Colloquia/Spring 2025
| date | speaker | title | host(s) | |
|---|---|---|---|---|
| Feb 7 in VV 911 | Peter Smillie (MPI) (Job Talk) | Harmonic maps and geometrization | Waldron | |
| Feb 21 | Alex Wright (Michigan) | Curve graphs and totally geodesic subvarieties of moduli spaces of Riemann surfaces | Apisa | |
| Feb 24 (Monday) | Daniel Bragg (Univ. of Utah) | Murphy’s Law for the moduli stack of curves | Caldararu | |
| Mar 5 (Wednesday) | Eli Weinstein (Columbia) | Probabilistic Experimental Design for Petascale DNA Synthesis | Cochran | |
| Mar 7 | Daniel Groves (UIC) | 3-manifold groups? | Uyanik | |
| Mar 14 | Yue M. Lu (Harvard) | TBA | Li | |
| March 19 (Wed) | Xuan-Hien Nguyen (Iowa State) | The fundamental gap in Euclidean, spherical, and hyperbolic spaces | Tran | Ph.D. Prospective Student Visit Day |
| Mar 21 | Aaron Brown (Northwestern) | Schneider LAA Lecture | Zimmer | |
| Mar 28 | Spring Break | |||
| April 4 | Caglar Uyanik | TBA | ||
| April 11 | Special Colloquium
(combined with Differential Geometry Workshop) |
TBA | Zhang | |
| April 18 | Jack Xin (UC Irvine) | Tran | ||
| April 29 | Mladen Bestvina (Utah) | Distinguished Lecture Series Part I (room B130) | Uyanik | |
| April 30 | Mladen Bestvina (Utah) | Distinguished Lecture Series Part II (room B239) | Uyanik | |
| May 1 | Mladen Bestvina (Utah) | Distinguished Lecture Series Part III (room B130) | Uyanik | |
| May 2 | Henri Berestycki (Maryland–College Park / EHESS) | Graham |
Abstracts
February 7: Peter Smillie (MPI)
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.
February 24: Daniel Bragg (Utah)
Title: Murphy’s Law for the moduli stack of curves
Abstract: Murphy's Law states "Anything that can go wrong will go wrong". In the context of algebraic geometry, "Murphy's Law" is used to refer to the philosophy that moduli spaces of algebro-geometric objects should be expected to have arbitrarily complicated structure, absent a good a-priori reason to think otherwise. In this talk I will explain my work verifying that a certain precise formulation of this philosophy holds for the moduli of curves, as well as a number of other natural moduli problems. This implies that the moduli space of curves fails to be a fine moduli space in every possible way, and that there exist curves which are obstructed from being defined over their fields of moduli by every possible mechanism. This is joint work with Max Lieblich.
March 5: Eli Weinstein (Columbia)
Title: Probabilistic Experimental Design for Petascale DNA Synthesis
Abstract: Generative modeling offers a powerful paradigm for designing novel functional DNA, RNA and protein sequences. In this talk, I introduce experimental design methods to efficiently manufacture samples from a distribution over biomolecules in the real world. The algorithms implement numerical techniques for approximate sampling using stochastic chemical reactions. I demonstrate synthesizing ~10^16 samples from a generative model of human antibodies, at a sample quality comparable to state-of-the-art protein language models, and a cost of ~\$10^3. The library yields candidate therapeutics for "undruggable" cancer targets. Using previous methods, manufacturing a DNA library of the same size and quality would cost roughly ~\$10^15.March 7: Daniel Groves (UIC)
Title: 3-manifold groups?
Abstract: Due to a vast amount of work over the last decades, the fundamental groups of 3-manifolds are by now very well understood. I will focus on the following (wide open) question: When is a discrete group the fundamental group of a compact 3-manifold? I'll discuss the background to this question, what is known in various dimensions, and then focus on the case of greatest interest in 3-dimensional topology - the hyperbolic case. Finally, I'll report on some recent work around this question in joint work with Haissinsky, Manning, Osajda, Sisto, and Walsh.
March 19 (Wed): Xuan-Hien Nguyen (Iowa State)
Title: The fundamental gap in Euclidean, spherical, and hyperbolic spaces
Abstract: The fundamental gap is the difference between the first two eigenvalues of the Dirichlet problem for the Laplace operator. We will give a brief history of the problem, state the main conjecture, and give a survey of recent results for the subject.