# Oberseminar Algebra/Zahlentheorie

## Vortragsankündigungen

Bitte beachten Sie auch die Vorträge im Mathematischen Kolloquium.

### SS2020

Dienstag, den 26. Mai 2020, in JENA, SR 3517, Ernst-Abbe-Platz 2
Algebra-Seminar Halle-Jena,
Gemeinsames Oberseminar mit dem Mathematischen Institut der Universität Halle-Wittenberg
Dr. Thomas Breuer   (RWTH Aachen)
"Verification of ATLAS data"
Dienstag, den 28. April 2020, in HALLE/Saale, SR 3, Georg-Cantor-Haus, Theodor-Lieser-Str. 5
Algebra-Seminar Halle-Jena,
Gemeinsames Oberseminar mit dem Mathematischen Institut der Universität Halle-Wittenberg

### WS2019/2020

Mittwoch, den 5. Februar 2020, 14:15 Uhr, SR 3517, Ernst-Abbe-Platz 2 Achtung! Ausfall wegen Erkrankung
Prof. Boris Kunyavskii   (Bar-Ilan University, Israel)
"Word equations on groups and Lie algebras"
Dienstag, den 4. Februar 2020, 14:15 Uhr, SR 3517, Ernst-Abbe-Platz 2
Dr. Ksenija Kitanov   (Universität Jena)
"Higher-order congruence relations on affine moment graphs"
Abstract: With any moment graph one can associate its structure algebra, a certain graded commutative algebra over a polynomial ring. For the case of affine moment graphs, after evaluating one variable of this polynomial ring at 0, quite surprising divisibility relations emerge. These relations can be regarded as a generalization of ordinary moment graph relations that define sections of sheaves on moment graphs, and thus we call them higher-order congruence relations.
Dienstag, den 28. Januar 2020, 14:15 Uhr, SR 3517, Ernst-Abbe-Platz 2
PD Dr. Simon King   (Universität Jena)
"Vertices, Sources and the Green Correspondence"
Dienstag, den 21. Januar 2020, 14:15 Uhr, SR 3517, Ernst-Abbe-Platz 2
Prof. Giovanna Carnovale   (Universita` degli Studi di Padova)
"Jordan classes in Lie algebras and algebraic groups"
Abstract: Reductive algebraic groups and Lie algebras can be stratified by means of irreducible, locally closed, smooth unions of elements that have similar Jordan decomposition, called Jordan classes or decomposition classes. In the Lie algebra context they were introduced by Borho and Kraft to describe sheets for the adjoint action, whereas in the algebraic group context they firstly appeared in the work of Lusztig on the generalised Springer correspondence. After showing difference and similarities between the group and the Lie algebra case, I will show how locally the two stratifications can be related and how to deduce geometric properties of the group stratification from properties of the Lie algebra one. The talk is based on joint work with Filippo Ambrosio and Francesco Esposito.
Dienstag, den 14. Januar 2020, 14:15 Uhr, SR 3517, Ernst-Abbe-Platz 2 Achtung! Ausfall wegen Erkrankung
Dr. Karin Schaller   (FU Berlin)
"Polyhedral Divisors and Orbit Decompositions of Normal Affine Varieties with Torus Action"
Dienstag, den 7. Januar 2020, in JENA, SR 3517, Ernst-Abbe-Platz 2
Algebra-Seminar Halle-Jena,
Gemeinsames Oberseminar mit dem Mathematischen Institut der Universität Halle-Wittenberg
14:15 Uhr
Andriy Regeta   (Universität Jena)
"On the Lie algebras of vector fields of smooth affine surfaces"
Abstract: In this talk we will study the Lie algebra of volume preserving vector fields on affine plane. We will show that this algebra is simple and study its finite-dimensional subalgebras. At the end we will discuss some interesting subalgebras of the Lie algebras of vector fields on the so-called Danielewski surfaces.
15:45 Uhr
Imke Toborg  (MLU Halle-Wittenberg)
"Isolated elements of order p in finite groups without elementary abelian subgroups of order p3"
Abstract: Let $p$ be an odd prime, and let $G$ be a finite group which does not contain elementary abelian subgroups of order $p^3$. Moreover, let $x \in G$ be an element of order $p$ such that $x^G \cap C_G(x) = \{x\}$.
Then $G = C_G(x) \cdot O_{p'}(G)$, or $F^*(G/O_{p'}(G))$ is simple. In the second case we will investigate the structure of a Sylow $p$-subgroup and determine it precisely in case $p=3$.
16:45 Uhr s.t.
Susanne Danz  (KU Eichstätt)
"On Ext-quivers of weight-2 blocks of symmetric groups"
Abstract: Blocks of symmetric groups of weight 2 over fields of odd characteristic p have been studied a lot. Thanks to work of Scopes, Martin, Richards and others the structure of these blocks is now comparatively well understood.
In 1995 Scopes, for instance, proved that all decomposition numbers of a block of weight 2 are at most 1, and the Ext-space of two simple modules is at most one-dimensional. Her proof (in principle) also provides an algorithm to compute the Ext-quiver of any given weight-2 block. In this talk we shall combine this with results of Richards and Chuang--Tan, in order to explicitly determine the Ext-quivers of all weight-2 blocks whose p-cores are hook partitions. As a consequence, we shall also gain information on possible Morita equivalences between different blocks of weight 2.
This is joint work with Karin Erdmann.

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