Publications

Preprints

  1. P. Hochs, B.-L. Wang and H. Wang, `An equivariant Atiyah-Patodi-Singer index theorem for proper actions II: the K-theoretic index', ArXiv:2006.08086.
  2. P. Hochs, Y. Song and X. Tang, `An index theorem for higher orbital integrals', ArXiv:2005.06119.
  3. H. Guo, P. Hochs and V. Mathai, `Positive scalar curvature and an equivariant Callias-type index theorem for proper actions', ArXiv:2001.07336.
  4. P. Hochs, B.-L. Wang and H. Wang, `An equivariant Atiyah-Patodi-Singer index theorem for proper actions I: the index formula', ArXiv:1904.11146.
  5. H. Guo, P. Hochs and V. Mathai, `Equivariant Callias index theory via coarse geometry', ArXiv:1902.07391.

Journal papers

  1. H. Guo, P. Hochs and V. Mathai, `Coarse geometry and Callias quantisation', Trans. Amer. Math. Soc., to appear, DOI:10.1090/tran/8202,  ArXiv:1909.11815.
  2. P. Hochs, Y. Song and S. Yu, `A geometric realisation of tempered representations restricted to maximal compact subgroups', Math. Annalen, to appear, DOI:10.1007/s00208-020-02006-4, ArXiv:1705.0208.
  3. P. Hochs and H. Wang, `An equivariant orbifold index for proper actions', J. Geom. Phys. 154 (2020), special issue `Index Theory, Duality and Related Fields', DOI:10.1016/j.geomphys.2020.103710. (ArXiv).
  4. P. Hochs, Y. Song and S. Yu, `A geometric formula for multiplicities of K-types of tempered representations', Trans. Amer. Math. Soc, 372(12) (2019), 8553-8586, DOI:10.1090/tran/7857. (ArXiv)
  5. P. Hochs and A.J. Roberts, `Normal forms and invariant manifolds for nonlinear, non-autonomous PDEs, viewed as ODEs in infinite dimensions', J. Differential Equations 267(12) (2019), 7263-7312, DOI:10.1016/j.jde.2019.07.021. (ArXiv)
  6. P. Hochs and H. Wang, `Orbital integrals and K-theory classes', Ann. K-theory 4(2) (2019), 185-209. (ArXiv)
  7. P. Hochs and Y. Song, `An equivariant index for proper actions II: properties and applications', J. Noncommut. Geometry, 12(1) (2018), 157-193, DOI:10.4171/jncg/273. (ArXiv)
  8. P. Hochs and H. Wang, `Shelstad's character identity from the point of view of index theory', Bull. London Math. Soc. 50 (2018), 759-771, DOI:10.1112/blms.12182. (ArXiv)
  9. P. Hochs and H. Wang, `A fixed point theorem on noncompact manifolds', Ann. K-theory 3 (2) (2018), 235-286, DOI 10.2140/akt.2018.3.235. (ArXiv)
  10. P. Hochs, J. Kaad and A. Schemaitat, `Algebraic K-theory and a semi-finite Fuglede-Kadison determinant', Ann. K-theory, 3(2) (2018), 193-206, DOI 10.2140/akt.2018.3.193. (ArXiv)  
  11. P. Hochs and H. Wang, `A fixed point formula and Harish-Chandra's character formula', Proc. London Math. Soc. (3) 116 (2018), 1-32, DOI:10.1112/plms.12066. (ArXiv)
  12. P. Hochs and V. Mathai, `Quantising proper actions on Spinc-manifolds', Asian J. Math., 21(4) (2017), 631-686, DOI:10.4310/AJM.2017.v21.n4.a2. (ArXiv)
  13. P. Hochs and Y. Song, `Equivariant indices of Spinc-Dirac operators for proper moment maps', Duke Math. J. 166(6) (2017), 1125-1178, DOI:10.1215/00127094-3792923. (ArXiv)
  14. P. Hochs and Y. Song, `On the Vergne conjecture' Arch. Math., 108(1) (2017), 99-112, DOI:10.1007/s00013-016-0997-9. (ArXiv)
  15. P. Hochs and Y. Song, `An equivariant index for proper actions I', J. Funct. Anal. 272(2) (2017), 661-704, DOI:10.1016/j.jfa.2016.08.024. (ArXiv)
  16. P. Hochs and V. Mathai, `Formal geometric quantisation for proper actions', J. Homotopy Relat. Struct. 11(3) (2016), 409-424, DOI:10.1007/s40062-015-0109-8. (ArXiv)
  17. P. Hochs and Y. Song, `An equivariant index for proper actions III: the invariant and discrete series indices', Differential Geom. Appl. 49 (2016), 1-22, DOI:10.1016/j.difgeo.2016.07.003. (ArXiv)
  18. P. Hochs and V. Mathai, `Spin-structures and proper group actions', Adv. Math. 292 (2016), 1-10, DOI:10.1016/j.aim.2016.01.010. (ArXiv)
  19. P. Hochs and V. Mathai, `Geometric quantization and families of inner products', Adv. Math. 282 (2015), 362-426, DOI:10.1016/j.aim.2015.07.004. (ArXiv)
  20. P. Hochs, `Quantisation of presymplectic manifolds, K-theory and group representations', Proc. Amer. Math. Soc. 143 (2015), 2675-2692, DOI:10.1090/S0002-9939-2015-12464-1. (ArXiv)
  21. P. Hochs, `Quantisation commutes with reduction at discrete series representations of semisimple Lie groups', Adv. Math. 222 (2009) 862-919, DOI:10.1016/j.aim.2009.05.011. (ArXiv)
  22. P. Hochs and N.P. Landsman, `The Guillemin-Sternberg conjecture for noncompact groups and spaces', J. K-theory 1(3) (2008) 473-533, DOI:10.1017/is008001002jkt022. (ArXiv)

Conference proceedings

  1. P. Hochs, `Quantisation commutes with reduction at nontrivial representations', extended abstract, workshop  Geometric quantization in the noncompact setting, Mathematisches Forschungsinstitut Oberwolfach report no. 09/2011 (2011).

Thesis

  1. P. Hochs, `Quantisation commutes with reduction for cocompact Hamiltonian group actions', ISBN 978-90-9022607-1, Ph.D. thesis, Radboud University, Nijmegen (2008).