TALKS / ABSTRACTS

• 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.
  
  
• 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.
  
  
• 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.