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

Recent talks

• Mon 27 Apr 2026 14:00: Stephen Theriault (Southampton): Moment-angle manifolds associated to neighbourly triangulations of spheres
  unroll abstract

  A result credited to McGavran that predates toric topology states that a moment-angle manifold associated to a neighbourly triangulation of a sphere that is polytopal is diffeomorphic to a connected sum of products of two spheres. It has been an open problem for several years to give a homotopy theoretic proof that replaces the diffeomorphism with a homotopy equivalence, but with the aim of extending McGavran's result. This talk discusses a solution to this problem, allowing for an extension to all neighbourly triangulations of spheres, and a further extension from moment-angle manifolds to generalised moment-angle manifolds. This is joint work with Amaranta Membrillo-Solis.

• Mon 20 Apr 2026 16:00: Antonio Ceres Sánchez (Málaga): An approach to stable proper homotopy
  unroll abstract

  Proper homotopy theory is a standard framework in the study of non-compact spaces. The goal of this talk is to show how this theory can be refined by considering the so-called exterior category. We will discuss some of its properties and recall a version of Brown Representability within this context. Finally, we sketch how a suitable stable exterior category may be constructed following the general theory of stabilization of model categories of Hovey and Schwede. This is joint work in progress with José Manuel García Calcines and Aniceto Murillo.

• 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.

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