2024-2025

Junior Analysis and Probability Seminar (2024–2025)

The Junior Analysis and Probability Seminar hosts talks from early-career researchers working broadly in analysis and probability.

Organisers: Hefin Lambley ( ), Grega Saksida ( ), Phoebe Valentine ( ), and Pietro Wald ( ).

Time: Mondays, 15:00–16:00, weeks 1–10.

Room: D1.07, Zeeman, followed by discussions in Zeeman Common Room.

30 September 2024: Anna Skorobogatova (SLMath). Regularity for critical points of semilinear elliptic variational problems with a topological constraint.
I will discuss the regularity of critical points for a free boundary problem arising from the diffuse interface/Allen-Cahn approximation of the set-theoretic Plateau problem recently introduced by Maggi-Novack-Restrepo. Here, a homotopic spanning constraint, first considered by Harrison-Pugh, forces the surfaces (and also the corresponding interface for the diffuse approximation), to remain attached to the given wire frame. The presence of the spanning condition allows for minimizers of this problem to exhibit codimension 1 singularities such as triple junctions and tetrahedral singularities, in stark contrast to the work of Tonegawa-Wickramasekera which shows that any stable minimal hypersurface arising as a limit of interfaces for stable critical points of classical Allen-Cahn is smooth outside of a codimension 7 set. I will further discuss free boundary regularity for minimizers of this problem. This is a joint work with Mike Novack (Louisiana State University) and Daniel Restrepo (Johns Hopkins University).
7 October 2024: Ryan Acosta Babb (Warwick)
14 October 2024
21 October 2024
28 October 2024
4 November 2024
11 November 2024
18 November 2024: Toby Sheldon (Warwick)
25 November 2024
2 December 2024