Géométrie et dynamique dans les espaces de modules

Séminaire Mensuel

Séminaire - Janvier

Le séminaire aura lieu un mercredi par mois de 14h à 15h à l'Institut Henri Poincaré à Paris.  Pour télécharger l'affiche du mois: janvier.pdf.

  • 05/01/2022Maxim Kontsevich (IHES)  -  salle 421

  • Titre: Higher-dimensional generalisation of theory of flat surfaces.

    Resumé: Let \(X\) be a smooth compact manifold of an arbitrary dimension, endowed with a closed complex-valued 1-form \(\alpha\) which is "almost-holomorphic" in the following sense: at each point \(x\) of \(X\) either \(\alpha\) vanishes at \(x\), or the real and the imaginary parts of \(\alpha\) at \(x\) are linearly independent. Using ideas from Morse-Novikov theory and from the wall-crossing formalism, I'll define a topological invariant which is roughly the number of saddle connections in a given homology class. There is an \(SL(2,\mathbb{R})\) action on the moduli space pairs \((X,\alpha)\) (generalising the moduli space of abelian differentials on complex curves). Despite the absence of finite invariant measure, one can still ask questions about generic Lyapunov exponents etc.