Abstracts

Week of February 21, 2021

February 22, 2021
Applied Mathematics Fighting drug resistance with math 1:00pm -
Zoom Meeting ID: 97670014308

Abstract: The emergence of drug-resistance is a major challenge in chemotherapy. In this talk we will overview some of our recent mathematical models for describing the dynamics of drug-resistance in solid tumors. These models follow the dynamics of the tumor, assuming that the cancer cell population depends on a phenotype variable that corresponds to the resistance level to a cytotoxic drug.  Under certain conditions, our models predict that multiple resistant traits emerge at different locations within the tumor, corresponding to heterogeneous tumors. We show that a higher drug dosage may delay a relapse, yet, when this happens, a more resistant trait emerges. We will show how mathematics can be used to propose an efficient drug schedule aiming at minimizing the growth rate of the most resistant trait, and how such resistant cells can be eliminated.

email tatianna.curtis@yale.edu for info.
Group Actions and Dynamics Cusped Hitchin representations 4:00pm -
Zoom
We develop a theory of cusped Hitchin representations of
geometrically finite Fuchsian groups into SL(d,R). When d=3, cusped
Hitchin representations arise as holonomy maps of finite area real
projective surfaces. We develop general criteria for when one can obtain counting and equidistribution  results for potentials on countable Markov shifts. We show that these general criteria are satisfied by roof functions associated to linear functionals giving “length functions” for cusped  Hitchin representations. 
 
The long term goal of this project is to develop a metric theory of the
augmented Hitchin component which generalizes the fact that augmented
Teichmuller space is the metric completion of Teichmuller space with the
Weil-Petersson metric. (This is joint work with Tengren Zhang and Andy Zimmer,
and with Harry Bray, Nyima Kao and Giuseppe Martone).
Geometry, Symmetry and Physics Quasimodular forms from Betti numbers 4:30pm -
https://yale.zoom.us/j/92811265790 (Password is the same as last semester)

This talk will be about refined curve counting on local P^2, the noncompact Calabi-Yau 3-fold total space of the canonical line bundle of the projective plane. I will explain how to construct quasimodular forms starting from Betti numbers of moduli spaces of dimension 1 coherent sheaves on P^2. This gives a proof of some stringy predictions about the refined topological string theory of local P^2 in the Nekrasov-Shatashvili limit. Partly based on work with Honglu Fan, Shuai Guo, and Longting Wu.
February 23, 2021
Algebra and Number Theory Seminar Geometrically non-reduced varieties 9:00am -
Zoom

In positive characteristic, there exist fibrations between smooth varieties where every fiber is singular or even non-reduced. In the latter case, the generic fiber of the fibration is geometrically non-reduced. We study the failure of generic smoothness by showing a generalization of Tate's genus change formula, and obtain a structural result about geometrically non-reduced varieties. Our result has applications to Fano varieties. This is joint work with Joe Waldron.
Geometry & Topology Cubulated relatively hyperbolic groups and virtual specialness. 4:00pm -
https://yale.zoom.us/j/96501374645

Ian Agol showed that hyperbolic groups acting geometrically on CAT(0) cube complexes are virtually special in the sense of Haglund-Wise, the last step in the proof of the virtual Haken and virtual fibering conjectures. I will talk about a generalization of this result (also obtained independently by Groves and Manning), which states that cubulated relatively hyperbolic groups are virtually special provided the peripheral subgroups are virtually special in a way that is compatible with the cubulation. In particular, we deduce virtual specialness for cubulated groups that are hyperbolic relative to virtually abelian groups, extending Wise's results for limit groups and fundamental groups of cusped hyperbolic 3-manifolds. The main ingredient of the proof is a relative version of Wise's quasi-convex hierarchy theorem, obtained using recent results by Einstein, Groves and Manning.
February 25, 2021
Mathematics for Humans 8:00pm -

The product of mathematics is clarity and understanding. Not theorems, by themselves.  - Bill Thurston

Does one have to be a genius to do mathematics? The answer is an emphatic NO.  - Terry Tao

Why do mathematics? This is a simple question, but worth considerable reflection. Because how you answer will strongly determine who you think should be doing mathematics, and how you will teach it. - Francis Su

The “Mathematics for Humans” reading group will have its second meeting on Thursday February 25 at 8pm. Sponsored by the departmental climate committee, the goal of this group is to promote discussion in the department about what it means to do mathematics and be a mathematician. All are invited! From undergraduate students through senior faculty, we hope that diverse members of the department are represented. Unlike most reading groups, no homework or reading is required outside of the meetings. Each meeting will feature a short piece, and we will begin with a silent period to read it, followed by discussion in small groups. In advance of his colloquium on March 3 we will be reading a piece by Francis Su.