Dr Peter Hochs
Lecturer
School of Mathematical Sciences
Faculty of Engineering, Computer and Mathematical Sciences
Eligible to supervise Masters and PhD  email supervisor to discuss availability.
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.

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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

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Journals
Year Citation 2019 Hochs, P., & Roberts, A. (2019). Normal forms and invariant manifolds for nonlinear, nonautonomous PDEs, viewed as ODEs in infinite dimensions. Journal of Differential Equations, 267(12), 72637312.
2018 Hochs, P., & Wang, H. (2018). A fixed point theorem on noncompact manifolds. Annals of KTheory, 3(2), 235286.
2018 Hochs, P., & Song, Y. (2018). An equivariant index for proper actions II: Properties and applications. JOURNAL OF NONCOMMUTATIVE GEOMETRY, 12(1), 157193.
2018 Hochs, P., Kaad, J., & Schemaitat, A. (2018). Algebraic Ktheory and a semifinite Fuglede–Kadison determinant. Annals of KTheory, 3(2), 193206.
2018 Hochs, P., & Wang, H. (2018). A fixed point formula and HarishChandra's character formula. Proceedings of the London Mathematical Society, 116(1), 132.
Scopus1 WoS22018 Hochs, P., & Wang, H. (2018). Shelstad's character identity from the point of view of index theory. Bulletin of the London Mathematical Society, 50(5), 759771.
WoS12017 Hochs, P., & Mathai, V. (2017). Quantising proper actions on SpinCmanifolds. Asian Journal of Mathematics, 21(4), 631686.
Scopus5 WoS52017 Hochs, P., & Song, Y. (2017). Equivariant indices of Spin(c)Dirac operators for proper moment maps. Duke Mathematical Journal, 166(6), 11251178.
Scopus6 WoS62017 Hochs, P., & Song, Y. (2017). On the Vergne conjecture. Archiv der Mathematik, 108(1), 99112.
Scopus1 WoS22017 Hochs, P., & Song, Y. (2017). An equivariant index for proper actions I. Journal of Functional Analysis, 272(2), 661704.
Scopus1 WoS32016 Hochs, P., & Varghese, M. (2016). Formal geometric quantisation for proper actions. Journal of Homotopy and Related Structures, 11(3), 409424.
Scopus1 WoS12016 Hochs, P., & Mathai, V. (2016). Spinstructures and proper group actions. Advances in Mathematics, 292, 110.
Scopus2 WoS32016 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.
Scopus4 WoS42015 Hochs, P. (2015). Quantisation of presymplectic manifolds, Ktheory and group representations. Proceedings of the American Mathematical Society, 143(6), 26752692.
Scopus8 WoS82015 Hochs, P., & Mathai, V. (2015). Geometric quantization and families of inner products. Advances in Mathematics, 282, 362426.
Scopus11 WoS122009 Hochs, P. (2009). Quantisation commutes with reduction at discrete series representations of semisimple groups. Advances in Mathematics, 222(3), 862919.
Scopus12 WoS132008 Hochs, P., & Landsman, N. (2008). The GuilleminSternberg conjecture for noncompact groups and spaces. Journal of KTheory, 1(3), 473533.
Scopus11 WoS11— Hochs, P., & Wang, H. (n.d.). Orbital integrals and $K$theory classes. Th., 4, 185209.
— Hochs, P., Song, Y., & Yu, S. (n.d.). A geometric formula for multiplicities of $K$types of tempered
representations.— Guo, H., Hochs, P., & Mathai, V. (n.d.). Equivariant Callias index theory via coarse geometry. — Hochs, P., Wang, B. L., & Wang, H. (n.d.). An equivariant AtiyahPatodiSinger index theorem for proper actions. — Hochs, P., Song, Y., & Yu, S. (n.d.). A geometric realisation of tempered representations restricted to
maximal compact subgroups.— Guo, H., Hochs, P., & Mathai, V. (n.d.). Coarse geometry and Callias quantisation. 
Conference Papers
Year Citation 2011 Hochs, P. (2011). Quantisation commutes with reduction at nontrivial representations. In Oberwolfach Reports. 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

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Current Higher Degree by Research Supervision (University of Adelaide)
Date Role Research Topic Program Degree Type Student Load Student Name 2019 CoSupervisor Properties of the Spectra of an Infinite Random Cayley Graph Master of Philosophy Master Full Time Mr Matthias Eduard Fresacher 2018 CoSupervisor Computations in Higher Twisted Ktheory Master of Philosophy Master Full Time Mr David Leonard Brook 2018 Principal Supervisor I will investigate convergence and continuity of functionals defined by orbital integrals, on subalgebras of group C*algebras, generalising results by Samurkas from discrete to nondiscrete groups. I will also investigate applications to Ktheory. Master of Philosophy Master Part Time Mr Nicholas Lawson McLean 
Past Higher Degree by Research Supervision (University of Adelaide)
Date Role Research Topic Program Degree Type Student Load Student Name 2017  2019 CoSupervisor Geometric Khomology and the AtiyahSinger index theorem Master of Philosophy Master Full Time Mr Samuel Mills 
Other Supervision Activities
Date Role Research Topic Location Program Supervision Type Student Load Student Name 2015  2016 CoSupervisor Determinants by Ktheory Radboud University — Master Full Time André Schemaitat 2015  2016 CoSupervisor Towards faster internet connections: connecting cabinets to the fiber glass network Radboud University — Master Full Time Niels Nuemasnn
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External Profiles