This is the website for the weekly Geometry and Topology seminar at MIT. The seminar meets on Mondays at 4:30-5:30PM, in room 2-449. Please contact Jonathan Zung (jzung@mit.edu) if you'd like to be added to our seminar mailing list.
Fall 2024
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Sep 9: Floer homology and square pegs
by Josh Greene
The Toeplitz square peg problem (1911) asks whether every Jordan curve in the plane contains the vertices of a square. I will describe a construction in symplectic geometry aimed at proving the existence of such inscribed squares and rectangles in a Jordan curve. The construction is a variation on Lagrangian Floer homology, and its associated spectral invariants give some information about the sizes of rectangles in a smooth Jordan curve. The main application I will describe is that in a rectifiable (a.k.a. finite length a.k.a. Lipschitz continuous) Jordan curve, one can find a large family of inscribed rectangles. Joint work with Andrew Lobb.
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Oct 7: TBA
by Anthony Conway
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Oct 21: TBA
by Beibei Liu
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Oct 26: TBA
by Ian Biringer
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Nov 18: TBA
by Lvzhou Chen