# Researchers

## Tenured staff

Ieke Moerdijk

Moerdijk's interests lie in algebraic and differential topology, and in applications of topology to logic.
Recently, he has worked on Lie groupoids and algebroids with Crainic and Mrcun, and on operads and model categories with Berger. Currently, in collaboration with Berger, Cisinski and Weiss, he is trying to develop the theory of dendroidal sets (an extension of simplicial sets closely related to operads). With Van den Berg, he also works on sheaf models for predicative logical systems.

Andre Henriques

I do algebraic topology using geometric tools and I study category
theory from the point of view of examples. I also like low dimensional
geometry. My ambitious goal is to use conformal nets and their defects
(which are an analog of algebras and bimodules), in order to construct
a geometric model for elliptic cohomology. Right now, I investigate
the categorical structure of conformals nets. I expect to find
connections with low dimensional topology: knot invariants and
Chern-Simons invariants of 3-manifolds.

Marius Crainic

M. Crainic's general interest is Geometry. His research is at the border
between differential geometry, topology and analysis (the last two often
providing the tools for attacking the geometrical problems).

More specific fields of interest: Poisson and symplectic geometry, moment maps,
Lie groupoids and their applications to geometry, Noncommutative Geometry.
He is also interested (but not yet active as a researcher) in the Geometry
of PDE's and its applications to geometry.

Long time project: Poisson topology . More specific current projects: geometric approach
to Conn's linearization in Poisson geometry, stability of symplectic leaves (with R.L. Fernandes),
and cohomology of classifying spaces (with C.Arias Abad and Benoit Dherin).

## Postdocs

Benoit Dherin

Research interests:

- deformation / geometric quantization

- symplectic / Poisson geometry

- groupoid / algebroid / foliation theory

- graph combinatorics, graph complexes

- operads, algebraic structures "up to homotopy"

Urs Schreiber

My research interest is in understanding the differential geometric and categorical structures underlying what should be called differential nonabelian cohomology: the theory of connections on principal bundles and their generalization to gerbes and principal infinity-bundles.

Ittay Weiss

I'm carrying out research in Algebraic Topology, specifically the study
of up-to-homotopy algebraic structures. I'm mainly concentrating on
research related to dendroidal sets, mots notably I'm working on the
problem of geometric realization of dendroidal sets.

## Phd. students

David Carchedi

David Carchedi is a PhD student of Ieke Moerdijk. His research interests are in higher structures in topology and geometry. Of particular interest are topological and differentiable stacks and their applications (for instance to foliation theory).

Andor Lukacs

My general interest lies in algebraic topology.

I have been working on the homotopy theory of cyclic operads recently.
Currently I study higher categories from the point of view of dendroidal sets,
my first goal is to compare the classical notions of bicategories and tricategories
with the corresponding dendroidal ones. I am also involved in a joint
project with Javier Gutierrez and Ittay Weiss: we are investigating dendroidal
analogs of the Dold-Kan correspondence for simplicial abelian groups.

Ioan Marcut

I am studying for my PhD. under the supervision of Marius Crainic.
The project for my thesis is proving a form of the Reeb stability Theorem in Poisson Geometry.
This should generelize Conn's linearization theorem for smooth Poisson structures, which I am currently trying to understand.
Proving such a theorem should involve geometric techniques (Lie Groupoids/Algebroids), but also techniques from functional analysis.

Wouter Stekelenburg

My research interests in general: category theory and foundations of mathematics. More specifically: by considering structures in topoi, one can make models for theories, that have no classical models. Currently I'm working on structures that model provability: structures that force provable statements only.

## Former Phd. students

Camilio Arias Abad finished his Phd. thesis on Representations up to homotopy and cohomology of classifying spaces under the supervision of Marius Crainic in december 2008.

Giorgio Trentinaglia finished his Phd. thesis on Tannaka Duality for Lie Groupoids under the supervision of Ieke Moerdijk in september 2008.

Ittay Weiss finished his Phd. thesis on Dendroidal Sets under the supervision of Ieke Moerdijk in september 2008.