About Me

Currently, I am a postdoc in mathematics at the University of Luxembourg, part of the research group of Sarah Scherotzke and Pieter Belmans. In September I will start a postdoc at SISSA Trieste.

I got my PhD at the University of Glasgow in 2021 under the supervision of Michael Wemyss and Ben Davison. In 2021/2022 I was a guest researcher at the Max-Planck institute in Bonn.

My research centers on the interaction between enumerative geometry and representation theory. I am interested in enumerative invariants, moduli spaces of quivers, Hall algebras, deformation theory, derived categories, A-infinity algebras, among many other things.



Contact:

Email ogier.vangarderen@uni.lu
Address

Maison du Nombre
6, Avenue de la Fonte
L-4364 Esch-sur-Alzette


Research

My main research area is the part of enumerative algebraic geometry called refined Donaldson--Thomas theory, which is concerned with counting sheaves on complex threefolds. To compute these sheaf counts one has to understand various moduli spaces, which are often quite complicated beasts.

There are various tools one can use to study the moduli spaces appearing in DT theory. The ones I care about are:

The main goal of my research is to make new contributions in these areas, in order to advance our understanding of enumerative geometry. In particular, I am looking to develop techniques that work in noncompact settings, which would allow us to reason about moduli spaces and their invariants using local arguments. Typical examples of such noncompact spaces are crepant resolutions of singularities appearing in the threefold minimal model program, which I studied during my PhD and afterwards.

Currently I am finishing a project on the categorification of certain operations coming from the knots-quivers correspondence.

I am also looking into noncommutative projective geometry, together with other members of the working group in Luxembourg.


Papers

Published

Pre-prints

My PhD thesis is available here.


Talks

Below is a list of talks and presentations I have given in seminars and conferences:

I am always happy to talk about my research, so please feel free to invite me to your seminar!