Monday, February 22, 2021
02/22/2021 - 1:00pm
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 firstname.lastname@example.org for info.
Zoom Meeting ID: 97670014308
02/22/2021 - 4:00pm
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).
02/22/2021 - 4:30pm
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.
https://yale.zoom.us/j/92811265790 (Password is the same as last semester)