Hausel Group
Geometry and Its Interfaces
How can we understand spaces too large for traditional analysis? Combining ideas from representation theory and combinatorics, the Hausel group develops tools to study the topology of spaces arising from string theory and quantum field theory.
Suppose you have many particles, and consider the space made up of all the ways each particle can move between two points. Now, play the same game with more complicated objects, such as vector fields. The resulting spaces are too large to analyze, but it is possible to simplify them along structural symmetries, giving rise to moduli spaces that are finite-dimensional, but non-compact – again, defying traditional methods. The Hausel group studies the topology, geometry, and arithmetic of these moduli spaces, which include the moduli spaces of Yang-Mills instantons in four dimensions, and Higgs bundles in two dimensions, among others. One question is the number of high-dimensional holes of the spaces. Using methods from representation theory and combinatorics, Hausel and his team are able to give results and conjectures that have previously been described by physicists and number theorists in other terms – connecting a wide variety of fields and ideas.
Group Leader
Administrative Support
Birgit Oosthuizen-Noczil
Assistant to Professors
+43 2243 9000 2150
Team
Current Projects
Geometry, topology, and arithmetic of moduli spaces arising in supersymmetric quantum field theories | Representation theory of quivers, finite groups, Lie and Hecke algebras
Publications
Sisak MA. 2024. T-dual branes on hyperkähler manifolds. Institute of Science and Technology Austria. View
Löwit J. 2024. On modulo ℓ cohomology of p-adic Deligne–Lusztig varieties for GLn. Journal of Algebra. 663, 81–118. View
Hausel T. 2024. Commutative avatars of representations of semisimple Lie groups. Proceedings of the National Academy of Sciences of the United States of America. 121(38), e2319341121. View
Vernet T. 2024. Rational singularities for moment maps of totally negative quivers. Transformation Groups. View
Rychlewicz KP. 2024. Equivariant cohomology and rings of functions. Institute of Science and Technology Austria. View
ReX-Link: Tamas Hausel
Career
Since 2016 Professor, Institute of Science and Technology Austria (ISTA)
2012 – 2016 Professor and Chair of Geometry, EPFL, Lausanne, Switzerland
2007 – 2012 Tutorial Fellow, Wadham College, Oxford, UK
2007 – 2012 University Lecturer, University of Oxford, UK
2005 – 2012 Royal Society University Research Fellow, University of Oxford, UK
2002 – 2010 Assistant, Associate Professor, University of Texas, Austin, USA
1999 – 2002 Miller Research Fellow, Miller Institute for Basic Research in Science, University of California, Berkeley, USA
1998 – 1999 Member, Institute for Advanced Study, Princeton, USA
1998 PhD, Trinity College, University of Cambridge, UK
Selected Distinctions
2013 ERC Advanced Grant
2009 EPSRC First Grant
2008 Whitehead Prize
2005 Sloan Research Fellow
