Fakultäten der RUB » Fakultät für Mathematik » Lehrstühle » Algebraische Kombinatorik


Annika Schulte
Tel.: +49 (0)234/32-22291
Raum IB 3/185

Das neue Semester hat begonnen, hier geht es zu den Veranstaltungen.


AG AlgKomb Lunch Seminar

Mittwoch, 6. November 2019, 12:15 - 13:15, Gebäude IB Raum 2/141

Robert Löwe, TU Berlin
Computing the discriminant of a quaternary cubic form

Abstract: We determine the 166104 extremal monomials of the discriminant of a quaternary cubic form. These are in bijection with D-equivalence classes of regular triangulations of the 3-dilated tetrahedron. We describe how to compute these triangulations and their D-equivalence classes in order to arrive at our main result.
The computation poses several challenges, such as dealing with the sheer number of triangulations effectively, as well as devising a suitably fast algorithm for computation of a D-equivalence class. This is joint work with Lars Kastner.

Kolloquium Algebra-Geometrie-Kombinatorik

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.