# MATH - members

## Academic staff (11)

### Pierre-Emmanuel Caprace

### Marino Gran

Research interests: categorical algebra, universal algebra, Galois and descent theory, non-abelian homology, Hopf algebras

Research interests: categorical algebra, universal algebra, Galois and descent theory, non-abelian homology, Hopf algebras

### Pascal Lambrechts

My work is in algebraic topology. My recent theme of research are
motivated by the study of moduli spaces coming from
differential topology, like spaces of smooth embeddings and of
diffeomorphisms, using manifold functor calculus, rational homotopy
theory, configuration spaces, operads of little disks, ...

My work is in algebraic topology. My recent theme of research are
motivated by the study of moduli spaces coming from
differential topology, like spaces of s...

### Timothée Marquis

Research interests: Geometric group theory; Kac-Moody groups and algebras; Groups with a BN-pair, Coxeter groups and buildings; Infinite-dimensional Lie groups and algebras; Locally compact groups

Research interests: Geometric group theory; Kac-Moody groups and algebras; Groups with a BN-pair, Coxeter groups and buildings; Infinite-dimensional Lie groups...

### Heiner Olbermann

Mes intérets de recherche se trouvent dans le domaine des équations aux dérivées partielles. Surtout je travaille sur des questions en calcul des variations. En particulier, je m'intéresse à l'élasticité non-linéaire, et à des problèmes variationels qui contiennent en même temps des aspects physiques et géométriques.

Mes intérets de recherche se trouvent dans le domaine des équations aux dérivées partielles. Surtout je travaille sur des questions en calcul des variations. En...

### Augusto Ponce

Partial differential equations; nonlinear analysis

Partial differential equations; nonlinear analysis

### Tim Van der Linden

Research in homological algebra: study of homology and cohomology of non-algebraic objects using categorical methods, such as Galois theory of higher central extensions

Research in homological algebra: study of homology and cohomology of non-algebraic objects using categorical methods, such as Galois theory of higher central extensions

### Jean Van Schaftingen

I am working in mathematical analysis, on problems in the fields of partial differential equations, calculus of variations and function spaces, including endpoint L¹ estimates for differential operators, Sobolev mappings, Ginzburg-Landau functionals, vortices
in fluid dynamics, magnetic Sobolev spaces and semi-linear elliptic problems.

I am working in mathematical analysis, on problems in the fields of partial differential equations, calculus of variations and function spaces, including endpoi...

### Pedro Vaz

Knot theory and quantum topology,
Higher representation theory and its applications in low-dimensional topology,
Categorification of quantum algebras and its 2-representation theory.

Knot theory and quantum topology,
Higher representation theory and its applications in low-dimensional topology,
Categorification of quantum algebras and its...

### Enrico Vitale

Je participe à la recherche de l’équipe de théorie des catégories. Notre recherche se concentre sur l'algèbre catégorique: plus particulièrement, nous développons certains nouveaux aspects de la théorie des catégories utiles en algèbre homologique non abélienne, algèbre homotopique de dimension supérieur, algèbre universelle et algèbre topologique, théorie de la descente et théorie de Galois, théorie des algèbres de Hopf et des quandle.

Je participe à la recherche de l’équipe de théorie des catégories. Notre recherche se concentre sur l'algèbre catégorique: plus particulièrement, nous développo...

## Professors emeriti (2)

### Yves Felix

topologie algébrique, homotopie rationnelle

topologie algébrique, homotopie rationnelle

### Michel Willem

nonlinear partial differential equations, global analysis, calculus of variations,
functional analysis, real analysis, history of mathematics

nonlinear partial differential equations, global analysis, calculus of variations,
functional analysis, real analysis, history of mathematics

## Postdocs (10)

### Sebastian Bischof

### Federico Campanini

My research interests are quite various and include substantially different topics in Commutative and non-Commutative Algebra, Module Theory and Category Theory. They may be listed as follows:
- Weak forms of the Krull-Schmidt Theorem in additive and module categories;
- Prüfer-like conditions in commutative rings with zero-divisors;
- Factorizations in commutative monoids;
- Homological algebra;
- Torsion and pretorsion theories in general categories.

My research interests are quite various and include substantially different topics in Commutative and non-Commutative Algebra, Module Theory and Category Theory...

**Office: **
B428

### Arnaud Duvieusart

I work on new applications of Categorical Galois Theory in Mal’tsev and semi-abelian categories, especially in relation to internal groupoids and crossed modules.

I work on new applications of Categorical Galois Theory in Mal’tsev and semi-abelian categories, especially in relation to internal groupoids and crossed modules.

**Office: **
B.430

### Pierre-Alain Jacqmin

My main research interests lie in Category Theory, and more specifically in Categorical Algebra and Universal Algebra. My aim is to deeper understand algebraic categorical properties such as the Mal'tsev, unital or semi-abelian properties; in particular via some embedding theorems or preservation under the cofiltered limit completion. I am also interested in internal groupoids, weak equivalences and their bicategory of fractions as well as in finiteness spaces and generalized rings of power series.

My main research interests lie in Category Theory, and more specifically in Categorical Algebra and Universal Algebra. My aim is to deeper understand algebraic...

### Geoffrey Janssens

My research has spanned several areas of mathematics, however always centered around the study of the representations of the given object. Nowadays my focus is on finite dimensional representations of quantum affine algebras via geometric realisations. Hereby the angle is additive and monoidal categorification of an underlying cluster algebras.
Earlier my research focused on integral representation theory of finite groups, via connections to arithmetic groups. The latter can be thought as the integer points of semisimple linear algebraic groups of which the group of units of the integral group ring is an example of. The overarching quesiton here is which properties of the finite group can reconstructed out of the geometric group theoretical properties of the simple factors of the overlying algebraic group.

My research has spanned several areas of mathematics, however always centered around the study of the representations of the given object. Nowadays my focus is...

**Office: **
B403

### Benjamin Lledos

I am interested in the uniqueness, regularity, and qualitative properties of solutions to minimization problems in the calculus of variations or elliptic PDEs.

I am interested in the uniqueness, regularity, and qualitative properties of solutions to minimization problems in the calculus of variations or elliptic PDEs.

### Julia Ramos González

My main research interests are category theory and homological algebra. I am particularly interested in the interplay of these fields with algebraic geometry in order to approach noncommutative algebraic geometry, where both abelian categories and enhancements of triangulated categories are used as models for noncommutative spaces. I am therefore interested in many different related areas: topos theory, localizations and categories of fractions, algebraic categories, triangulated and dg categories, infinity-categories, deformation theory…

My main research interests are category theory and homological algebra. I am particularly interested in the interplay of these fields with algebraic geometry in...

## PhD students (18)

### Robynn Corveleyn

I am interested in a wide range of topics within geometric group theory and representation theory of (locally compact) groups. Currently my focus is on understanding the finite simple quotients of Kac-Moody-Steinberg groups and their relationship to high-dimensional expanders.

I am interested in a wide range of topics within geometric group theory and representation theory of (locally compact) groups. Currently my focus is on understa...

**Office: **
B.323

### Maxime Culot

Working in the area of homological algebra in a non-abelian context. More precisely, I am working a non-additive version of the left derived functors. This leads me to the study of homotopy of chain complex and a bit of model theory.

Working in the area of homological algebra in a non-abelian context. More precisely, I am working a non-additive version of the left derived functors. This lead...

**Office: **
B.422

**Email: ** maxime.culot@uclouvain.be

### David Forsman

My PhD-topic is to develop a non-abelian theory of spectral sequences. Double semi-simplicial groups have certain spectral sequences associated to them. The motivating question is how much can we generalize this to the semi-abelian context.

My PhD-topic is to develop a non-abelian theory of spectral sequences. Double semi-simplicial groups have certain spectral sequences associated to them. The mot...

**Office: **
B.404

**Email: ** david.forsman@uclouvain.be

### Maximilien Forte

I am a first year PhD student in Geometric Group Theory. I am currently working in the construction of t.d.l.c groups containing uniform lattices. Keywords : wall space, polyhedral complex, CAT(0) metric.

I am a first year PhD student in Geometric Group Theory. I am currently working in the construction of t.d.l.c groups containing uniform lattices. Keywords : wa...

**Office: **
B.303

### Lucy Grossman

Projet principal actuel: une généralisation des théories de prétorsion aux catégories infinies.
Autres intérêts de recherche: structures supérieures et fondaments des mathématiques, K-théorie algébrique, physique mathématique.

Projet principal actuel: une généralisation des théories de prétorsion aux catégories infinies.
Autres intérêts de recherche: structures supérieures et fondam...

**Office: **
B.429

**Email: ** lucy.grossman@uclouvain.be

### Alex Loué

I am interested in various aspects of discrete groups such as their geometric and combinatorial features, or their representation theory. Currently, my focus is set on the construction and description of new families of hyperbolic groups with property (T).

I am interested in various aspects of discrete groups such as their geometric and combinatorial features, or their representation theory. Currently, my focus is...

**Office: **
B.321

**Email: ** alex.loue@uclouvain.be

### Sébastien Mattenet

Did my masters thesis in topos theory.
Currently writing about Lyapunov theory in categorical terms, specifically the converse lyapunov theorem that a system with an equilibrium point must have a corresponding "energy function" (lyapunov fucntion, ie a function that decrease on trajectory and "sufficiently" smooth) that serve as a certificate for the stability.

Did my masters thesis in topos theory.
Currently writing about Lyapunov theory in categorical terms, specifically the converse lyapunov theorem that a system w...

**Office: **
Euler a1.01

### Léo Schelstraete

I work on the interplay between knot theory and higher representation theory. More precisely, I'm interested in an invariant of knots called odd Khovanov homology, which can be thought as a categorification of the Jones polynomial. I try to understand it through the categorification of (the representation theory of) quantum algebras.

I work on the interplay between knot theory and higher representation theory. More precisely, I'm interested in an invariant of knots called odd Khovanov homolo...

**Office: **
B.429

### Corentin Vienne

Research in categorical algebra, in particular semi-abelian categories. We are studying consequences of categorical conditions, such as action representability, in varieties of non-associative algebras.

Research in categorical algebra, in particular semi-abelian categories. We are studying consequences of categorical conditions, such as action representability,...

**Office: **
B.427

**Email: ** corentin.vienne@uclouvain.be

### Leon Winter

I am working on open problems regarding Sobolev mappings (valued in a manifold). The set of all Sobolev mappings is in general not a vector space and its study is therefore very different from a vector valued Sobolev space.

I am working on open problems regarding Sobolev mappings (valued in a manifold). The set of all Sobolev mappings is in general not a vector space and its study...

**Office: **
B.322

**Email: ** leon.winter@uclouvain.be

### Daniel Zimmer

The goal of my research is to investigate the topology of spaces of embeddings, using tools from algebraic topology ; more precisely, I investigate cosimplicial models for such spaces built using the calculus of functors.

The goal of my research is to investigate the topology of spaces of embeddings, using tools from algebraic topology ; more precisely, I investigate cosimplicial...