Research Interests
- Noncommutative geometry
& index theory & operator algebras - Representation theory
& quantum groups & harmonic analysis - Pseudodifferential operators
Books
- C. Voigt & R. Yuncken, Complex semisimple quantum groups and representation theory.
Lecture Notes in Mathematics, 2264, Springer-Verlag. [arXiv]
Articles
- J. Bradd, N. Higson & R. Yuncken, Lie groupoids, the Satake compactification and the tempered dual, II: The Satake groupoid, [arXiv]
- J. Bradd, N. Higson & R. Yuncken, Lie groupoids, the Satake compactification and the tempered dual, II: The Harish-Chandra principle, [arXiv]
- J. Bradd, N. Higson & R. Yuncken, Operator K-theory and tempiric representations, [arXiv]
- R. Yuncken, Algebraic isomorphisms of quantized homogeneous spaces, [arXiv]
- N. Couchet & R. Yuncken, A groupoid approach to the Wodzicki residue, »
J. Funct. Anal. 296 (2024) [arXiv] - M. Matassa & R. Yuncken, Crystal limits of compact semisimple quantum groups as higher-rank graph algebras,
J. Reine Agnew. Math. 802 (2023), 173-221. [arXiv] -
N. Couchet & R. Yuncken, On polyhomogeneous symbols and the Heisenberg pseudodifferential calculus, [arXiv]
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C. Voigt & R. Yuncken, The Plancherel formula for complex semisimple quantum groups,
Ann. Sci. Éc. Norm. Supér. (4) 56, No. 1, 299-322 (2023). [arXiv] -
I. Androulidakis, O. Mohsen & R.Yuncken, The convolution algebra of Scwartz kernels on a singular foliation,
J. Operator Theory 85, No. 2, 475-503 (2021). [arXiv] -
E. van Erp & R. Yuncken, A groupoid approach to pseudodifferential operators
,
J. Reine Agnew. Math 756 (2019), 151-182. [arXiv] - M. Matassa & R. Yuncken, Regularity of twisted spectral triples and pseudodifferential calculus,
J. Noncommut. Geom., 13 (2019), No. 3, 985-1009. [arXiv] - E. van Erp & R. Yuncken, On the tangent groupoid of a filtered manifold,
Bull. London Math. Soc. 49 (2017) 1000-1012. [arXiv] - H. Emerson & R. Yuncken, Equivariant correspondences and the Borel-Bott-Weil theorem,
Münster J. of Math. 10 (2017), 59-74. [arXiv] - C. Voigt & R. Yuncken, Equivariant Fredholm modules for the full quantum flag manifold of SUq(3),
Documenta Math. 20 (2015), 433-490. [arXiv] - J. Bichon & R. Yuncken, Quantum subgroups of the compact quantum group SU-1(3),
Bull. London Math. Soc. 46 (2014), no. 2, 315-328. [arXiv] - R. Yuncken, Foliation C*-algebras on multiply fibred manifolds,
J. Funct. Anal. 265 (2013), no. 9, 1829-1839. [arXiv] - R. Yuncken, On coarse spectral geometry in even dimension,
C. R. Math. Acad. Sci. Soc. R. Can. 33 (2011), no. 2, 57-64. [arXiv] - R. Yuncken, The Bernstein-Gelfand-Gelfand complex and Kasparov Theory for SL(3.C),
Adv. Math. 226 (2011) 1474-1512. [arXiv] - R. Yuncken, Products of longitudinal pseudodifferential operators on flag varieties,
J. Funct. Anal. 258 (2010), no. 4, 1140-1166. [arXiv] - R. Yuncken, Regular tessellations of the hyperbolic plane by fundamental domains of a Fuchsian group,
Mosc. Math. J. 3 (2003), no. 1, 249-252. [arXiv] - R. Yuncken, Analytic structures for the index theory of SL(3,C). (Thesis) [pdf]
Other documents
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R. Fioresi, R. Yuncken, “Quantized semisimple Lie groups,”
Notes from a mini-course given at the training school on Quantum Groups and Noncommutative Geometry in Prague, 11–15 Sept 2023,
Arch. Math. (Brno) 60, No. 5, 311-349 (2024). [arXiv] - Rough lecture notes on Quantized Semisimple Lie Groups, from the Winter School on Functional analysis in Seoul, December 2019: [pdf]
- A short article on the experiences of a non-French mathematician for the collection Des Mathématiques en Auvergne, histoire, progrès et interactions (published by the Alliance Universitaire d’Auvergne, 2014).