Recent breakthroughs in Mathematics and General Assembly 2025
The Belgian Mathematical Society is happy to invite you to its "Recent breakthroughs in Mathematics" symposium which will take on Wednesday December 17 2025 at ULB, Campus Solbosch (room Somville, building S). On this occasion we will also organise the society's general assembly.
Registration is now closed.
Programme
- 10h30-11h00: Welcome coffee
- 11h00-12h00: Olivier Schiffmann (on Kashiwara – Abel ‘25)
From Young diagrams to Kashiwara crystals
Abstract. The aim of this talk is to give a glimpse of the monumental work of M. Kashiwara in representation theory, by focusing on one topic : the notion of crystal bases and crystal graphs of representations of (semisimple or Kac-Moody) Lie algebras defined via the theory of quantum groups and motivated by statistical physics. If time allows it we will also describe some more recent work of Kashiwara on the problem of categorification. - 12h00-14h00: lunch
- 13h00-13h30: BMS Board meeting
- 13h30-14h00: BMS General assembly
- 14h00-15h00: Dennis Gaitsgory (on his own work – Breakthrough prize ‘25)
Proof of the geometric Langlands conjecture
Abstract. I will explain the various contexts in which the geometric Langlands
conjecture (GLC) can be stated and various logical implications. I will
then outline the main steps involved in the proof in the de Rham context. - 15h00-15h30: Stijn Cambie (YSA'25)
On two resolved Erdős problems
Abstract. The database erdosproblems.com has been released two years ago, and in August 2025 also a forum feature was added.
In this talk, I will present two problems by Erdős that have been resolved through this forum, one in graph theory and one in number theory.
Based on joint work with Koishi Chan and Zach Hunter, and Vjeko Kovač and Terence Tao. - 15h30-16h00: Kevin Iván Piterman (YSA '25)
Fixed points on contractible spaces
Abstract. A fundamental question in mathematics is whether a function on a space must have a fixed point. Classical theorems of Brouwer and Lefschetz show that this often holds when the space is contractible, meaning it has no “holes”. A natural strengthening asks whether an entire family of maps—such as a group of homeomorphisms—must share a common fixed point. Serre proved that this is true for finite groups acting on trees, a result with deep algebraic and geometric consequences.
However, the situation changes sharply in higher dimensions: in 1959, Floyd and Richardson constructed an action of a finite group on a compact contractible 3-complex with no fixed points. By contrast, the 2-dimensional case resisted resolution for many years, appearing as a question of Aschbacher and Segev and independently as a conjecture of Casacuberta and Dicks in 1992.
In this talk, I will discuss recent progress on two problems I have worked on concerning fixed-point properties for group actions on contractible spaces. This includes the resolution of the Casacuberta–Dicks conjecture, joint with I. Sadofschi Costa: Every finite group acting on a compact contractible 2-complex has a fixed point. - 16h00-16h30: coffee break
- 16h30-17h30: Timothée Bénard (on Margulis – Abel ‘20 and Lindenstrauss – Fields ‘10)
On unipotent flows: past and future.
Abstract. Ratner's theorems from the 90s are a cornerstone of dynamical systems. They describe equidistribution properties of unipotent flows on homogeneous spaces and arose from a long series of works involving, among others, Dani, Furstenberg, Hedlund, Margulis, Ratner, and Shah. I will recall those theorems and survey their numerous applications to number theory. I will also explain how the topic has evolved since the 90s, in particular thanks to the use of random walks, and how it reaches today a new key focal point through the question of effectivity. The latest developments involve new methods stemming from harmonic analysis in the spirit of Bourgain's projection theory. - 17h30-18h30: drink