Kolloquium
Algebra - Geometrie - Kombinatorik
an der Fakultät für Mathematik der Ruhr-Universität Bochum
Markus Reineke, Gerhard Röhrle, Christian Stump
Vorträge Sommersemester 2020 bis Sommersemester 2022
Die Vorträge wurden abgesagt.
Vorträge Wintersemester 2019/20
Mittwoch, 16. Oktober 2019, 16:00-17:00, Gebäude IA Raum 01/473
Bernd Sturmfels, Max-Planck-Institut Leipzig
The geometry of Gaussoids
Abstract: Gaussoids offer a new link between combinatorics, statistics and algebraic geometry. Introduced by Lnenicka and Matus in 2007, their axioms describe conditional independence for Gaussian random variables. We explain this theory and how it relates to matroids. The role of the Grassmannian for matroids is now played by a projection of the Lagrangian Grassmannian. We discuss the classification and realizability of gaussoids, and we explore oriented gaussoids, valuated gaussoids, and the analogue to positroids. This is joint work with Tobias Boege, Alessio D'Ali and Thomas Kahle.
Mittwoch, 13. November 2019, 16:00-17:00, Gebäude IA Raum 01/473
Peter Littelmann, Universität zu Köln
Towards a Riemann-Roch type character formula
Abstract: Standard monomial theory has its origin in the work of Hodge, where he constructed a nice basis for the coordinate of the Grassmann variety, embedded via the canonical Plücker embedding in a projective space. Seshadri, Musili, Lakshmibai (and many others) tried to generalize this approach to the setting of Schubert varieties in flag varieties associated to arbitrary semisimple algebraic groups. They came up with a remarkable conjectural combinatorial character formula for the homogeneous coordinate ring of an embedded Schubert variety. By combining combinatorial tools with methods from Newton-Okounkov theory and ideas developed by Rees and Samuel, we present a new approach towards a general construction of standard monomials. The classical Riemann-Roch theorem calculates the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles on a compact Riemann surface. Our aim is to give a similar interpretation of the character formula conjectured by Lakshmibai: it counts functions with prescribed vanishing multiplicities along a sequence of Schubert varieties, subsequently contained in each other. This is ongoing joint work with Rocco Chirivì and Xin Fang.
Mittwoch, 29. Januar 2020, 16:00-17:00, Gebäude IA Raum 01/473
Eric Opdam, Universiteit van Amsterdam
Square integrable hypergeometric functions for root systems
Abstract: Classifying the square integrable solutions of the system of hypergeometric equations for root systems is relevant to understanding the discrete series for real symmetric spaces. We will discuss this connection and explain some aspects of this classification.