Colloquia/Spring 2025

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date speaker title host(s)
Jan 24 TBA
Jan 31 TBA
Feb 7 Peter Smillie (MPI) (Job Talk) Harmonic maps and geometrization Waldron
Feb 14 TBA
Feb 21 Alex Wright (Michigan) Curve graphs and totally geodesic subvarieties of moduli spaces of Riemann surfaces Apisa
Feb 28 TBA
Mar 7 Daniel Groves (UIC) TBA Uyanik
Mar 14 Yue M. Lu (Harvard) TBA Li
March 19 (Wed) Xuan-Hien Nguyen (Iowa State) Tran Ph.D. Prospective Student Visit Day
Mar 21 Aaron Brown (Northwestern) Schneider LAA Lecture Zimmer
Mar 28 Spring Break
April 4
April 11 Special Colloquium

(combined with Differential Geometry Workshop)

TBA Zhang
April 18 Jack Xin (UC Irvine) Tran
April 29, April 30, May 1 Mladen Bestvina (Utah) Distinguished Lecture Series Uyanik
May 2 Henri Berestycki (Maryland–College Park / EHESS) Graham

Abstracts

February 7: Peter Smillie (MPI) (Job Talk)

Title: Harmonic maps and geometrization

Abstract: Many problems in differential geometry can be studied via the space of representations from the fundamental group $\Gamma$ of a manifold $M$ to a Lie group $G$. Conversely, much of what we know about the space of representations is through this sort of geometrization. For $M$ a closed surface, two fields have emerged in the last thirty years with distinct yet overlapping methods: Higher Teichm\"uller theory focusing more on dynamics and coarse geometry, and Non-Abelian Hodge Theory more algebro-geometric and analytic. A central point of overlap between these two fields is the study of equivariant harmonic maps.

I will give an introduction to both fields, and explain two foundational conjectures of Higher Teichm\"uller theory on the relationship between them. I will then present the resolution of one of these conjectures in the negative (joint work with Nathaniel Sagman) and ongoing work on the resolution of the other in the positive (joint with Max Riestenberg). Time permitting, I will also explain the solution (joint with Philip Engel) of a problem in carbon chemistry, and how it fits into this picture.

February 21: Alex Wright (Michigan)

Title: Curve graphs and totally geodesic subvarieties of moduli spaces of Riemann surfaces

Abstract: Given a surface, the associated curve graph has vertices corresponding to certain isotopy classes of curves on the surface, and edges for disjoint curves. Starting with work of Masur and Minsky in the late 1990s, curve graphs became a central tool for understanding objects in low dimensional topology and geometry. Since then, their influence has reached far beyond what might have been anticipated. Part of the talk will be an expository account of this remarkable story.

Much more recently, non-trivial examples of totally geodesic subvarieties of moduli spaces have been discovered, in work of McMullen-Mukamel-Wright and Eskin-McMullen-Mukamel-Wright. Part of the talk will be an expository account of this story and its connections to dynamics.

The talk will conclude with new joint work with Francisco Arana-Herrera showing that the geometry of totally geodesic subvarieties can be understood using curve graphs, and that this is closely intertwined with the remarkably rigid structure of these varieties witnessed by the boundary in the Deligne-Mumford compactification.