I will explain how to approach the question of E2-formality of differential graded algebras over a prime field via obstruction theory. In particular, E2-algebras whose cohomology ring is a polynomial algebra on even degree classes are intrinsically formal. As a consequence we can prove E2-formality of the classifying space of some compact Lie group or of Davis-Januszkiewicz spaces.

Hyperbolic reflection groups appear in various fields of mathematics such as algebraic geometry, discrete subgroups of Lie groups, geometric group theory, geometric topology, and number theory. Cofinite and cocompact hyperbolic reflection groups have the following feature: their fundamental domains are Coxeter polyhedra having simple geometric and combinatorial properties. Based on these properties, Vinberg initiated the theory of hyperbolic reflection groups and proved several fundamental and remarkable theorems related to their arithmeticity and commensurability classes. I will give a survey of this field, and will mention a few recent results in this direction. This talk is partially based on my work with S. Douba and J. Raimbault.

LaTeX is a document preparation system widely used in mathematics. Every mathematician is expected to know how to use LaTeX. It is used not only for typesetting papers and theses but also for graphics, presentations and CVs. At its core, LaTeX is a mark-up language (similar to markdown or HTML) where plain text special commands produce well-formatted math and other document constructs. Computer programs (such as pdflatex or lualatex) compile LaTeX source files to create beautiful PDFs.

The LaTeX workshop is facilitated by Kelvin Chan. Everyone is welcome, even if you already know some LaTeX. The workshop will be tailored to the needs of the audience.

We will gain some hands-on experience with LaTeX. At the end of the workshop, you will

know the basics of LaTeX to typeset a wide range of mathematical entities, have created a basic paper or presentation, have successfully produced PDFs from your skeleton document, know how to manage multi-file projects know some LaTeX technical terms so you know how to ask for help and have references for more LaTeX-related goodies.

Participants should bring a laptop with a local LaTeX installation (see https://tug.org/texlive/) or an Overleaf.com account.

Overleaf is free and suitable for learning LaTeX and typesetting short documents. However, collaboration features require a paid subscription. You can get paid Overleaf features for free with a local installation. Windows users should follow the easy install instructions. The full package includes an editor called TeXworks. Mac users should install MacTeX. It includes an editor called TeXShop. If you can run TeXworks on Windows or TexShop on Mac, your installation is ready. Don't worry if you run into problems. We will help you get a local installation up and running.

In many applications, matrices are often only partially known or contain elements influenced by randomness. This raises the question: what can we say about the eigenvalues of such matrices? Do they follow any patterns, and can we make meaningful predictions about them? In this talk, I will begin with basic examples of matrices with random independent entries and, with the help of computer calculations and accessible undergraduate mathematics, explore the surprising regularities that emerge. I will conclude by sketching a proof of Wigner's Semicircle Law, which shows that, for random matrices, the bell curve familiar from probability theory is replaced by a semicircular distribution.

Free Probability is used to study non-commutative random variables and has its roots in Voiculescu’s work on operator algebras in the 1980s. The notion of free independence serves as the non-commutative analogue of independence in classical probability theory. One of the most famous results in probability theory is the central limit theorem and in this talk we will prove the analogous result in free probability theory, known as the free central limit theorem.  The proof is combinatorial in nature and all relevant notions of Free Probability will be introduced beforehand.