GAPT Seminar
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This is the seminar homepage of the GAPT group at Cardiff University.
The research interests of the GAPT group sweep a broad range of topics, from algebra, geometry, topology, including operator algebras, and non-commutative geometry in pure mathematics, to algebraic and conformal quantum field theory and integrable statistical mechanics in mathematical physics.
Usually the seminar takes place every Thursday from 15:10-16:00.
The GAPT group has a mailing list.
Upcoming Seminar Talk
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.
Seminar Talks – Autumn 2025
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.
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Apurva Seth (University of Oxford)
Thursday, 29th October 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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Johannes Nordström (University of Bath)
Thursday, 17th December 2026 15:10-16:00