2025 meeting of the National Committee for Mathematics
The 2025 annual meeting of the National Committee will take place on Thursday, October 2, 2025, at the Palace of the Academies.
Registration is now open until September 26, 2025. Please fill in this form below.
Program:
- 14.00 h: Coffee and welcome; meeting of the national committee (only for members committee)
- 14.30 h: Jozefien D’haeseleer (UGent)
Exploring finite geometry through different codes, intersecting families, and spectral graph theory
Abstract. In this talk I will discuss three distinct but interconnected areas of research that I have investigated in recent years, all linked by the theme of finite geometry.
In the first part, we delve into Erd˝os-Ko-Rado (EKR) problems, a classical topic in combinatorics that explores intersection properties within mathematical structures. The foundational question concerns the maximum size of a family of k-subsets of an n-set, where every pair of subsets have at least one element in common. Erd˝os, Ko, and Rado proved that for n > 2k, the optimal construction involves subsets containing a fixed element. This result, known as the EKR theorem, extends to various other settings, including multisets, permutations, and finite geometries. In this talk, I will discuss both classical and recent results in the context of finite geometries.
The second part will be about generalized Johnson and Grassmann graphs, within the field of spectral graph theory. A central question is whether a graph is uniquely determined by its spectrum (the eigenvalues of its adjacency matrix). While many graphs are known to have this property, numerous well-known graphs possess cospectral mates (non-isomorphic graphs with identical spectra). This phenomenon appears prominently in highly symmetrical graphs, including Johnson and Grassmann graphs. Using techniques such as switching, Aida Abiad, Willem H. Haemers, Robin Simoens and I found a construction of cospectral mates for several specific generalized Johnson and Grassmann graphs.
In the final part, we make the link with coding theory, specifically trifferent codes, also known as perfect q-hash codes for q = 3, which has gained much attention since the 1980s because of their connections to various topics in cryptography, information theory, and computer science. Trifferent codes are ternary codes of length n with the property that for any three distinct codewords there is a coordinate where they all have distinct values. Over the finite field F3, Anurag Bishnoi, Dion Gijswijt, Aditya Potukuchi and I could prove that minimal codes are equivalent to linear trifferent codes, which in turn are equivalent to strong blocking sets in the corresponding projective space. Using this equivalence, we could improve the known upper and lower bounds on the size of linear trifferent codes of length n.
- 15.30 h: Tribute to Marc de Wilde by Pierre Mathonet (ULiège)
- 15.50 h: Lecture by Ann Dooms (VUB)
Can machines think?
Abstract. This question was posed by Alan Turing in his seminal paper, Computing Machinery and Intelligence, laying the cornerstone for artificial intelligence. Mathematics emerged as the critical tool driving this revolution — but how?
In this talk, I will unveil the mathematical foundations powering the technologies that enable machines to “think.” From early theoretical concepts to cutting-edge algorithms, from classification techniques to generative AI. Let us explore how the art of mathematics pushes the limits of machine intelligence.
- 16.50 h: Reception
Everybody is cordially invited. Registration is free but mandatory.
Address: Palace of the Academies, Hertogstraat 1, 1000 Brussel - Rue Ducale 1, 1000 Bruxelles, auditorium Maria-Theresia