Équipe RGR
The RGR team is part of the Arithmetic, Geometry, Logic and Representations (AGLR) scientific group.
Topics include Lie groups, Poisson-Lie groups, reductive groups, automorphic forms, infinite-dimensional groups and representations. Around the above themes, participants meet regularly in working groups that also call on outside speakers(RGR seminar, organized by Volker Heiermann).
The other themes come from the former “Operator Algebras and Geometry” (AOG) team:
Topics include operator algebras and representation theory, and their links with topology, geometry, probability, ergodic theory, number theory and theoretical physics. Note that operator algebras = von Neumann algebras + K-theory + cyclic cohomology, the non-commutative versions of measure theory, topology and differential geometry.
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Barsotti-Tate groups and Shimura variety
– Solution to a Traverso conjecture.Automorphic forms
– Study of unitary base change and its applications to automorphic forms.Representations of p-adic groups
– Study smooth representations with coefficients in C or ℓ-modular representations of the group GLn(D), where D is a division algebra.Harmonic analysis
– The beginnings of harmonic analysis on p-adic symmetric reductive spaces.Quantum field theory
– The study of moment applications for Poisson-Lie groups and links with integrable models.Operator Algebras and Geometry
Novikov conjecture and K-theory of arithmetic groups
– K-theoretic index theorem for transversely elliptic operators.
– Proof of Novikov’s conjecture for groups that admit a uniform coarse plunge in a suitable Banach space.Neveu-Schwarz algebra and discrete series
– Connes fusion and subfactors for Neveu-Schwarz algebra.Cyclic cohomology and K-theory
– Cyclic cohomology: Hodge filtration for classes of split and invertible extensions.
– K-theory: Generalization of the Atiyah-Singer index theory.
– Explicit character calculation for a suitable Fredholm modulus.
– Existence theorem for certain Fredholm modules on higher rank groups and networks.
– Isospectral subalgebras of C*-algebras.Von Neumann algebras and quantum groups
– von Neumann algebras, quantum subgroups and conformal field theory at the edge. C*-algebras and affine quantum groups.
– Actions of compact Lie groups on von Neumann algebras.
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Novikov conjecture and K-theory of arithmetic groups
– K-theoretic index theorem for transversely elliptic operators.
– Proof of Novikov’s conjecture for groups that admit a uniform coarse plunge in a suitable Banach space.Neveu-Schwarz algebra and discrete series
– Connes fusion and subfactors for Neveu-Schwarz algebra.Cyclic cohomology and K-theory
– Cyclic cohomology: Hodge filtration for classes of split and invertible extensions.
– K-theory: Generalization of the Atiyah-Singer index theory.
– Explicit character calculation for a suitable Fredholm modulus.
– Existence theorem for certain Fredholm modules on higher rank groups and networks.
– Isospectral subalgebras of C*-algebras.Von Neumann algebras and quantum groups
– von Neumann algebras, quantum subgroups and conformal field theory at the edge. C*-algebras and affine quantum groups.
– Actions of compact Lie groups on von Neumann algebras.
