Symplectic geometry seminar

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17 February 2020
15:15-16:30

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no seminar

24 February 2020
15:15-16:30

Damien Gayet
Institut Fourier, Université de Grenoble

Event Details

Title	Systoles and Lagrangians of random projective hypersurfaces
Speaker, Affiliation	Damien Gayet, Institut Fourier, Université de Grenoble
Date, Time	24 February 2020, 15:15-16:30
Location	HG G 43
Abstract	The smooth degree $d$ complex curves of $\mathbb C P^2$ 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 $d^{-1/2}$ is bounded from below by a uniform positive constant, which gives an analogous result to one of Mirzakhani's theorem on random hyperbolic curves. Quite surprisingly, in higher dimensions, similar probabilistic arguments provide a new \emph{deterministic} result about Lagrangian submanifolds and the topology of complex projective hypersurfaces.

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2 March 2020
15:15-16:30

Chris Woodward
Rutgers University

Event Details

Title	Tropical Fukaya algebras
Speaker, Affiliation	Chris Woodward, Rutgers University
Date, Time	2 March 2020, 15:15-16:30
Location	HG G 43
Abstract	Joint with S. Venugopalan. A long-time expectation is that quantum cohomology decomposes into summands corresponding to transitions in the minimal model program. The categorical analog is that the Fukaya category has a similar decomposition, which in some sense is easier since one can often identify objects corresponding to the transitions. I will talk about a new tool that can be used to prove the existence of objects, called the "tropical Fukaya algebra", whose structure maps are sums of products of weights of vertices of tropical graphs (which already appeared in work of B. Parker .....) As a corollary we prove that any "tropical toric moment fiber" is weakly unobstructed. I will give some examples.