The Antwerp Algebra Colloquium takes place monthly. Each session consists of two one-hour-long colloquia sharing a common thread. The focus is set on learning the basics on different areas of algebra. The colloquia are thus meant to be accessible for researchers from all domains of algebra.

For now, due to the covid-19 pandemic, all colloquia are held online on Blackboard Collaborate.

If you want to be informed about the upcoming sessions of the colloquium and get the corresponding links to the talks on Blackboard Collaborate, you can subscribe to our mailing list.

If, moreover, you want to automatically update your calendar app with the schedule of the sessions, you can also subscribe to our calendar here.

## Upcoming session

The next session of the Antwerp Algebra Colloquium will be announced soon.

## Previous sessions

You can find the speakers and abstracts of our previous editions below.

## 2021

**23 April 2021**

Antwerp Algebra Colloquium on *higher structures*:

- 14:00 - 15:00 –
*Higher Structures in Algebra, Geometry, and Topology*–**Bruno Vallette**(Université Sorbonne Paris Nord) (slides, video)

The goal of this talk will be to introduce the audience with higher structures (homotopy algebras, operadic calculus and higher categories). These structures and the way to work efficiently with them were extensively studied over the past 30 years. We will show that their consideration is mandatory to formulate and to establish some open conjectures in Algebra, Geometry, and Topology.

- 5:15 - 16:15 –
*Endofunctors and Poincaré-Birkhoff-Witt theorems*–**Pedro Tamaroff**(Trinity College Dublin) (slides, video)

In joint work with V. Dotsenko, we developed a categorical framework for Poincaré-Birkhoff-Witt type theorems about universal enveloping algebras of various algebraic structures, and used methods of term rewriting for operads to obtain new PBW theorems, in particular answering a question of J.-L. Loday. Later, in joint work with A. Khoroshkin, we developed a formalism to study Poincaré–Birkhoff–Witt type theorems for universal envelopes of algebras over differential graded operads, motivated by the problem of computing the universal enveloping algebra functor on dg Lie algebras in the homotopy category. I will survey and explain the role homological algebra, homotopical algebra, and effective computational methods play in the main results obtained with both V. Dotsenko (1804.06485) and A. Khoroshikin (2003.06055), and mention further directions where these ideas have been or can be applied.

**5 March 2021**

Antwerp Algebra Colloquium on *combinatorics in algebra*:

- 14:00 - 15:00 –
*Buildings: what’s the point (set)?*–**Anneleen De Schepper**(Universiteit Gent) (slides)

It is my intention to give a gentle introduction to (spherical) buildings, from the viewpoint of incidence geometry. This means that I will consider point-line geometries (Grassmannians) associated to them, which amounts to selecting one type of objects of the building as the 'points' (the 'lines' then can be deduced from this). An elementary axiom system was introduced by Cooperstein in the 70'ies exactly to capture the behaviour of such point-line geometries associated to spherical buildings, giving rise to the notion of 'parapolar spaces'. I will mention some old and recent partial classification results in the theory of parapolar spaces, giving surprisingly easy descriptions of geometries related to the exceptional algebraic groups F_{4}, E_{6}, E_{7}, E_{8}, and their classical subgeometries.

- 15:15 - 16:15 –
*Mustafin degenerations: Between applied and arithmetic geometry*–**Marvin Anas Hahn**(Max-Planck-Institut für Mathematik in den Naturwissenschaften) (video)

The study of degenerations is at the core of algebraic and arithmetic geometry. An especially interesting class of degenerations is provided by so-called "Mustafin degenerations", which may be studied via combinatorics in Bruhat-Tits buildings. Moreover, this class is accessible by computer algebra. In this talk, we will give an introduction to their beautiful theory and outline some of their applications in arithmetic and applied geometry. In particular, we will report on recent advances towards a p-adic Narasimhan-Seshadri theorem and a connection between computer vision and Hilbert schemes.

**19 February 2021**

Antwerp Algebra Colloquium at the* intersection of algebra and logic:*

- 14:00-15:00 –
*An introduction to the theory of Borel complexity of classification problems*–**Julien Melleray**(Université Lyon 1) (video)

A common theme throughout mathematics is to try and classify a class of objects according to some notion of isomorphism, and try to produce some nice invariants for this classification. Sometimes, nice invariants cannot exist; and one is led to the idea of comparing complexities of classification problems. Many such problems fit in a framework introduced by Friedman and Stanley in the eighties: Borel complexity of equivalence relations. I will explain this framework and give some examples related to classification of some classes of countable groups up to isomorphism (abelian groups, torsion-free abelian groups of finite ranks, locally finite simple groups...).

- 15:15-16:15 –
*An introduction to o-minimality*–**Siegfried Van Hille**(KU Leuven) (video)

In this talk we discuss various properties of o-minimal structures. The goal is to explain how the simple o-minimality property ensures a “tame” geometry, where tame is the idea envisaged by Grothendieck in his “Esquisse d’un progamme”. I will highlight some important algebraic and geometric concepts that are used to prove that a structure is o-minimal. Finally, if time permits, I will also discuss more recent developments in the study of rational points on transcendental sets.

## 2020

**18 December 2020 **

Antwerp Algebra Colloquium on *semigroups and lattices*:

- 14:00-15:00 -
*Two Dimensional Inverse Semigroups/Categories*-**Darien DeWolf**(St. Francis Xavier University)

Double inverse semigroups were defined by Kock in 2007 to be sets equipped with two compatible inverse semigroup operations. However, we showed that such structures exhibit an Eckmann-Hilton property: such a double inverse semigroup is always proper (both operations are equal) and commutative. This talk will present double inverse semigroups instead as certain double categories, following the program of Brown’s double group theory. We will show that this approach is further justified by internalizing Cockett and Lack’s restriction categories.

- 15:15-16:15 -
*Set-theoretic solutions of the Yang-Baxter equation and associated algebraic structures*-**Charlotte Verwimp**(VUB) (video)

The Yang-Baxter equation originates from papers by Yang and Baxter on quantum and statistical mechanics, and the search for solutions has attracted numerous studies both in mathematical physics and pure mathematics. As the study of arbitrary solutions is complex, Drinfeld proposed in 1992 to focus on the class of set-theoretic solutions. The goal is simple, find all set-theoretic solutions of the Yang-Baxter equation. One part of this research domain focuses on describing the algebraic structures that arise from set-theoretic solutions, for example the structure group and monoid. Another part attempts to find algebraic structures that provide set-theoretic solutions, like braces and skew lattices.

In this talk we try to give a glimpse in the world of set-theoretic solutions of the Yang-Baxter equation. We briefly introduce all notions mentioned above, give some background and motivation, and discuss important results.