Research Seminars @ Illinois

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Tailored for undergraduate researchers, this calendar is a curated list of research seminars at the University of Illinois. Explore the diverse world of research and expand your knowledge through engaging sessions designed to inspire and enlighten.

To have your events added or removed from this calendar, please contact OUR at ugresearch@illinois.edu

Department Colloquium: Curve counts and cluster varieties

Event Type: Seminar/Symposium
Sponsor: Department of Mathematics
Location: Altgeld 245
Date: May 1, 2025 4:00 pm
Speaker: Gus Schrader (Northwestern)
Views: 137
Originating Calendar: Mathematics Colloquium & Named Lectures; Abstract: One can often solve counting problems depending on a discrete parameter by assembling the different counts as coefficients of a generating function, deriving a differential or algebraic equation for this generating function, and finally solving that equation. I will explain how this method can be applied to a problem of counting holomorphic maps from Riemann surfaces with boundary into $\mathbb{C}^3$, such that the boundary lands on a fixed real (Lagrangian) 3-manifold $L$. It turns out that the equations satisfied by the corresponding generating functions associated to different choices of boundary conditions $L$ can be encoded via a single algebro-geometric object known as a cluster Poisson variety. The rigid combinatorial structure of this auxiliary geometry can then be used to find an explicit formula for the solution of these equations, making manifest nontrivial properties of the original curve counts.
Based on joint works with Mingyuan Hu, Linhui Shen, and Eric Zaslow.

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