Analysis, 258(5), pp. 1466-1503. (doi: 10.1016/j.jfa.2009.10.015)
Voigt, C. (2009) Chern character for totally disconnected groups. Mathematische Annalen, 343(3), pp. 507-540. (doi: 10.1007/s00208-008-0281-9)
Voigt, C. (2008) Bornological quantum groups. Pacific Journal of Mathematics, 235(1), pp. 93-135. (doi: 10.2140/pjm.2008.235.93)
Voigt, C. (2008) A new description of equivariant cohomology for totally disconnected groups. Journal of K-theory: K-theory and its Applications to Algebra, Geometry and Topology, 1(3), pp. 431-472. (doi: 10.1017/is007011019jkt020)
Voigt, C. (2007) Equivariant local cyclic homology and the equivariant Chern-Connes character. Documenta Mathematica, 12, 313-359 (electronic).
Voigt, C. (2007) Equivariant periodic cyclic homology. Journal of the Institute of Mathematics of Jussieu, 6(4), pp. 689-763. (doi: 10.1017/S1474748007000102)
Books
Voigt, C. and Yuncken, R. (2020) Complex Semisimple Quantum Groups and Representation Theory. Series: Lecture notes in mathematics, 2264. Springer: Cham. ISBN 9783030524623 (doi: 10.1007/978-3-030-52463-0)
Conference Proceedings
Voigt, C. (2008) Equivariant cyclic homology for quantum groups. In: ICM Satellite Conference on K-theory and Noncommutative Geometry, Valladolid, pp. 151-179.
