Exactification of eQCAs on abstract spin chains

Siddharth Vadnerkar (University of Copenhagen)
Thursday, 12th November 2026 15:10-16:00

Abstract:
QCAs are invertible operations that preserve strict locality. Due to this, they play a crucial role in understanding topological phases and their symmetries. In recent years there’s been much progress in our understanding of QCAs in various spatial dimensions, with the GNVW index being a landmark result for (ordinary) spin chains.

However it is well-known that finite time dynamics from Hamiltonians do not generically preserve strict locality, even when they have “nice” properties like having finitely supported interactions. To remedy this, one defines the concept of an eQCA, which sends local observables to approximately local observables. Surprisingly little has been said about eQCAs, with the only result being Ranard-Walter-Witteeveen, who extended the GNVW index to eQCAs and showed that in (ordinary) spin chains, eQCAs do not exhibit any new behavior beyond that of QCAs.

In this talk, based on a soon-to-appear preprint, we understand the properties of eQCAs on abstract spin chains, which do not have a tensor product decomposition in general. Abstract spin chains can be understood as a holographic shadow of 2D topological order, due to a construction called DHR bimodules. So this work represents a first step toward understanding eQCA in higher-than-1 spatial dimensions. This work was done jointly with Albert Werner.

A generalized winding number formula for the Witten index of a Toeplitz operator

Masaki Izumi (Kyoto University)
Thursday, 1st October 2026 11:00-12:00

Abstract: 
It is well known that a Toeplitz operator with a continuous symbol is Fredholm if and only if the symbol has no zeros on the circle, and in this case the Fredholm index is given by (-1 times) the winding number of the symbol. In this talk, I will present a generalized winding number formula for the Witten index of a Toeplitz operator. The proof uses only the Helton-Howe trace formula. If time permits, I will also talk about a related trace formula involving operator monotone functions.

Q-Manifolds, Their Derived Algebra, and Cyclic Cohomology

Andrew Bruce
Thursday, 8th October 2026 15:10-16:00

Abstract: 
After reviewing the notion of a Q-manifold—a supermanifold equipped with an odd integrable vector field—we will describe its derived algebra following ideas of Loday. In particular, we will show how a shift in Grassmann parity yields an associative noncommutative superalgebra. From there, we will apply a super version of Connes’ cyclic cohomology to this derived algebra. Remarkably, the resulting derived cyclic cocycles are interpreted as classically BRST-invariant functionals within the BV–BFV–BRST formalism.

The talk will be colloquium-style, assuming only standard familiarity with basic differential geometry and homological algebra.

Acyclic groups and C*-algebraic constructions

Raz Slutsky (University of Oxford)
Thursday, 15th October 2026 15:10-16:00

Abstract:
Groups give rise to various operator algebras, including the reduced group C*-algebra. A natural question is how much of the group can be recovered from this algebra. A closely related question is which familiar C*-algebras arise from group-theoretic constructions.
In this talk, we will see how acyclic groups can be a very useful tool for answering such questions. I will discuss joint work with Curda and Hua, in which we give the first examples of non-isomorphic torsion-free groups with isomorphic reduced C*-algebras. I will then turn to the Jiang-Su algebra, an important object in the structure and classification theory of C*-algebras. Using related ideas, we realize it as a crossed product arising from a group action.

An introduction to plethysms of symmetric functions

Mark Wildon (University of Bristol)
Thursday, 22nd October 2026 15:10-16:00

Abstract:
The plethysm product on symmetric functions corresponds to composition of polynomial representations of general linear groups. A typical example is the exterior power. Decomposing a plethysm product into Schur functions, or equivalently, writing the corresponding composition of Schur functors as a direct sum of Schur functors, is one of the main open problems in algebraic combinatorics. I will give an introduction to these mathematical objects emphasising the beautiful interplay between representation theory and combinatorics. I will end with new results obtained in joint work with my two Ph.D students Álvaro Gutiérrez, Michał Szwej and our collaborator Álvaro R. Martinez (Columbia University, New York) on plethysms in prime characteristic. No specialist background knowledge will be assumed.

Subfactors and module categories for charge conjugation

Hans Wenzl (University of California at San Diego)
Wednesday, 28th October 2026 14:00-15:00

Abstract:
We give a realization of modular invariants and construction of subfactors
coming from charge conjugation for general SU(N).

Nonstable K-Theory for C*-Algebras.

Apurva Seth (University of Oxford)
Thursday, 29th October 2026 15:10-16:00

Abstract:
Nonstable K-theory is the study of homotopy groups of the unitary groups of a C*-algebra. A central problem in the subject is to understand when these homotopy groups are determined by ordinary K-theory, which leads to the notion of K-stability.
In this talk, we shall discuss K-stability for tensor products of diagonal AH-algebras. We will present a characterization of when such tensor products are K-stable, outline the main ideas behind the proof, and conclude with some applications.

Exactification of eQCAs on abstract spin chains

Siddharth Vadnerkar (University of Copenhagen)
Thursday, 12th November 2026 15:10-16:00

Abstract:
QCAs are invertible operations that preserve strict locality. Due to this, they play a crucial role in understanding topological phases and their symmetries. In recent years there’s been much progress in our understanding of QCAs in various spatial dimensions, with the GNVW index being a landmark result for (ordinary) spin chains.

However it is well-known that finite time dynamics from Hamiltonians do not generically preserve strict locality, even when they have “nice” properties like having finitely supported interactions. To remedy this, one defines the concept of an eQCA, which sends local observables to approximately local observables. Surprisingly little has been said about eQCAs, with the only result being Ranard-Walter-Witteeveen, who extended the GNVW index to eQCAs and showed that in (ordinary) spin chains, eQCAs do not exhibit any new behavior beyond that of QCAs.

In this talk, based on a soon-to-appear preprint, we understand the properties of eQCAs on abstract spin chains, which do not have a tensor product decomposition in general. Abstract spin chains can be understood as a holographic shadow of 2D topological order, due to a construction called DHR bimodules. So this work represents a first step toward understanding eQCA in higher-than-1 spatial dimensions. This work was done jointly with Albert Werner.

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Masoumeh Zarei (University of Hamburg)
Thursday, 19th November 2026 15:10-16:00

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Xiao-Qi Lu (University of Glasgow)
Thursday, 26th November 2026 15:10-16:00

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Michal Szwej (University of Bristol)
Thursday, 3rd December 2026 15:10-16:00

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Georgii Shuklin (University of Sheffield)
Thursday, 10th December 2026 15:10-16:00

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Johannes Nordström (University of Bath)
Thursday, 17th December 2026 15:10-16:00