Schedule

• 11:00 – 11:50: Indira Chatterji (Université de Nice) Rapid Decay property

• 12:00 – 12:30: Ryan O’Loughlin (University of Reading) The Numerical Range as a Spectral Set

• 12:30 – 14:00: Lunch break

• 14:00 – 14:50: Marius Dadarlat (Purdue University) On Chern classes of quasi-representations

• 15:00 – 15:20: Estelle Boffy (Université Marie et Louis Pasteur) Positive and Contractive Projections on Schatten spaces

• 15:20 – 15:50: Coffee/tea

• 15:50 – 16:20: Greg Patchell (University of Oxford) Selfless Inclusions of C*-Algebras and Quantum Groups

• 16:30 – 16:50: Pénélope Azuelos (University of Bristol) Narrow graphs and virtual fibre subgroups

• 16:50 – 17:00: Break

• 17:00 – 17:50: Andrew Toms (Purdue University) Homotopy groups of Cuntz classes in C*-algebras

• 18:15 -TBD   Drinks and dinner at Zero Degrees 

Abstracts (in order of talks)

• Indira Chatterji - Rapid Decay property
  
  I will discuss the Rapid Decay property and its relevance to the Baum-Connes conjecture. I will also discuss a relative version of the Rapid Decay property. This is joint work with Benjamin Zarka.

• Ryan O’Loughlin - The Numerical Range as a Spectral Set
  
  Crouzeix’s Conjecture is an open conjecture which claims that the operator norm of a polynomial applied to a matrix is bounded above by 2 times supremum of the polynomial over the numerical range of the matrix. In this talk I will first give a historical background on Crouzeix’s Conjecture starting from the von Neumann inequality, and then present some new recently published results on the conjecture.

• Marius Dadarlat - On Chern classes of quasi-representations
  
  The talk aims to give a friendly introduction to certain topological invariants associated with finite-dimensional quasi-representations of groups.  For a discrete group G, we study vector bundles E(f)  on compact subsets of the classifying space BG associated to almost multiplicative maps f from G to unitary groups U(n). We compute the first Chern class of E(f) in terms of f. When f is both projective and almost multiplicative, we determine its Chern character. These invariants yield obstructions to perturbing quasi-representations to those arising from projective representations. For residually finite amenable groups, the K-theory classes of E(f) classify quasi-representations up to stable equivalence. Joint work with Forrest Glebe.

• Estelle Boffy - Positive and Contractive Projections on Schatten spaces
  
  A subspace of a Banach space E is said to be 1-complemented if it is the range of a contractive projection, and positively 1-complemented if the projection is, in addition, positive. In the commutative Lp spaces, the description of contractive projections is well known (see, e.g., Ando's Theorem, 1966). In 1992, Arazy and Friedman provided a characterization of the 1-complemented subspaces of S^p(H), the noncommutative Lp space associated with B(H), for p≠2. In this talk, I will focus on the positively 1-complemented subspaces of S^p(H), and briefly on the case p=2.

• Greg Patchell - Selfless Inclusions of C*-Algebras and Quantum Groups
  
  Recently, strong asymptotic freeness, or selflessness, in C*-algebras has emerged as a powerful technique to prove important regularity properties including simplicity, unique trace, stable rank 1, and strict comparison. In particular, in Fall 2024, Amrutam, Gao, Kunnawalkam Elayavalli, and I showed that the reduced group C*-algebras of all hyperbolic groups with trivial finite radical are selfless, which resolved the open problem of strict comparison for the reduced group C*-algebra of the free group on two generators. Since then, our result has been expanded to include a much larger class of groups. Work has also begun on isolating selflessness for C*-algebras not arising from groups, including the result of Hayes, Kunnawalkam Elayavalli, and Robert on selflessness of the reduced free product of a large class of C*-algebras. I will introduce the general notion of a selfless inclusion of C*-algebras, with which we will see the selflessness of the unitary compact quantum groups. This work is joint with Ben Hayes, Srivatsav Kunnawalkam Elayavalli, and Leonel Robert.

• Pénélope Azuelos - Narrow graphs and virtual fibre subgroups
  
  

A finitely generated subgroup H of a finitely generated group G is a virtual fibre subgroup if G admits a finite index subgroup which surjects onto the integers and the kernel has finite index in H. This condition is very strong; it implies many nice properties of the subgroup and imposes a number of geometric properties on the quotient H∖G. In this talk, I will discuss the extent to which these geometric properties characterise virtual fibre subgroups.

• Andrew Toms - Homotopy groups of Cuntz classes in C*-algebras

The Cuntz semigroup of a C*-algebra A consists of equivalence classes of positive elements, where equivalence means roughly that two positive elements have the same rank relative to A.  It can be thought of as a generalization of the Murray von Neumann semigroup to positive elements and is an incredibly sensitive invariant.  We give a brief introduction to this object and its relevance to the classification theory of separable nuclear C*-algebras.  We then present a calculation of the homotopy groups of these Cuntz classes as topological subspaces of A when A is classifiable in the sense of Elliott.