Oberseminar Geometrie, Topologie und Analysis

Oberseminar Geometrie, Topologie und Analysis

H. Geiges, I. Mărcuț, G. Marinescu, S. Sabatini, D. V. Vu

Wintersemester 2026/27

Freitag, 10:30-11:30, Seminarraum 2 (Raum 204)

6.11.26 Erfan Rezaei Gharehbolagh (Göttingen)
Deformation quantization of prequantizable symplectic fibrations

Abstract: In a recent preprint we have studied prequantizations of symplectic fibration to contact fibrations and compared it to other notions of prequantization of the underlying Poisson manifold and the associated fibered pair groupoid. Using the Heisenberg calculus for contact fibrations, we were able to construct a star product for the Poisson manifold underlying the symplectic fibration with analytical tools, generalizing a theorem of Guillemin. Joint work with Clément Cren.

The preprint can be found here for those interested.

20.11.26 Teije Kuiper (Aarhus)
Zonal spherical functions on partial flag manifolds and its application to random matrix theory

Abstract: The modern theory of zonal spherical functions was developed by Gelfand, Harish-Chandra, Heckman, and others in the second half of the 20th century for symmetric spaces. In this talk we will discuss an extension of parts of this theory to a class of homogeneous spaces, the partial flag manifolds. For partial flag manifolds we are able to obtain expressions for the elementary zonal spherical functions in terms of polynomials in the coefficients of multiple Hermitian matrices which are invariant under simultaneous conjugation by unitary matrices and calculate the corresponding eigenvalues. The original motivation of this work was to study properties of the submatrices of a unitary Brownian motion.

This talk starts with a brief overview of the results about the submatrices of a unitary Brownian motion. Subsequently, a general overview of orthogonal polynomials in the coefficients of a Hermitian matrix invariant under conjugation by unitary matrices, and its multivariate extension will be provided. In particular, the Schur polynomials and its multivariate extensions are given as examples. These polynomials can be used to obtain expressions for the elementary zonal spherical functions on partial flag manifolds, the Hermitian Jacobi polynomials on the simplex, and their eigenvalues. If time permits, a matrix variate version of Koornwinder's method will be discussed including its relation to the zonal spherical functions on the partial flag manifolds.

H. Geiges, 30.3.26


6.11.26	Erfan Rezaei Gharehbolagh (Göttingen) Deformation quantization of prequantizable symplectic fibrations Abstract: In a recent preprint we have studied prequantizations of symplectic fibration to contact fibrations and compared it to other notions of prequantization of the underlying Poisson manifold and the associated fibered pair groupoid. Using the Heisenberg calculus for contact fibrations, we were able to construct a star product for the Poisson manifold underlying the symplectic fibration with analytical tools, generalizing a theorem of Guillemin. Joint work with Clément Cren. The preprint can be found here for those interested.
20.11.26	Teije Kuiper (Aarhus) Zonal spherical functions on partial flag manifolds and its application to random matrix theory Abstract: The modern theory of zonal spherical functions was developed by Gelfand, Harish-Chandra, Heckman, and others in the second half of the 20th century for symmetric spaces. In this talk we will discuss an extension of parts of this theory to a class of homogeneous spaces, the partial flag manifolds. For partial flag manifolds we are able to obtain expressions for the elementary zonal spherical functions in terms of polynomials in the coefficients of multiple Hermitian matrices which are invariant under simultaneous conjugation by unitary matrices and calculate the corresponding eigenvalues. The original motivation of this work was to study properties of the submatrices of a unitary Brownian motion. This talk starts with a brief overview of the results about the submatrices of a unitary Brownian motion. Subsequently, a general overview of orthogonal polynomials in the coefficients of a Hermitian matrix invariant under conjugation by unitary matrices, and its multivariate extension will be provided. In particular, the Schur polynomials and its multivariate extensions are given as examples. These polynomials can be used to obtain expressions for the elementary zonal spherical functions on partial flag manifolds, the Hermitian Jacobi polynomials on the simplex, and their eigenvalues. If time permits, a matrix variate version of Koornwinder's method will be discussed including its relation to the zonal spherical functions on the partial flag manifolds.