Sylvie Paycha, Professor

Universität Potsdam - Institut für Mathematik

Research Topics

A brief overview

My work has been centered for many years on regularisation and renormalisation methods

  • in geometry, e.g. to make sense of the Ricci curvature on an infinite dimensional manifold,
  • in combinatorics, e.g. to count integer lattice points on cones,
  • in number theory, e.g. to evaluate multizeta functions at poles,
by means of

  • analytic tools such as pseudodifferential operators and symbols,
  • differential geometric tools such as Chern-Weil forms and determinant bundles,
  • algebraic tools such as Hopf algebras,

and borrowing ideas and methods from both physics and mathematics, namely from perturbative quantum field theory, noncommutative geometry, index theory and the geometry of cones.