Iosif Polterovich

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Iosif Polterovich (born July 24, 1974 ) is an Israeli-Canadian mathematician who deals with geometric and global analysis.

Polterovich (2nd from left) in Oberwolfach 2012, with from left Daniel Grieser, Thomas Hoffmann-Ostenhof, Michiel van den Berg

Polterovich graduated from Lomonosov University in 1995 and received his doctorate from the Weizmann Institute under Yakar Kannai in 2000 ( Computation of Heat Invariants and the Agmon-Kannai Method ). As a post-doctoral student , he was at the Center de Recherches Mathematiques (CRM) of University of Montreal , at the MSRI and at the Max Planck Institute for Mathematics . From 2002 he was a professor at the University of Montreal. Since 2002 he has held the Canada Research Chair in Geometry and Spectral Theory there.

He deals with geometric spectral theory (i.e. the spectrum, for example, of the Laplace-Beltrami operator on manifolds). In 2000, he presented explicit formulas for the heat conduction equation invariants on manifolds in his dissertation , which allow them to be given in a closed form. These invariants are the coefficients of the expansion for small times of the kernel of the heat conduction equation on manifolds (which in the stationary case changes to the Laplace-Beltrami operator).

Further contributions by Polterovich concerned isospectral domains, the asymptotics of the eigenvalues ​​of the Laplace operator and isoperimetric inequalities for eigenvalues.

In 2011 he received the Coxeter James Prize and in 2006 the André Aisenstadt Prize .

In 2008 he received the G. de B. Robinson Award with Dmitry Jakobson and Nikolai Nadirashvili for their work Extremal metric for the first eigenvalue on a Klein bottle (Canad. J. Math. 58, 2006, 381-400). The problem of finding Riemannian metrics for closed surfaces, which make the lowest eigenvalue of the Laplace-Beltrami operator (suitably normalized with the area) extremal, was previously discussed for the 2-sphere ( Joseph Hersch 1970), the real projective plane (P. Li, Shing-Tung Yau 1982) and solved the 2-torus (A. El Soufi, S. Ilias 2000). Polterovich and colleagues solved the difficult case of the Klein bottle .

Fonts

  • with D. Jakobson, N. Nadirashvili: Extremal metric for the first eigenvalue on a Klein bottle. Canad. J. Math. 58 (2006), no. 2, 381-400.

Web links

Individual evidence

  1. ^ Mathematics Genealogy Project
  2. ↑ Polterovich Heat invariants of Riemannian Manifolds , Preprint 1999
  3. ^ Coxeter-James Prize
  4. ^ Aisenstadt Prize
  5. ↑ Arxiv
  6. ↑ Laudation for the Robinson Prize, pdf
  7. ↑ According to Hersch, Yau and others, the product of the first eigenvalue (the keynote of the area) and the area is limited by a constant that increases linearly with the gender of the area. Extremal metrics are minima of the first eigenvalue as a function of gender in the space of Riemannian metrics.
personal data
SURNAME Polterovich, Iosif
BRIEF DESCRIPTION Canadian mathematician
DATE OF BIRTH July 24, 1974