Oberseminare
Below you can find all talks, presentations, and lectures of our seminars (Oberseminare).
winter term 2024/2025
Giulia Iezzi (RWTH Aachen)
Seminar: Lie-Theorie
Vortrag am Montag, 18.11.2024, 16:15 Uhr, in IA 1/109
Titel: "Linear degenerations of Schubert varieties via quiver Grassmannians"
Abstract:
Quiver Grassmannians are projective varieties parametrising subrepresentations of quiver representations. Their geometry is an interesting object of study, due to the fact that many geometric properties can be studied via the representation theory of quivers. For instance, this method was used to study linear degenerations of flag varieties, obtaining characterizations of flatness, irreducibility and normality via rank tuples. We provide a construction for realising smooth Schubert varieties as quiver Grassmannians and desingularizing non-smooth Schubert varieties. We then exploit this construction to define linear degenerations of Schubert varieties, giving a combinatorial description of the correspondance between their isomorphism classes and the B-orbits of certain quiver representations.
Dmitriy Rumynin (Warwick, zZt MPIM Bonn)
Seminar: Lie-Theorie
Vortrag am Montag, 04.11.2024, 16:15 Uhr, in IA 1/109
Titel: "Disconnected Reductive Groups"
Abstract:
A disconnected reductive group is a linear algebraic group whose connected component of the identity is a reductive group. If one is only interested in connected reductive groups, disconnected ones enter the picture as subgroups.
In this talk I will explain how to classify disconnected reductive groups up to an isomorphism. Time permitting, I will also briefly discuss the representation ring of such a group. The talk is based on joint work with Dylan Johnston and Diego Martin Duro.
Matilde Maccan (RUB)
Seminar: Lie-Theorie
Vortrag am Montag, 28.10.2024, 16:15 Uhr, in IA 1/109
Titel: "Parabolic subgroup schemes in small characteristics"
Abstract:
Any rational projective homogeneous variety can be written as a quotient of a semi-simple algebraic group by a so-called parabolic subgroup. In this talk we complete the classification of parabolic subgroup schemes (which can be non-reduced) and formulate it in a uniform way, independent of type and characteristic. The cases we focus on are of a base field of characteristic two or three. We will then move on to a few geometric consequences.
summer term 2024
Alexander Ivanov (RUB)
Seminar: Lie-Theorie
Talk on Monday, 08.07.2024, 14:15 Uhr, in IA 1/75
Title: "An introduction to the Langlands correspondences"
Abstract:
I will try to explain some basics of the Langlands program, with as few prerequisites as possible. More concretely, I will concentrate on the case of number fields (the original case, where Langlands program took its origin) and discuss in detail the one-dimensional case --that is, global class field theory. Then I will sketch the n-dimensional conjecture.
Jakub Löwit (IST)
Seminar: Lie-Theorie
Talk on Monday, 03.06.2024, 14:15 Uhr, in IA 1/75
Title: "On modular p-adic Deligne--Lusztig theory for GL_n"
Abstract:
In 1976, Deligne--Lusztig realized the characteristic zero representation theory of finite groups of Lie type inside cohomology of certain algebraic varieties. This picture has two interesting generalizations. In one direction, one can replace finite groups by p-adic groups. In another direction, one can consider modular coefficients. After recalling the key players, I will discuss what happens in the p-adic case with modular coefficients for GL_n. In particular, I will explain how to deduce such results from the case of characteristic zero coefficients.
David Schwein (University of Bonn)
Seminar: Lie-Theorie
Talk on Monday, 15.04.2024, 14:15 Uhr, in IA 1/75
Title: "Tame supercuspidals at very small primes"
Abstract:
Supercuspidal representations are the elementary particles in the representation theory of reductive p-adic groups. Constructing such representations explicitly, via (compact) induction, is a longstanding open problem, solved when p is large. When p is small, the remaining supercuspidals are expected to have an arithmetic source: wildly ramified field extensions. In this talk I'll discuss ongoing work joint with Jessica Fintzen that identifies a second, Lie-theoretic, source of new (tame!) supercuspidals: special features of reductive groups at very small primes. We'll summarize some of these features and explain how they contribute to the construction of supercuspidals.
