Events
Department of Mathematics and Statistics
Texas Tech University
We study collections of measures that are negligible in a sense of "modules". The idea is originated in complex analysis as "a conformal module of a family of curves" in looking for an invariant object under conformal transformations on the complex plane. Later the definition of the module was successfully applied to the nonlinear potential theory and quasiconformal analysis in a wider sense in Euclidean spaces. B. Fuglede, by studying the completion of functional spaces, generalized the notion of the module of a family of curves to the module of a family of measures. A collection of measures is exceptional if the corresponding module vanishes. We are interested in finding exceptional families of measures on Carnot groups, related to geometric objects such as "intrinsic graphs". It leads to the notion of a Grassmannian on specific Carnot groups.
The tumor suppressor p53 oscillates in response to DNA double-strand breaks, a behavior that has been suggested to be essential to its anti-cancer function. Nearly all human cancers have genetic alterations in the p53 pathway; a number of these alterations have been shown to be oncogenic by experiment. These alterations include somatic mutations and copy number variations as well as germline polymorphisms. Intriguingly, they exhibit a mixed pattern of interactions in tumors, such as co-occurrence, mutual exclusivity, and paradoxically, mutual antagonism. Using a differential equation model of p53-Mdm2 dynamics, I employ Hopf bifurcation analysis to show that these alterations have a common mode of action, to abolish the oscillatory competence of p53, thereby impairing its tumor suppressive function. In this analysis, diverse genetic alterations, widely associated with human cancers clinically, have a unified mechanistic explanation of their role in oncogenesis. In this talk, I will also discuss the role of physiological oscillations in health and disease broadly.
Zoom link:
https://texastech.zoom.us/j/94471029838?pwd=ZlJXR2JhU0ZjUHhYOUlmVGN3VFFJUT09