Pure Lunchtime 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 ( a (dot) guidolin (at) soton.ac.uk ) if you have questions.

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

Upcoming talks

• Mon 12 May 2025 12:00 (in B54 Room 7033 (7C)): Francesco Fournier-Facio (Cambridge): Title TBA
  No abstract yet.

Recent talks

• Mon 28 Apr 2025 12:00: Tristan Madeleine: Data has shape, shape matters: an introduction to Topological Data Analysis and its application
  unroll abstract

  Topological Data Analysis stemmed from the idea that data has shape and that this shape is meaningful. It covers a wide range of topological and geometrical tools designed to understand and quantify this shape.
  In the age of big data, which saw an explosion in the size and complexity of data, this is particularly interesting as it offers unique approaches to extract relevant information, where more standard analysis may fail.
  In this talk, we will review the fundamentals of Topological Data Analysis and explore the scope of its potential using examples of its usage in medicine, nanoscience and up to the cosmological scale.

• Mon 24 Mar 2025 12:00: Salv Elia: Path homology of polyhedral products of digraphs
  unroll abstract

  Polyhedral products are topological spaces constructed by gluing topological pairs of spaces in a way determined by a simplicial complex. Bahri, Bendersky, Cohen, and Gitler introduced a stable homotopy splitting of the polyhedral product.

  In this talk, I will begin by providing a brief summary of diagraphs as directed graphs, including certain operations on them and their associated path homology. I will then introduce the concept of polyhedral products of digraphs and demonstrate that their path homology admits a splitting analogous to the BBCG splitting. To achieve this, I'll define a notion of pointed chain complexes and study polyhedral products of these.

• Mon 10 Mar 2025 12:00: Briony Eldridge: Loop spaces of polyhedral products associated with polyhedral join products
  unroll abstract

  Polyhedral products are a topological space formed by gluing together ingredient spaces in a manner governed by a simplicial complex. They appear in many areas of study, including toric topology, combinatorics, commutative algebra, complex geometry and geometric group theory. A fundamental problem is to determine how operations on simplicial complexes change the topology of the polyhedral product. In this talk, we obtain a description of the loop space of polyhedral products associated with polyhedral join complexes, and build a new family of simplicial complexes such that the homotopy type of the loop space of the moment angle complex is a product of spheres and loops on spheres.

• Mon 24 Feb 2025 12:00: Ashot Minasyan: Generating RAAGs in 1-relator groups
  unroll abstract

  Given a finite simplicial graph $\Gamma$, the right angled Artin group (RAAG) $A(\Gamma)$ is generated by the vertices of $\Gamma$ subject to the relations that two vertices commute if and only if they are adjacent in $\Gamma$. RAAGs play an important role in Geometric Group Theory and in Low Dimensional Topology.

  Given a group $G$, a finite graph $\Gamma$ and a homomorphism $\phi: A(\Gamma) \to G$ one can ask for conditions ensuring that this homomorphism can be promoted to an injective one. In my talk I will discuss such criteria in the case when $G$ is a one-relator group and $\Gamma$ is a forest. In particular, I will sketch an argument showing that it is sufficient for $\phi$ to be injective on the positive sub-monoid of $A(\Gamma)$. The talk will be based on joint work with Motiejus Valiunas

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