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Dr Peter Hochs

Peter Hochs
Lecturer
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.

Eligible to supervise Masters and PhD (as Co-Supervisor) — email supervisor to discuss availability.

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

Journals

Year Citation
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
2018 Hochs, P., & Song, Y. (2018). An equivariant index for proper actions II: Properties and applications. JOURNAL OF NONCOMMUTATIVE GEOMETRY, 12(1), 157-193.
DOI
2017 Hochs, P., & Song, Y. (2017). On the Vergne conjecture. Archiv der Mathematik, 108(1), 99-112.
DOI WoS1
2017 Hochs, P., & Song, Y. (2017). An equivariant index for proper actions I. Journal of Functional Analysis, 272(2), 661-704.
DOI Scopus1 WoS3
2017 Hochs, P., & Mathai, V. (2017). Quantising proper actions on Spin$^c$-manifolds. Asian Journal of Mathematics, 21(4), 631-686.
DOI Scopus3 WoS3
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 Scopus2 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 WoS2
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 Scopus7 WoS7
2015 Hochs, P., & Mathai, V. (2015). Geometric quantization and families of inner products. Advances in Mathematics, 282, 362-426.
DOI Scopus10 WoS10
2009 Hochs, P. (2009). Quantisation commutes with reduction at discrete series representations of semisimple groups. Advances in Mathematics, 222(3), 862-919.
DOI Scopus12 WoS12
2008 Hochs, P., & Landsman, N. (2008). The Guillemin-Sternberg conjecture for noncompact groups and spaces. Journal of K-Theory, 1(3), 473-533.
DOI Scopus10 WoS10
Hochs, P., & Wang, H. (n.d.). A fixed point theorem on noncompact manifolds. Th., 3, 235-286.
DOI
Hochs, P., Song, Y., & Yu, S. (n.d.). A geometric realisation of tempered representations restricted to
maximal compact subgroups.
Hochs, P., & Wang, H. (n.d.). Shelstad's character identity from the point of view of index theory.
Hochs, P., & Wang, H. (n.d.). Orbital integrals and $K$-theory classes.
Hochs, P., Song, Y., & Yu, S. (n.d.). A geometric formula for multiplicities of $K$-types of tempered
representations.
Hochs, P., Kaad, J., & Schemaitat, A. (n.d.). Algebraic $K$-theory and a semi-finite Fuglede-Kadison determinant. Th., 3, 193-206.
DOI

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

Current Higher Degree by Research Supervision (University of Adelaide)

Date Role Research Topic Program Degree Type Student Load Student Name
2018 Co-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 Full Time Mr Nicholas Lawson McLean
2018 Co-Supervisor Computations in Higher Twisted K-theory Master of Philosophy Master Full Time Mr David Leonard Brook
2017 Co-Supervisor Non-Commutative Index Theory on Singular Spaces 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
Position
Lecturer
Phone
83134891
Fax
8313 3696
Campus
North Terrace
Building
Ingkarni Wardli Building, floor 7
Room Number
7 35
Org Unit
Mathematical Sciences

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