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.
- 05/01/2022 - Maxim 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.