MATHEMATICS AND COMPUTER SCIENCE

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


On this site:


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

Hausel T, Mereb M, Wong M. Arithmetic and representation theory of wild character varieties. Journal of the European Mathematical Society. View

Ganev IV. 2018. The wonderful compactification for quantum groups. Journal of the London Mathematical Society. View

Kalinin N, Guzmán Sáenz A, Prieto Y, Shkolnikov M, Kalinina V, Lupercio E. 2018. Self-organized criticality and pattern emergence through the lens of tropical geometry. PNAS: Proceedings of the National Academy of Sciences of the United States of America. 115(35), E8135–E8142. View

Ganev IV. 2018. Quantizations of multiplicative hypertoric varieties at a root of unity. Journal of Algebra. 506, 92–128. View

Lang M, Shkolnikov M. 2018. Harmonic dynamics of the Abelian sandpile. ArXiv. View

View All Publications

Career

since 2016 Professor, IST Austria
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


Additional Information

Download CV
Open Hausel group website



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