TALKS / ABSTRACTS

• Georges Neaime [Universität Bielefeld]
  Titel: Non-crossing partitions for exceptional hereditary curves
  Abstract: We introduce the notion of reflection groups of canonical type, arising from the $K$-theoretic study of the canonical algebras introduced by Ringel. We establish a bijection between the non-crossing partitions associated with these groups and certain subcategories of coherent sheaves on an exceptional hereditary curve defined over an arbitrary field. Combined with a result of Hubery and Krause, this completes the programme of categorification of generalised non-crossing partitions.
  The results presented in this talk are available in a recent preprint (https://arxiv.org/abs/2512.01729).
  
  
• Gaëtan Emmanuel Mancini [Bergische Universität Wuppertal]
  Titel: On the inductive Alperin--McKay conditions for groups of exceptional type
  Abstract: In 2013, B. Späth has reduced the Alperin--McKay conjecture to the verification of certain conditions on blocks of (quasi-)simple groups. In this talk we will discuss the methods used to prove these conditions for certain blocks of groups of exceptional type. In particular we will discuss the construction and role of the group $M$ related to $d$-split Levi subgroups.
  
  
• Frank Lübeck [RWTH Aachen]
  Title: The GAP package CCTab for constructing character tables
  Abstract: There are essentially two algorithms to compute the ordinary character tables of arbitrary finite groups, which are used in practice: the Dixon-Schneider method (in GAP and Magma) and the (often much more powerful) approach by Bill Unger, implemented in Magma, which is based on Brauer's characterization of characters via elementary subgroups and lattice reduction.
  In this talk I will comment on some aspects of an attempt to implement a new method in GAP which is efficient and more flexible and interactive (if needed in difficult cases) than the method in Magma.
  
  
• Thomas Breuer [RWTH Aachen]
  Titel: On the total degree of a finite group
  Abstract: For a finite group $G$, the total degree $T(G)$ is defined as the sum of the degrees of the complex irreducible characters of $G$. We classify the groups with $T(G) \leq 100$, using computational methods, and investigate special cases such as groups of prime power order and groups with total degree the square of a prime.
  This is joint work with László Héthelyi, Burkhard Külshammer, and Magdolna Szöke.
  
  
• Nicola Grittini [RPTU Kaiserslautern-Landau]
  Titel: On Huppert’s $ρ-σ$ conjecture and its connection with some arithmetic properties of group actions
  Abstract: For a finite group $G$, we may call $\rho(G)$ the set of all prime numbers dividing the degree of at least one irreducible character of $G$, and we may call $\sigma(G)$ the maximal number of primes dividing the degree of a single irreducible character of $G$. Huppert’s $ρ-σ$ conjecture states that, for any group $G$, $|\rho(G)| \le 3\sigma(G)$. A stronger version of this conjecture claims that it is actually possible to find three irreducible characters $\psi_1,\psi_2,\psi_3 \in Irr(G)$ such that every prime in $\rho(G)$ divides the degree of at least one of them.
  In this seminar, we will present an overview of the current progress on this conjecture, which is still not reduced to simple groups, and we will see how any possible approach to a general proof needs to involve the study of some properties of group action on sets and vector spaces.
  
  
• Deniz Yilmaz [Bilkent University]
  Titel: Alperin’s weight conjecture and diagonal $p$-permutation functors
  Abstract: Alperin’s weight conjecture asserts that the number of isomorphism classes of simple modules of a block is equal to the number of conjugacy classes of weights. In this talk, we will present an equivalent reformulation of the conjecture in terms of diagonal $p$- permutation functors.
  Joint work with Robert Boltje and Serge Bouc.
  
  
• Edoardo Salati [RPTU Kaiserslautern-Landau]
  Titel: Embeddability of partial groups
  Abstract: Partial groups were introduced by Chermak to assign to every saturated fusion system a topological space, which is analogous to the classifying space $BG$ of a group $G$. The fundamental group $\pi(\mathcal{F})$ of a fusion system $\mathcal{F}$ is then that of such topological space; this comes paired with a canonical map from the partial group associated to $\mathcal{F}$ to $\pi(\mathcal{F})$.
  Intuition suggests such map being an embedding, but known examples show this statement to be false in general. We identify and show that there is only one type of obstruction to this embeddability problem, related to ``local failures of associativity" in partial groups, and characterize the embeddable ones as an orthogonality class.
  This is joint work with Philip Hackney and Justin Lynd.
  
  
• Lucas Ruhstorfer [Bergische Universität Wuppertal]
  Title: Galois automorphisms and blocks covering unipotent blocks
  Abstract: Many interesting problems in the representation theory of finite groups aim to relate information about a group's structure to information that can be obtained from the character table. One of these problems is the recent question of Lyons-Martínez-Navarro-Tiep regarding the field of values of extensions of characters in principal blocks.
  We will discuss how this question is related to understanding the distribution of characters of unipotent blocks of almost simple groups of Lie type.