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Systoles and Lagrangians of random complex projective hypersurfaces

Damien Gayet
Institution: 
Institut Fourier
Schedule: 
Wednesday, May 6, 2020 - 16:00
Location: 
Online
Location: 
Zoom (sign in to get the link)
Abstract: 

Let $\Sigma\subset \mathbb{R}^n$ be a connected smooth compact hypersurface with non-vanishing Euler characteristic (which implies that $n$ is odd).I will explain that for any $d$ large enough, the homology of any degree $d$ complex hypersurface of $\mathbb{C}P^n$ possesses a basis such that a uniform positive proportion of its members can be represented by a submanifold diffeomorphic to $\Sigma$. Quite surprisingly, the proof is of probabilistic nature.

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