Dr Peter Hochs

Peter Hochs
Marie Curie Fellow
School of Mathematical Sciences
Faculty of Engineering, Computer and Mathematical Sciences

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, K-theory and KK-theory.

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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, K-theory and KK-theory.

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 K-theory, K-homology 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

Algebraic and Differential Geometry, Lie Groups, Harmonic and Fourier Analysis, Operator Algebras and Functional Analysis

Journals

Year Citation
2017 Hochs, P. & Song, Y. (2017). On the Vergne conjecture. Archiv der Mathematik, 108, 1, 99-112.
10.1007/s00013-016-0997-9
2017 Hochs, P. & Mathai, V. (2017). Quantising proper actions on Spin$^c$-manifolds. Asian Journal of Mathematics, 21, 4, 631-686.
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, 661-704.
10.1016/j.jfa.2016.08.024
2017 Hochs, P. & Song, Y. (2017). Equivariant indices of Spinc-Dirac operators for proper moment maps. Duke Mathematical Journal, 166, 6, 1125-1178.
10.1215/00127094-3792923
2016 Hochs, P. & Mathai, V. (2016). Spin-structures and proper group actions. Advances in Mathematics, 292, 1-10.
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, 409-424.
10.1007/s40062-015-0109-8
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, 1-22.
10.1016/j.difgeo.2016.07.003
2015 Hochs, P. (2015). Quantisation of presymplectic manifolds, K-theory and group representations. Proceedings of the American Mathematical Society, 143, 2675-2692.
10.1090/S0002-9939-2015-12464-1
2015 Hochs, P. & Mathai, V. (2015). Geometric quantization and families of inner products. Advances in Mathematics, 282, 362-426.
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, 862-919.
10.1016/j.aim.2009.05.011
2008 Hochs, P. & Landsman, N. (2008). The Guillemin-Sternberg conjecture for noncompact groups and spaces. Journal of K-Theory, 1, 3, 473-533.
10.1017/is008001002jkt022
Hochs, P. & Wang, H. (). A fixed point formula and Harish-Chandra'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 semi-finite Fuglede-Kadison 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

Position
Marie Curie Fellow
Phone
83134891
Fax
8313 3696
Campus
North Terrace
Building
Ingkarni Wardli Building
Room Number
7 35
Org Unit
Mathematical Sciences

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