# 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

## Journals

Year | Citation |
---|---|

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 |

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. & Mathai, V. (2017). Quantising proper actions on spinc-manifolds. Asian Journal of Mathematics, 21, 4, 631-686. 10.4310/AJM.2017.v21.n4.a2 |

2017 | Hochs, P. & Song, Y. (2017). On the Vergne conjecture. Archiv der Mathematik, 108, 1, 99-112. 10.1007/s00013-016-0997-9 |

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. & 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. & Song, Y. (2016). An equivariant index for proper actions III: the invariant and discrete series indices. Differential Geometry and its Applications, 49, 1-22. |

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. & 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. & Wang, H. (). A fixed point theorem on noncompact manifolds. -. | |

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., 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