M. S. Adamo
On an operator algebraic construction of full 2D CFTs: the case of the Heisenberg conformal net
In this talk we will explicitly construct 2D conformal nets that extend the non-rational Heisenberg chiral conformal net, where DHR representations are all automorphisms. To this aim, we define charged fields acting as (twisted) shifts between DHR sectors and labelled by the elements of an even lattice Q of the real linear space of charges. In order to recover locality for the 2D conformal net that we construct, we introduce a 2-cocycle on Q that encodes the interplay between the DHR categories of the left and right chiral components.
This talk is based on a joint project with L. Giorgetti, Y. Tanimoto, arXiv:2301.12310, arXiv:2506.01008.
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C. Anantharaman-Delaroche
Groupoid exactness and the weak containment problem
In this talk, I will discuss the weak containment problem for locally compact groupoids: is it true that a locally compact groupoid is amenable if and only if its full and reduced C*-algebras coincide (as it is the case for locally compact groups)? We will see that some notions of exactness are involved in this topic.
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J. Bassi
Boundary amenability of certain group actions
I will present examples of non-amenable transitive actions of discrete groups which extend to amenable actions on the Stone-Cech boundaries of the given coset spaces. In some cases these will give examples of C*-algebras with a unique ideal, namely the ones associated to the corresponding quasi-regular representations. The techniques involved rely on a study of the dynamics on certain extensions of these boundaries.
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F. Bracci
Shift-invariant closed subspaces of ℓ²(H²)
The classical Beurling theorem describes the invariant subspaces for the shift (multiplication by z) in the Hardy space H² (holomorphic functions in the unit disc with a boundary trace in L². From Beurling's characterisation, it's easy to see that the only maximal shift-invariant subspaces in H² have codimension 1. This solves the invariant subspace problem for linear contractions with defect ≤1 in Hilbert space, as per Rota's universality theorem. The Beurling-Lax theorem provides a theoretical framework for shift-invariant subspaces in any Hilbert space but is too general for a full description of maximal ones. In a recent paper (F. Bracci, E. A. Gallardo-Gutierrez: Invariant subspaces for finite index shifts in Hardy spaces, Ann. Scuola Norm. Sup., Cl. Sci., to appear), the speaker and Eva Gallardo-Gutierrez developed a concrete characterisation of shift-invariant subspaces in the finite direct sum of H² using a new class of linear operators called determinantal operators. This gives a positive answer to the invariant subspace problem for finite defect contractions in Hilbert spaces. This talk, based on ongoing joint work with Eva Gallardo-Gutierrez, will demonstrate how to classify all shift-invariant subspaces in ℓ²(H²) using limits of determinantal spaces. This approach provides new insights into these maximal subspaces.
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R. Duvenhage
From recurrence to Wasserstein distance, Part 2: Noncommutative joinings and optimal transport
In this talk we discuss work ultimately inspired by the theory around multiple recurrence. The latter is connected to joinings of state preserving systems, which can be viewed as a way of comparing systems by correlations between them. This in turn led to a similar theory for the case of unital completely positive maps (quantum channels) as dynamics. A quantitative version of this theory is given by quadratic Wasserstein distances defined between systems. The connecting thread in this development is the role of couplings between systems, which form the basis for both the theory of joinings and the Kantorovich formulation of optimal transport.
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D. Evans
Quantum Symmetries
(joint work with Corey Jones)
This talk is part of a programme to understand non-invertible quantum symmetries. These symmetries arise through subfactors and twisted equivariant K-theory and their applications in conformal field theory. Here I discuss the question of constructing actions of these quantum symmetries on quantum spin systems and noncommutative tori.
This is based on joint work with Corey Jones.
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V.G. Kaftal
The Elliott-Kucerovsky theory for sigma-unital algebras and properly infinite von Neumann factors
In their 2001 paper ``An abstract Voiculescu-Brown-Douglas-Fillmore absorption theorem" Elliott and Kucerovsky characterized in the case of a separable ideal B those extensions that absorb weakly nuclear trivial extensions in terms of their notions of purely large algebras with respect to B. We found a further characterization of the purely large property that permits to streamline their proof and apply it also to the case when B is sigma-unital. In the case that B is the Breuer ideal of a separable infinite type II von Neumann factor, we show that by replacing strict convergence with SOT convergence and weak nuclearity with a notion we call SOT weak nuclearity, a remarkably similar proof yields the same results. A different approach based on the abundance of projections in von Neumann factors holds for asymptotic absorption for type III factors and that approach applies also to infinite type II factors.
Then we obtain also a Voicluscu double commutant theorem (resp. asymptotic double commutant theorem) for the type II (resp III case).
This is joint work with Thierry Giordano and Ping W. Ng.
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R.Longo
von Neumann algebras and entropy/energy inequalities in QFT
In this talk I will present certain entropy/energy inequalities that have been recently obtained by operator algebraic methods.
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G. Lusztig
Fourier transform as a triangular matrix
Let V be a vector space of dimension 2n over the field 𝔽₂ with two elements. Assume that we are given a nondegenerate symplectic form on V with values in 𝔽₂ . Let X be the vector space of complex valued functions on V. We show that there exists an interesting basis of X in which the Fourier transform is upper triangular. This follows the tradition of Hermite who showed that the usual Fourier transform on the real line can be diagonalized.
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M. Mathieu
Derivations, local multipliers, and sheaf cohomology of C*-algebras
Starting from various results by Laszlo Zsido on derivations on W*-algebras, we will explore appropriate generalisations to C*-algebras which naturally lead us to the concept of the local multiplier algebra. Originally devised by Gert Pedersen, this algebra was recognised as an important tool to study a number of classes of operators on C*-algebras by Pere Ara and the speaker. In answering fundamental questions, posed by Pedersen, on the nature of derivations and local multiplier algebras we were led to develop a sheaf theory for C*-algebras which culminated in the construction of sheaf cohomology groups for C*-algebras.
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V. Müller
The numerical range and essential numerical range in ℓₚ
(joint work with Yu. Tomilov)
The numerical range of Hilbert space operators is a classical notion with many important applications in operator theory. By the Hausdorff-Toeplitz theorem it is always a convex set and convexity is closely connected with the Hilbert space geometry. The numerical range of Banach space operators has also been introduced and studied but it lacks many properties of the Hilbert spaces. In particular, the numerical range of Banach space operators is practically never convex.
We are going to discuss the numerical range of operators on ℓₚ and show that it possess many nice properties known in Hilbert spaces. In particular, the essential numerical range of ℓₚ operators is a closed convex set and it is equal to the algebraic numerical range in the Calkin algebra.
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M. Picardello
The spectrum of the Laplacian on semi-homogeneous trees
(joint work with E. Casadio~Tarabusi and S. Gindikin)
Harmonic analysis for groups of automorphisms of infinite homogeneous trees have been know since long (see Figà-Talamanca & Picardello, Marcel Dekker Lecture Notes (1983)] for details and references). The Poisson kernel is a fundamental tool in this theory [Cartier (1972), Furstenberg (1971)]. It is the trait d'union of harmonic analysis, potential theory and Markov chains on trees. But it is constant on horospheres... this leads to a new viewpoint where results in harmonic analysis are rephrased, and completed, via integral geometry, in the spirit of Gelfand and Helgason.
A by-product is the theory of spherical functions on semi-homogeneous trees, presented today.
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S. Popa
Approximate freeness in II1 factors: some applications, old and new
I will discuss approximate freeness phenomena in II1 factors, explaining how W*-algebra problems like vanishing Hochschild cohomology, subfactor problems, Kadison-Singer problems, led to uncovering such results. While the first applications of approximate freeness go back to 1984, they were more recently applied to prove vanishing of the Connes-Shlyakhtenko-Thom 1-cohomology (Popa-Vaes 2014), approximate untwisting of 1-cocycles (Popa-Vaes-Shlyakhtenko 2018), quantitative Dixmier averaging (Popa 2023), contractibility of unitary groups of II1 factors (Jekel 2025) while also leading to developments in C*-algebras, through L. Robert notion of selflessness (2023-2026).
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F. Radulescu
On the Connes Embedding Problem and moments of word(s) maps
The Connes Embedding Problem remains an open problem for countable discrete groups. Equivalently it is unknown if all groups are hyperlinear (or sofic). For groups having a presentation with a finite number of relators, this has an equivalent statement in terms of mixed moments of several word maps. In joint work with L. Paunescu, we provide a complete method of computation for these moments starting with any finite dimensional unitary representation of a compact group (in particular U(N) and Sym(N) that are essential for hyperlinearity and soficity). This generalizes an early result obtained by Mingo, Sniady Speicher, and independently by Radulescu. It complements the analytic expansion that was later developed by Magee and Puder.
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A. Stroh
From recurrence to Wasserstein distance, Part 1: Noncommutative extensions of recurrence and related structure results
In these two talks we outline work we did with Zsidó, as well as some subsequent work influenced by it. The initial focus was on extending multiple recurrence results to a noncommutative framework, along with some of the structural aspects of dynamical systems in Furstenberg's work. The latter was later carried forward by Austin, Eisner and Tao, among others, who also gave extensive examples regarding limitations of the general theory. However, in the context of free probability, it appears that some of these limitations, like the need for asymptotic abelianness, do not apply.
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D. Timotin
Recent results in de Branges - Rovnyak spaces
de Branges - Rovnyak spaces represent a class of spaces of analytic functions that have received increased interest in the last years. We will present some recent results, obtained in joint work with Emmanuel Fricain, Andreas Hartmann, and William Ross. In particular, it is interesting to note how the search for a corona-type theorem for these spaces has lead to new interesting estimates concerning the classical Bezout formula.