About me
Currently, I am a postdoc in the Department of Mathematics of the University of Luxembourg, part of the research group of Sarah Scherotzke and Pieter Belmans.
Before that I was a PhD student at the University of Glasgow under the supervision of Michael Wemyss and Ben Davison. After finishing my PhD in 2021, I spent a year as a guest researcher at the Max-Planck institute in Bonn, before moving to Luxembourg.
My research centres 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:
| ogier.vangarderen@uni.lu | |
|---|---|
| Address |
Maison du Nombre |
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:
- stability conditions, which breaks down moduli spaces into more manageable strata,
- tilting theory, which relates moduli spaces of sheaves to moduli spaces of quivers,
- deformation theory, which expresses the local geometry of the space using homological algebra
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 working on a project involving differential-geometric deformation theory, in order to understand analytic open neighbourhoods of moduli spaces. I am also looking into noncommutative projective geometry, together with other members of the working group in Luxembourg.
Papers
The pre-prints for all my other articles can be found via the arXiv links below:
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Vanishing and Symmetries of BPS invariants for cDV singularities, submitted [arXiv:2207.13540]
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Stability over cDV singularities and other complete local rings, to appear in ASPM [arXiv:2107.07758]
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Donaldson-Thomas invariants of length 2 flops, submitted [arXiv:2008.02591]
My PhD thesis is available here.
Talks
Below is a list of talks and presentations I have given in seminars and conferences:
- "Geometric and Combinatorial Methods in Homological Algebra" (July 2022)
- Seminar Algebraic Geometry in Bonn (May 2022)
- Oberseminar at MPIM Bonn (April 2022)
- Nottingham Online Algebraic Geometry Seminar (November 2021)
- "The MCKay correspondence, mutation and related topics" at Kavli IPMU (August 2020)
- Algebra & Number Theory Seminar in Glasgow (November 2020)
- COW/CALF seminar in Warwick (September 2019)
- "The Geometry of Derived Categories" in Liverpool (September 2019)
- GEARS seminar in Edinburgh (April 2019)
- GEARS seminar in Edinburgh (April 2018)
I am always happy to talk about my research, so please feel free to invite me to your seminar!