Dr Peter Hochs
I got M.Sc. degrees in mathematics and physics from Utrecht University in the Netherlands in 2003. After that I did a Ph.D. project at the Radboud University in NIjmegen, the Netherlands, supervised by Klaas Landsman and Gert Heckman. That project was about the relations between index theory and representation theory of Lie groups, as well as the problem of quantising a classical theory in physics. After working in industry for a few years I came back to pure mathematics, working at the Leibniz University Hanover in Germany, and at the University of Adelaide.
I am most interested in research into relations between different areas in mathematics. My main area is index theory, where geometry, topology and analysis interact in fundamental ways. I am also interested in links to representation theory of Lie groups, and to noncommutative geometry, Ktheory and KKtheory.
I work in index theory, which is the study of relations between geometry, analysis and topology through differential equations on geometric spaces. I am particularly interested in equivariant index theory for noncompact groups and manifolds, and its relations with geometric quantisation, noncommutative geometry, differential geometry and geometric analysis, Lie theory, links between Ktheory, Khomology and representation theory.
Appointments
Date  Position  Institution name 

2013  Lecturer  The University of Adelaide 
2013  2016  Marie Curie Fellow  Radboud University 
2012  2013  Alexander von Humboldt Fellow  Leibniz University Hanover 
2009  2012  Research Geophysicist  Shell 
2007  2009  Researcher  Netherlands Organisation for Applied Scientific Research TNO 
Education
Date  Institution name  Country  Title 

2008  Radboud University  The Netherlands  PhD 
Research Interests
Journals
Year  Citation 

2017  Hochs, P. & Song, Y. (2017). On the Vergne conjecture. Archiv der Mathematik, 108, 1, 99112. 10.1007/s0001301609979 
2017  Hochs, P. & Mathai, V. (2017). Quantising proper actions on Spin$^c$manifolds. Asian Journal of Mathematics, 21, 4, 631686. 10.4310/AJM.2017.v21.n4.a2 
2017  Hochs, P. & Song, Y. (2017). An equivariant index for proper actions I. Journal of Functional Analysis, 272, 2, 661704. 10.1016/j.jfa.2016.08.024 
2017  Hochs, P. & Song, Y. (2017). Equivariant indices of SpincDirac operators for proper moment maps. Duke Mathematical Journal, 166, 6, 11251178. 10.1215/001270943792923 
2016  Hochs, P. & Mathai, V. (2016). Spinstructures and proper group actions. Advances in Mathematics, 292, 110. 10.1016/j.aim.2016.01.010 
2016  Hochs, P. & Varghese, M. (2016). Formal geometric quantisation for proper actions. Journal of Homotopy and Related Structures, 11, 3, 409424. 10.1007/s4006201501098 
2016  Hochs, P. & Song, Y. (2016). An equivariant index for proper actions III: the invariant and discrete series indices. Differential Geometry and its Applications, 49, 122. 10.1016/j.difgeo.2016.07.003 
2015  Hochs, P. (2015). Quantisation of presymplectic manifolds, Ktheory and group representations. Proceedings of the American Mathematical Society, 143, 26752692. 10.1090/S000299392015124641 
2015  Hochs, P. & Mathai, V. (2015). Geometric quantization and families of inner products. Advances in Mathematics, 282, 362426. 10.1016/j.aim.2015.07.004 
2009  Hochs, P. (2009). Quantisation commutes with reduction at discrete series representations of semisimple groups. Advances in Mathematics, 222, 3, 862919. 10.1016/j.aim.2009.05.011 
2008  Hochs, P. & Landsman, N. (2008). The GuilleminSternberg conjecture for noncompact groups and spaces. Journal of KTheory, 1, 3, 473533. 10.1017/is008001002jkt022 
Hochs, P. & Wang, H. (). A fixed point formula and HarishChandra's character formula. Proceedings of the London Mathematical Society, . 10.1112/plms.12066 

Hochs, P. & Wang, H. (). A fixed point theorem on noncompact manifolds. .  
Hochs, P. & Wang, H. (). Shelstad's character identity from the point of view of index theory. .  
Hochs, P. & Song, Y. (). An equivariant index for proper actions II: properties and applications. .  
Hochs, P., Kaad, J. & Schemaitat, A. (). Algebraic $K$theory and a semifinite FugledeKadison determinant. .  
Hochs, P., Song, Y. & Yu, S. (). A geometric realisation of tempered representations restricted to maximal compact subgroups. . 
Conference Papers
Year  Citation 

2011  Hochs, P. (2011). Quantisation commutes with reduction at nontrivial representations. Geometric quantization in the noncompact setting. Mathematisches Forschungsinstitut Oberwolfach. 
Marie Curie International Outgoing Fellowship, European Union, 2012 (personal fellowship).
Alexander von Humboldt Postdoctoral Fellowship, 2011 (personal fellowship).
Support for Workshop on Geometric Quantisation, AMSI/AustMS, 2015.
Support for workshop Representation theory and Operator algebras, AMSI, 2013