Topology Seminar talks at Southampton

The talks are all happening at University of Southampton (in person), on Highfield Campus (SO17 1BJ). For the building and the room, see the individual postings. Email the organiser ( d (dot) kasprowski (at) soton.ac.uk ) if you have questions.

More Pure Maths talks at Southampton: we run Pure Maths Colloquia, Pure Lunchtime Seminar, and Pure Postgraduate Seminar (link soon).

Upcoming talks

• Mon 27 Apr 2026 14:00 (in B54 / 8033 (8B)): Stephen Theriault (Southampton): TBA
  No abstract yet.

Recent talks

• Mon 16 Mar 2026 14:00: Daniel Marlowe (Warwick): Deriving the higher K-theory of forms
  unroll abstract

  Hermitian K-theory is a quadratic analogue of algebraic K-theory, bearing the same relation to oriented Chow groups that the usual K-theory does to Chow groups. Classically an invariant of exact or dg-categories with dualities, hermitian K-theory has enjoyed a homotopy-coherent revival in the last few years due to work of the 9 authors, following ideas of Lurie, situating it in the realm of (Poincaré) localising invariants on stable infinity categories equipped with an appropriate notion of a nondegenerate quadratic functor. In this talk, I'll present work from my thesis bridging the gap between the 1- and infinity-categorical formalisms. As an application, we'll see how to recover the genuine symmetric hermitian K-theory of a divisorial scheme from the classical hermitian K-theory of on-the-nose symmetric forms.

• Mon 9 Mar 2026 14:00: Ulrich Bunke (Regensburg): E-theory contexts and 6-functor calculus
  unroll abstract

  We revisit E-theory for X-C*-algebras from a homotopy theoretic point of view. We will introduce the notion of E-theory contexts as inputs for a general E-theory machine and show that X-C*-algebras are examples. We express all functorial properties of the E-theory of X-C*-algebras in a condensed form by stating that it forms a 6-functor calculus on locally compact Hausdorff spaces.

• Mon 2 Mar 2026 14:00: Mark Hagen (Bristol): A coarse flat torus theorem
  unroll abstract

  Hierarchically hyperbolic groups (HHGs) are a common generalisation of Gromov-hyperbolic groups, mapping class groups, and special cubical groups, and the class is now known to contain many other examples. The notion is a type of ``coarse nonpositive curvature'' designed to enable arguments reminiscent of Gromov hyperbolicity and cubical geometry to be made in more general settings. A basic fact about HHGs is that they satisfy a strong form of the Tits alternative: every subgroup contains a nonabelian free group, or it is virtually abelian. This motivates the question of what abelian subgroups look like. It has been known for several years that they are undistorted, but this was not known in any sort of uniform/quantitative way. In this talk, I will discuss a new hierarchically hyperbolic analogue of the flat torus theorem from CAT(0) geometry, which remedies this situation. This talk is based on joint work with Pénélope Azuelos.

• Mon 16 Feb 2026 14:00: Devarshi Mukherjee (Oxford): Equivariant bivariant K-theory for bornological algebras
  unroll abstract

  We introduce equivariant bivariant K-theory for bornological algebras by taking a presentable refinement of the bivariant K-theory defined by Cuntz-Meyer-Rosenberg. An upshot of this refinement is that we may purely formally define a Bost-Connes assembly map via localisation in the sense of Meyer-Nest. Another feature built into the refinement is a large UCT-class; on this UCT-class, we show that the (equivariant) rationalised Chern-Connes character from (equivariant) KK-theory to (equivariant) local cyclic homology is an equivalence. This is joint work with Anupam Datta.

• Mon 9 Feb 2026 14:00: Kamen Pavlov (Southampton): 4-manifolds with fundamental group a semidirect product of Z and Z/p
  unroll abstract

  The quadratic 2-type is a collection of invariants which plays a big role in the homotopy classification of 4-manifolds. I will recall a result from my talk last year that, for manifolds with fundamental group ZxZ/p, there are at most p many different homotopy types with fixed quadratic 2-type. I will explain how this has been improved to a complete classification by including an additional Z/p-valued intersection form, and also generalized to semidirect products of Z and Z/p.

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