\n
Acyclic groups and C*-algebraic constructions<\/h4>\n
Raz Slutsky<\/span> (University of Oxford)<\/span>
\nThursday, 15th October 2026 15:10-16:00<\/b><\/span><\/p>\nAbstract:
\nGroups 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.
\nIn 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.\n<\/div>\n
\nSeminar Talks – Autumn 2025<\/h2>\n\n
A generalized winding number formula for the Witten index of a Toeplitz operator<\/h4>\n
Masaki Izumi<\/span> (Kyoto University)<\/span>
\nThursday, 1st October 2026 11:00-12:00<\/b><\/span><\/p>\nAbstract:\u00a0
\nIt 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.\n<\/div>\n
\n
\n
Q-Manifolds, Their Derived Algebra, and Cyclic Cohomology<\/h4>\n
Andrew Bruce<\/span> <\/span>
\nThursday, 8th October 2026 15:10-16:00<\/b><\/span><\/p>\nAbstract:\u00a0
\nAfter reviewing the notion of a Q-manifold\u2014a supermanifold equipped with an odd integrable vector field\u2014we 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\u2013BFV\u2013BRST formalism.<\/p>\n
The talk will be colloquium-style, assuming only standard familiarity with basic differential geometry and homological algebra.\n<\/p><\/div>\n
\n
\n
Acyclic groups and C*-algebraic constructions<\/h4>\n
Raz Slutsky<\/span> (University of Oxford)<\/span>
\nThursday, 15th October 2026 15:10-16:00<\/b><\/span><\/p>\nAbstract:
\nGroups 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.
\nIn 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.\n<\/div>\n
\n
\n
An introduction to plethysms of symmetric functions<\/h4>\n
Mark Wildon<\/span> (University of Bristol)<\/span>
\nThursday, 22nd October 2026 15:10-16:00<\/b><\/span><\/p>\nAbstract:
\nThe 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 \u00c1lvaro Guti\u00e9rrez, Micha\u0142 Szwej and our collaborator \u00c1lvaro R. Martinez (Columbia University, New York) on plethysms in prime characteristic. No specialist background knowledge will be assumed.\n<\/div>\n
\n
\n
Title: tba<\/h4>\n
Apurva Seth<\/span> (University of Oxford)<\/span>
\nThursday, 29th October 2026 15:10-16:00<\/b><\/span>\n<\/div>\n\n
\n
Title: tba<\/h4>\n
Xiao-Qi Lu<\/span> (University of Glasgow)<\/span>
\nThursday, 26th November 2026 15:10-16:00<\/b><\/span>\n<\/div>\n\n
\n
Title: tba<\/h4>\n
Johannes Nordstr\u00f6m<\/span> (University of Bath)<\/span>
\nThursday, 17th December 2026 15:10-16:00<\/b><\/span>\n<\/div>\n","protected":false},"excerpt":{"rendered":"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 […]","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"categories":[],"class_list":["post-3","page","type-page","status-publish","hentry"],"meta_box":[],"_links":{"self":[{"href":"https:\/\/research-sites.cardiff.ac.uk\/gapt\/wp-json\/wp\/v2\/pages\/3","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/research-sites.cardiff.ac.uk\/gapt\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/research-sites.cardiff.ac.uk\/gapt\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/research-sites.cardiff.ac.uk\/gapt\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/research-sites.cardiff.ac.uk\/gapt\/wp-json\/wp\/v2\/comments?post=3"}],"version-history":[{"count":100,"href":"https:\/\/research-sites.cardiff.ac.uk\/gapt\/wp-json\/wp\/v2\/pages\/3\/revisions"}],"predecessor-version":[{"id":319,"href":"https:\/\/research-sites.cardiff.ac.uk\/gapt\/wp-json\/wp\/v2\/pages\/3\/revisions\/319"}],"wp:attachment":[{"href":"https:\/\/research-sites.cardiff.ac.uk\/gapt\/wp-json\/wp\/v2\/media?parent=3"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/research-sites.cardiff.ac.uk\/gapt\/wp-json\/wp\/v2\/categories?post=3"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}