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.


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

Yang Y, Zhao G. 2020. The PBW theorem for affine Yangians. Transformation Groups. 25, 1371–1385. View

Kalinin N, Shkolnikov M. 2020. Sandpile solitons via smoothing of superharmonic functions. Communications in Mathematical Physics. View

Rapcak M, Soibelman Y, Yang Y, Zhao G. 2020. Cohomological Hall algebras, vertex algebras and instantons. Communications in Mathematical Physics. 376, 1803–1873. View

Su C, Zhao G, Zhong C. 2020. On the K-theory stable bases of the springer resolution. Annales Scientifiques de l’Ecole Normale Superieure. 53(3), 663–671. View

Minets S. 2020. Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces. Selecta Mathematica, New Series. 26(2). View

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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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