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.
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.
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
Date Institution name Country Title 2008 Radboud University The Netherlands PhD
Year Citation 2019 Hochs, P., & Roberts, A. (2019). Normal forms and invariant manifolds for nonlinear, non-autonomous PDEs, viewed as ODEs in infinite dimensions. Journal of Differential Equations, 267(12), 7263-7312.
2018 Hochs, P., & Wang, H. (2018). A fixed point theorem on noncompact manifolds. Annals of K-Theory, 3(2), 235-286.
2018 Hochs, P., & Song, Y. (2018). An equivariant index for proper actions II: Properties and applications. JOURNAL OF NONCOMMUTATIVE GEOMETRY, 12(1), 157-193.
2018 Hochs, P., Kaad, J., & Schemaitat, A. (2018). Algebraic K-theory and a semifinite Fuglede–Kadison determinant. Annals of K-Theory, 3(2), 193-206.
2018 Hochs, P., & Wang, H. (2018). A fixed point formula and Harish-Chandra's character formula. Proceedings of the London Mathematical Society, 116(1), 1-32.
DOI Scopus1 WoS2
2018 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), 759-771.
2017 Hochs, P., & Mathai, V. (2017). Quantising proper actions on SpinC-manifolds. Asian Journal of Mathematics, 21(4), 631-686.
DOI Scopus5 WoS5
2017 Hochs, P., & Song, Y. (2017). Equivariant indices of Spin(c)-Dirac operators for proper moment maps. Duke Mathematical Journal, 166(6), 1125-1178.
DOI Scopus6 WoS6
2017 Hochs, P., & Song, Y. (2017). On the Vergne conjecture. Archiv der Mathematik, 108(1), 99-112.
DOI Scopus1 WoS2
2017 Hochs, P., & Song, Y. (2017). An equivariant index for proper actions I. Journal of Functional Analysis, 272(2), 661-704.
DOI Scopus1 WoS3
2016 Hochs, P., & Varghese, M. (2016). Formal geometric quantisation for proper actions. Journal of Homotopy and Related Structures, 11(3), 409-424.
DOI Scopus1 WoS1
2016 Hochs, P., & Mathai, V. (2016). Spin-structures and proper group actions. Advances in Mathematics, 292, 1-10.
DOI Scopus2 WoS3
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.
DOI Scopus4 WoS4
2015 Hochs, P. (2015). Quantisation of presymplectic manifolds, K-theory and group representations. Proceedings of the American Mathematical Society, 143(6), 2675-2692.
DOI Scopus8 WoS8
2015 Hochs, P., & Mathai, V. (2015). Geometric quantization and families of inner products. Advances in Mathematics, 282, 362-426.
DOI Scopus11 WoS12
2009 Hochs, P. (2009). Quantisation commutes with reduction at discrete series representations of semisimple groups. Advances in Mathematics, 222(3), 862-919.
DOI Scopus12 WoS13
2008 Hochs, P., & Landsman, N. (2008). The Guillemin-Sternberg conjecture for noncompact groups and spaces. Journal of K-Theory, 1(3), 473-533.
DOI Scopus11 WoS11
— Hochs, P., & Wang, H. (n.d.). Orbital integrals and $K$-theory classes. Th., 4, 185-209.
— Hochs, P., Song, Y., & Yu, S. (n.d.). A geometric formula for multiplicities of $K$-types of tempered
— 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 Atiyah-Patodi-Singer 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.
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
Current Higher Degree by Research Supervision (University of Adelaide)
Date Role Research Topic Program Degree Type Student Load Student Name 2019 Co-Supervisor Properties of the Spectra of an Infinite Random Cayley Graph Master of Philosophy Master Full Time Mr Matthias Eduard Fresacher 2018 Co-Supervisor Computations in Higher Twisted K-theory 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 non-discrete groups. I will also investigate applications to K-theory. 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 Co-Supervisor Geometric K-homology and the Atiyah-Singer 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 Co-Supervisor Determinants by K-theory Radboud University — Master Full Time André Schemaitat 2015 - 2016 Co-Supervisor Towards faster internet connections: connecting cabinets to the fiber glass network Radboud University — Master Full Time Niels Nuemasnn
Connect With Me