Colloquia/Spring 2025: Difference between revisions
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| | | [https://petersmillie.github.io/ Peter Smillie] (MPI) (Job Talk) | ||
| | |Harmonic maps and geometrization | ||
| | | Waldron | ||
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| | |[https://websites.umich.edu/~alexmw/ Alex Wright] (Michigan) | ||
|[[# | |[[#Wright| Curve graphs and totally geodesic subvarieties of moduli spaces of Riemann surfaces ]] | ||
| | | Apisa | ||
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|Daniel Groves (UIC) | |[https://homepages.math.uic.edu/~groves/ Daniel Groves] (UIC) | ||
|[[# TBA| TBA ]] | |[[# TBA| TBA ]] | ||
|Uyanik | |Uyanik | ||
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|Yue M. Lu (Harvard) | |[https://lu.seas.harvard.edu/ Yue M. Lu] (Harvard) | ||
|[[# TBA| TBA ]] | |[[# TBA| TBA ]] | ||
| | |Li | ||
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| | |[https://sites.math.northwestern.edu/~awb/ Aaron Brown] (Northwestern) | ||
|[[# TBA| | |[[# TBA| Schneider LAA Lecture ]] | ||
| | |Zimmer | ||
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==Abstracts== | == '''Abstracts''' == | ||
<div id="Wright"> | |||
=== '''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. | |||
Latest revision as of 18:23, 30 January 2025
| 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.