The Belgian Mathematical Society is happy to invite you to its "Recent breakthroughs and GA" symposium which will take place online on __Wednesday 15/12/2021 from 1:30 PM to 5:30 PM__.

Aside from the yearly general assembly of the BMS, the event will as usual consist in an afternoon's discussion by international experts on some of the more breathtaking breakthroughs in contemporary mathematics.

In light of the current sanitary situation, we have been obliged to migrate to a __ fully online version__ of the event. All information (including connection codes) will be disclosed in due course to registered participants.

This year the talks will focus on topics which were recently awarded prestigious prizes (particularly the Abel prize and the Shaw prize). All talks will be accessible to large audiences of mathematicians.

On this occasion, the BMS will also award its first "Young Scholar Award", about which more information is available on the dedicated website.

Participation is free but registration is mandatory, see below.

- 13h30-14h10: BMS General Assembly (members only) --
__if you wish to attend and have not received the connection information please send an email to yvik(dot)swan(at)ulb(dot)be__

- 14h20-14h35: Opening in honor of the memory of Jacques Tits (12 August 1930 – 5 December 2021), by Hendrik Van Maldeghem (UGent)

- 14h40-15h30: Shaw prize laureate Jean-Michel BISMUT (Orsay)
- Chair: Joel Fine (ULB)
- Title: Hypoelliptic Laplacian, Brownian motion and the geodesic flow
- Summary:
*I will review some properties of the hypoelliptic Laplacian, which I have been working on for some time now.*

*If X is a compact Riemannian manifold, the hypoelliptic Laplacian is a family of differential operators L_b^X, b>0 acting on mathcal{X}, the total space of the tangent bundle, that interpolates between −∆^X/2, the Laplacian of X, and the vector field Z on mathcal{X}, the generator of the geodesic flow. There is a dynamical counterpart, an interpolates between Brownian motion and the geodesic flow through the Langevin dynamics.*

*The hypoelliptic Laplacian has been applied in many different geometric contexts, in particular to orbital integrals and in complex geometry.*

*In this talk, the case of the circle will be described in detail. We will also explain applications of the hypoelliptic Laplacian in the context of Selberg’s trace formula.*

- 15h35-16h25: Abel prize laureate Avi WIGDERSON (IAP, Princeton)

- Chair: Samuel Fiorini (ULB)
- Title: The Value of Errors in Proofs (a fascinating journey from Turing's seminal 1936 R ≠ RE to the 2020 breakthrough of MIP* = RE)
- Slides
- Summary:
*Last year, a group of theoretical computer scientists posted a paper on the Arxiv with the strange-looking title "MIP* = RE", impacting and surprising not only complexity theory but also some areas of math and physics. Specifically, it resolved, in the negative, the "Connes' embedding conjecture" in the area of von-Neumann algebras, and the "Tsirelson problem" in quantum information theory. You can find the paper here https://arxiv.org/abs/2001.04383*

As it happens, both acronyms MIP* and RE represent proof systems, of a very different nature. To explain them, we'll take a meandering journey through the classical and modern definitions of proof. I hope to explain how the methodology of computational complexity theory, especially modeling and classification (both problems and proofs) by algorithmic efficiency, naturally leads to the generation of new such notions and results (and more acronyms, like NP). A special focus will be on notions of proof which allow interaction, randomness, and errors, and their surprising power and magical properties.

The talk does not assume any special background.

- 16h30-17h20: Professor Imre BARANY (Alfréd Rényi Mathematical Institute and and University College London)
- Chair: Leo Storme (UGent)
- Title: The mathematics of Laszlo Lovasz, a treasure trove of results, proofs, and ideas.
- Slides
- Summary:
*I will review a selection of beautiful results and ideas of Laszlo Lovasz that have mesmerised the mathematical community (and the speaker) for the last 50 years.*

- 17h20-17h30: Announcement of "Young Scholar Award" laureate and closing

Registration is closed; if you want to register please send an email to yvik(dot)swan(@)ulb.be