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Systoles and Lagrangians of random complex projective hypersurfaces

Recent developments in microlocal analysis October 14, 2019 - October 18, 2019

October 17, 2019 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Damien Gayet (Université de Grenoble I (Joseph Fourier))
Location: MSRI: Simons Auditorium
Tags/Keywords
  • Geodesic

  • random submanifolds

  • Lagrangian submanifolds

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

15-Gayet

Abstract

The smooth degree d complex curves of are Riemann surfaces of the same genus   . If we equip them with the restriction of the ambient metric and choose them at random, what can be say about the length of their systole? I will explain that the probability that the systole is of the order  is bounded from below by a uniform positive constant. This gives an partial analogous result to Mirzakhani's theorem on random hyperbolic curves. If I have time, I will explain that in higher dimensions, these probabilistic arguments provide a new deterministic result about Lagrangian submanifolds and the topology of complex projective hypersurfaces.

Supplements
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Video/Audio Files

15-Gayet

H.264 Video 899_27589_8049_15-Gayet.mp4
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