Archive Winter Term 2022/23

M.Sc. Seminar / master theses
Luca Remke talks about: "Co-Higgs bundles on projective spaces"
room 7.530

follow-up appointment "Seminar 42"
auditorium 57.04

Speaker: Prof. Maxim Smirnov, university Augsburg
second presentation on 18/01/2023, 10.00 p.m., room 8.122, within the framework IDSC-seminar

Title: Residual categories for Grassmannians

Abstract: Exceptional collections in derived categories of coherent sheaves have a long history going back to the pioneering work of A. Beilinson. After recalling the general setup, I will concentrate on some recent developments inspired by the homological mirror symmetry. Namely, I will define residual categories of Lefschetz decompositions and discuss a conjectural relation between the structure of quantum cohomology and residual categories. I will illustrate this relationship in the case of some isotropic Grassmannians. The talk is based on the joint work with Alexander Kuznetsov.

Speaker: Prof. Maxim Smirnov, university Augsburg
first presentation on 17/01/2023, 6.15 p.m. in IGT-Seminar room 7.530 within the framework of the IGT Seminar
(https://www.igt.uni-stuttgart.de/oberseminar/)

Title: Quantum cohomology of coadjoint varietie

Abstract: Quantum cohomology is defined by deforming the usual cup-product using the genus zero Gromov-Witten invariants. We’ll begin with a background on quantum cohomology and its role in mirror symmetry. Then we will discuss properties of quantum cohomology, both small and big, of coadjoint varieties of simple algebraic groups. If time permits, we’ll make predictions on the structure of the derived category of coherent sheaves of coadjoint varieties. The talk is based on the joint work with Nicolas Perrin.

TüS\S takes place in Tübingen:
our next Tübingen-Stuttgart-Seminar (TüSS) will take place in Tübingen:
Eberhard Karls University Tübingen, Department of Mathematics, Auf der Morgenstelle 10, room: C4H33

4.pm-5.pm
Speaker: Jonas Hetz, university Stuttgart

Titel: Characters and Character Sheaves of Finite Groups of Lie Type

Abstract: An important task in the representation theory of finite groups is the determination of their character tables. As the classification of finite simple groups shows, the main difficulties in this context concern the finite groups of Lie type, which arise as an infinite series of finite groups associated to a certain algebraic group over a field of positive characteristic. In order to generically tackle the problem of determining the character tables of finite groups of Lie type, Lusztig developed the theory of character sheaves in the 1980s. In this framework, due to the work of Lusztig and Shoji, the problem is in principle reduced to determining certain roots of unity. We report on some recent progress in this area.

3.30 p.m.-4.00 p.m.
Speaker: Matilde Manzaroli, university Tübingen

Title: Betti numbers of real semi-stable degenerations via real logarithmic geometry

Abstract: In a work in progess with Eminiano Ambrosi, we study the real topology of totally real semistable degenerations, with certain technical conditions on the special fiber X0, and we give a bound for the individual real Betti numbers of a smooth fiber near 0 in terms of the complex geometry of X0. The main ingredient is the use of real logarithmic geometry, which allows to work with degenerations which are not necessarily toric and hence to go beyond the case of tropically smooth degenerations. This, in particular, generalises previous work of Renaudineau-Shaw, obtained via tropical techniques, to a more general setting.

Seminar 42
room: 7.122

M.Sc. seminar / master theses:
Kathrin Hertäg talks about: "Critical Brain Hypothesis from a Mathematical Point of View"
room 7.530