Systoles and Lagrangians of random complex projective hypersurfaces

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.

Mathematics

Audience: researchers in the topic

SISSA Mathematical Glimpses

Series comments: Description: Online colloquia

The list of seminars in this series, together with their Zoom links, is available at:

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