22nd meeting, London

Speakers

Daniel Hendron, University of York

Anthea Monod, Imperial College London cancelled, sorry!

Sergey Sergeev, University of Birmingham

Primoz Skraba, Queen Mary University of London

Date

Monday 15th September 2025

Location

The meeting will run hybrid. 

In person: Queen Mary University of London, Mile End campus, Arts Two building (#35 on this map), room 3.20

On Microsoft Teams: link to join

Local organiser

Alex Fink, Queen Mary University of London

Registration

If you wish to attend the meeting, even remotely, please register by sending an e-mail 📬 to Alex Fink (a.fink@qmul.ac.uk). We have some funds to support ECRs and PhDs, please let us know if you would like financial support with travel to attend the meeting by emailing Alex Fink (a.fink@qmul.ac.uk) or Nelly Villamizar (n.y.villamizar@swansea.ac.uk).

Schedule

Monday 15th September 2025

11:30–12:50 Gather for lunch at The Curve (#47 on the map). Find Primoz Skraba and Felipe Rincón when you arrive: they will have lunch vouchers.

13:00–13:50 Primoz Skraba 

14:00–14:45 Coffee

14:45–15:35 Daniel Hendron 

16:00–16:50 Sergey Sergeev

17:00 Proceed to informal pub gathering with dinner options

Titles and abstracts

Anthea Monod, Imperial College London

Title: Topological Graph Kernels from Tropical Geometry 

Abstract: We introduce a new class of graph kernels based on tropical geometry and the topology of metric graphs. Unlike traditional graph kernels that are defined by graph combinatorics (nodes, edges, subgraphs), our approach considers only the geometry and topology of the underlying metric space. A key property of our construction is its invariance under edge subdivision, making the kernels intrinsically well-suited for comparing graphs that represent different underlying spaces. We develop efficient algorithms for their computation which depend only on the graph genus rather than size. In label-free settings, our kernels outperform existing methods, which we showcase on synthetic, benchmark, and real-world data road network data. Joint work with Yueqi Cao.

Primoz Skraba, Queen Mary University of London

Title: Geometry and (Co)Homology Computation

Abstract: In this talk I will discuss the theory and practice of the computational complexity of computing homology.  After a brief overview of the history of the problem, I will discuss when and how geometry can help us compute it. Some examples will be taken from persistent (co)homology of geometric complexes, but the problems will be more generally stated and no prior familiarity will be assumed. Finally, in addition to the theory, I will discuss what is works in practice and what are the challenging scenarios for current techniques.

Daniel Hendron, University of York

Title: Computational Invariant Theory, with Macaulay2

Abstract: Suppose one has an algebraic group G over a field k acting on an algebraic variety V. Perhaps the central question in invariant theory is: which polynomial functions on V are constant along the G-orbits? It turns out these polynomials form a k-algebra, generators for which can be computed explicitly in the case that G is a reductive group. Such computations are often very expensive, but can be useful in various applications. However, most publicly available computer algebra packages focus on the more specific case of G being a linearly reductive group. This is not a problem in characteristic zero, where the two notions coincide, but in positive characteristic it is a huge constraint. In this talk, I will present the basics of computational invariant theory, and showcase some recent work to implement algorithms for the more general reductive case in the language Macaulay2. In the latter part of the talk, I will speak briefly about the non-reductive case (where the situation gets significantly less 'well-behaved').

Sergey Sergeev, University of Birmingham

Title: Algebraic Cryptography based on Tropical Matrix Algebra

Abstract: The algebraic cryptography based on tropical matrix algebra was recently proposed by Grigoriev and Shpilrain, who developed, in particular, a new implementation of the Stickel protocol over the tropical semiring.  The promising features of tropical semiring and related idempotent semirings is the scarcity of invertible matrices which protects the protocols from direct linear algebraic attacks, and the relevance to the NP-hard problem of finding the smallest hitting set of a given family of m sets. Prominent weaknesses, however, are 1) the easy solvability of the tropical linear systems of the form Ax=b, 2) the ultimate periodic regimes of the tropical matrix power sequences. We will explore the effects of these strengths and weaknesses and the main attack techniques.

Based on my joint works with Sulaiman Alhussaini, Any Muanalifah and Craig Collett.

Sponsors

We are grateful for the financial support from the Isaac Newton Institute, the Glasgow Mathematical Journal Learning and Research Support Fund, the Edinburgh Mathematical Society and the London Mathematical Society.