Sylvie Paycha, Professor

Universität Potsdam - Institut für Mathematik

(Recent) Publications

Here is a selection of publications (updated August 2017):

  • -(book) Regularised integrals, sums and traces; analytic aspects, Amer. Math. Soc. Univ. Lecture Notes, Vol. 59 (2012)
  • -(with M.Arnaudon) Factorisation of semi-martingales on principal fibre bundles, Stochastics and Stochastic Reports 53, p. 81-107 (1995)
  • - (with M. Arnaudon) Sochastic tools on Hilbert manifolds; Interplay with geometry and physics, Comm. Math. Phys, 187, p.243-260 (1997)
  • - (with S. Rosenberg) Curvature on determinant bundles and first Chern forms, Journ. Geom. Phys. 45, p.393-429 (2003)
  • -(with S. Scott) A Laurent expansion for regularised integrals of holomorphic symbols, Geom. And Funct. Anal.(2) 17, p. 491-536 (2007)
  • -(with J.-M. Lescure) Traces on pseudodifferential operators and associated determinants, Proc. London Math. Soc. (2) 94, p. 772-812 (2007)
  • - (Second) quantised resolvents and regularised traces, Journ. Geom. Phys. 57, p. 1345-1369 (2007)
  • - (with J. Mickelsson) Renormalised Chern-Weil forms associated with families of Dirac operators, Journ. Geom. Phys. 57, p. 1789-1814 (2007)\\
  • -(with D. Manchon) Shuffle relations for regularised integrals of symbols, Comm. Math. Phys. 270, p. 13-51 (2007)
  • - Renormalised multiple integrals of symbols with linear constraints, Comm. Math. Phys. 266, p. 495-540 (2006)
  • - (with D. Manchon) Nested sums of symbols and renormalised multiple zeta values, Int. Math. Research Notices, Vol 2010, N. 24, p. 4628-4697
  • - A canonical trace associated with spectral triples, SIGMA 6 (2010), 077, 17 pages (http://www.emis.de/journals/SIGMA/2010/077/)
  • - (with J. Mickelsson) The logarithmic residue density of a generalized Laplacian, Journal of the Austral. Math. Soc. Vol. 90, N. 01, p. 53 -- 80 (2011)
  • - Noncommutative formal Taylor expansions and second quantised regularised traces, in Combinatorics and Physics, (Ed. K. Ebrahimi-Fard, M. Marcolli, W.D. van Suijlekom) Contemporary Mathematics 539, p. 349-376, Amer. Math. Soc. (2011)
  • -(with L.Guo and B. Zhang) Renormalization by Birkhoff factorization and by generalized evaluators; a study case in "Noncommutative Geometry, Arithmetic and Related Topics", (Ed. A. Connes, K. Consani) John Hopkins Univ. Press p. 183-- 211 (2011)
  • -(with M-F. Ouedraogo) The multiplicative anomaly for determinants revisited; locality, Comm. Math. Annal. 12 p. 28-63 (2012)
  • - Affine transformations on symbols, in Analysis, Geometry and Quantum Field Theory, (Ed. C. L. Aldana, M. Braverman, B. Iochum, C. Neira Jimenez), Contemporary Mathematics 584, Amer. Math. Soc. p. 199--222 (2012)
  • -(with L. Guo and B. Zhang) Conical zeta values and their double subdivision relations, Adv. in Math. 252 p. 343-381 (2014)
  • - (with C. Lévy and C. Neira-Jimenez) The canonical trace and the noncommutative residue on the noncommutative torus, Trans. Amer. Math. Soc., 368, N. 2, 1051-1095 (2016)
  • -(with L. Guo and B. Zhang) Algebraic Birkhoff Factorization and the Euler-Maclaurin formula on cones, Duke Math. Journ. 166, p. 537--571 (2016)
  • -(with L. Guo and B. Zhang) Renormalised conical zeta values, to appear in a publication (Springer Verlag) of the Scuola Normale Superiore in Pisa
  • -(with S. Azzali) Spectral Ζ-invariants lifted to coverings, to appear in the Trans. London Math. Soc.