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

Recent talks

• Mon 1 Jun 2026 12:00: Jennifer Williams (Southampton): The Geometry of Collatz Chains: A Coordinate System from 3-Smooth Factorisation
  unroll abstract

  Every odd positive integer admits a unique 3-smooth factorisation, and this talk develops that factorisation into a coordinate system that partitions the nonnegative integers into countably many infinite triangles whose rows are Collatz chains of alternating parity. Within each triangle, the Collatz map becomes a deterministic diagonal flow, with all number-theoretic difficulty concentrated at a single boundary. Inside this structure I will locate the Mersenne, Thabit, and Pierpont families, and prove that an entire infinite family of rows in the principal skeleton contains no primes, the unique class of rows where elementary algebra alone forces every element to be composite. The framework is independent of the Collatz conjecture. I will close with what it does and does not say about the conjecture itself, and open problems it raises.

• Mon 11 May 2026 12:00: Ka Man Yim (Oxford): Stable and consistent spectral features of vertices
  unroll abstract

  The eigenvalues and eigenvectors of the graph Laplacian has a long history in computational harmonic analysis, primarily utilised in creating local and global features of graphs. However, the eigenvectors are known to be unstable under perturbations to the graph, and subject to a choice of sign or basis in the eigenspace. Here, we show that these two issues can be solved by considering the projection-valued spectral measure of the Laplacian. By construction, it combines both eigenvalues and eigenvectors into one coherent object, and is independent of the choice of eigenbasis. Furthermore, we prove that vertex features derived from the projection-valued spectral measure is Lipschitz stable with respect to perturbations to the Laplacian, which overcomes the instability of using eigenvectors. We show that these vertex features empirically improve the performance of graph neural networks on graph regression tasks, and can be used to detect approximate symmetries in point clouds and graphs.

• Mon 27 Apr 2026 12:00: Jorge Fariña (Lund): Rigidity and first-order theory of weakly branch actions
  unroll abstract

  In 1971, Wilson introduced the structure lattice of a just-infinite group and provided a classification of just-infinite groups based on it. In the late 1990s, when Grigorchuk introduced the class of branch groups, Wilson showed that the structure graph, a subgraph of the structure lattice, encodes all the possible actions of a group as a branch group. This opened the door to the study of branch actions and, in particular it started the problem of classifying all the possible branch actions of a given branch group.

  In this talk, we generalize the notion of structure graph from branch groups to weakly branch groups and show its applications to the study of the rigidity of weakly branch actions, i.e. when the action of a group as a weakly branch group on a given tree is unique. We further discuss applications to the first-order theory of weakly branch groups generalizing analogous results of Wilson for branch groups.

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