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Documents  Paradan, Paul-Emile | enregistrements trouvés : 6

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Multiple Bernoulli series and volumes of moduli spaces of flat bundles over surfaces Boysal, Arzu | CIRM H

Post-edited

Research talks;Algebraic and Complex Geometry;Lie Theory and Generalizations;Number Theory

Using Szenes formula for multiple Bernoulli series, we explain how to compute Witten series associated to classical Lie algebras. Particular instances of these series compute volumes of moduli spaces of flat bundles over surfaces, and also certain multiple zeta values.
This is joint work with V. Baldoni and M. Vergne.

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Geometric quantization of toric and semitoric systems Miranda, Eva | CIRM H

Multi angle

Research talks;Geometry;Mathematical Physics;Topology

One of the many contributions of Kostant is a rare gem which probably has not been sufficiently explored: a sheaf-theoretical model for geometric quantization associated to real polarizations. Kostant’s model works very well for polarizations given by fibrations or fibration-like objects (like integrable systems away from singularities). For toric manifolds where the real polarization is determined by the fibers of the moment map, Kostant’s model yields a representation space whose dimension is the number of integer points inside the corresponding Delzant polytope. We will discuss extensions of this model to consider almost toric manifolds and integrable systems with non-degenerate singularities where “unexpected” infinities can show up even if the manifold is compact. One of the many contributions of Kostant is a rare gem which probably has not been sufficiently explored: a sheaf-theoretical model for geometric quantization associated to real polarizations. Kostant’s model works very well for polarizations given by fibrations or fibration-like objects (like integrable systems away from singularities). For toric manifolds where the real polarization is determined by the fibers of the moment map, Kostant’s ...

53D50

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Quantum footprints of symplectic rigidity Polterovich, Leonid | CIRM H

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Research talks;Geometry;Mathematical Physics

We discuss interactions between quantum mechanics and symplectic topology including a link between symplectic displacement energy, a fundamental notion of symplectic dynamics, and the quantum speed limit, a universal constraint on the speed of quantum-mechanical processes.
Joint work with Laurent Charles.

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Poisson-Lie duality and Langlands duality via Bohr-Sommerfeld Alekseev, Anton | CIRM H

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Research talks;Geometry;Lie Theory and Generalizations;Topology

Let $G$ be a connected semisimple Lie group with Lie algebra $\mathfrak{g}$. There are two natural duality constructions that assign to it the Langlands dual group $G^\lor$ (associated to the dual root system) and the Poisson-Lie dual group $G^∗$. Cartan subalgebras of $\mathfrak{g}^\lor$ and $\mathfrak{g}^∗$ are isomorphic to each other, but $G^\lor$ is semisimple while $G^∗$ is solvable.
In this talk, we explain the following non-trivial relation between these two dualities: the integral cone defined by the Berenstein-Kazhdan potential on the Borel subgroup $B^\lor \subset G^\lor$ is isomorphic to the integral Bohr-Sommerfeld cone defined by the Poisson structure on $K^∗ \subset G^∗$ (the Poisson-Lie dual of the compact form $K \subset G$). The first cone parametrizes canonical bases of irreducible $G$-modules. The corresponding points in the second cone belong to integral symplectic leaves of $K^∗$.
The talk is based on a joint work with A. Berenstein, B. Hoffman and Y. Li.
Let $G$ be a connected semisimple Lie group with Lie algebra $\mathfrak{g}$. There are two natural duality constructions that assign to it the Langlands dual group $G^\lor$ (associated to the dual root system) and the Poisson-Lie dual group $G^∗$. Cartan subalgebras of $\mathfrak{g}^\lor$ and $\mathfrak{g}^∗$ are isomorphic to each other, but $G^\lor$ is semisimple while $G^∗$ is solvable.
In this talk, we explain the following non-trivial ...

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Homogeneous vector bundles over abelian varieties Brion, Michel | CIRM H

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Research talks;Algebraic and Complex Geometry;Lie Theory and Generalizations

The objects of the talk are the translation-invariant vector bundles over an abelian variety. We will present a representation-theoretic description of these vector bundles, which displays a remarkable analogy with finite-dimensional representations of a compact connected Lie group: the weight lattice is replaced with the dual abelian variety, the Weyl group with the Galois group of the ground field...

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Witten non abelian localization for equivariant K-theory, and the $[Q, R] = 0$ theorem Paradan, Paul-Emile ; Vergne , Michele | American Mathematical Society 2019

Ouvrage

- v; 71 p.
ISBN 978-1-4704-3522-6

Memoirs of the American Mathematical Society , 1257

Localisation : Collection 1er étage

opérateur de Dirac # faisceau de Clifford # quantification géométrique # localisation non abélienne

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