This is the website for the weekly Geometry and Topology seminar at MIT. The seminar meets on Mondays at 3:30-4:30PM, in room 2-449. Please contact Jonathan Zung (jzung@mit.edu) if you'd like to be added to our seminar mailing list.
Fall 2025
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Sep 15: Boundary Currents of Hitchin Components
by Charlie Reid
A hyperbolic structure on a surface is described by a representation of the fundamental group into PSL(2,R). Higher rank Teichmüller theory aims to go beyond hyperbolic geometry by studying moduli spaces of representations into bigger Lie groups, most quintessentially SL(n,R). I will discuss a SL(n,R) version of a classic piece of hyperbolic geometry—Thurston's compactification of Teichmüller space. Boundary points of Thurston's compactification are measured laminations: certain analytic objects generalizing simple closed curves. One can define a compactification of the SL(n,R) Hitchin component in much the same way, whose boundary points are now geodesic currents which generalize closed curves with more intricate restrictions on self-intersection. Dual to these geodesic currents are n-1 dimensional polyhedral spaces which generalize R-trees.
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Oct 6: TBA
by Boyu Zhang
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Oct 20: TBA
by Seraphina Lee
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Nov 3: TBA
by Josh Wang
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Nov 17: TBA
by Andreas Stavrou
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Nov 24: TBA
by Ali Sadr
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Dec 1: TBA
by Antonio Alfieri
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Dec 8: TBA
by Mike Miller Eismeier