Events
Department of Mathematics and Statistics
Texas Tech University
This is an expository talk about a subject about which the speaker is currently learning. The theory of regularity structures was invented by Martin Hairer in 2014 (for which he won the Fields Medal). In short, many equations in physics such as Kardar-Parisi-Zhang equation, parabolic Anderson model, Phi4 model from quantum field theory, and even Navier-Stokes equations, were studied under the forcing by white noise (typically white in both space and time) which was so singular that the most fundamental question about the existence of its solution was not proven rigorously. In fact, solutions in the classical sense (or even weak sense) actually do not exist. The theory of regularity structures was a first (along with the theory of paracontrolled distributions due to Gubinelli et al.) systematic way to actually prove the existence of a limiting solution (after much work of renormalization, computing Wick products, and writing tree diagrams akin to Feynman diagrams). Its impact has been immense and has generated waves of new results in many related fields (even stochastic quantization of Yang-Mills).
Please virtually attend this seminar via this zoom link Wednesday the 14th at 3 PM.We study a theory of support varieties over a skew complete
intersection $R$. Color differential graded homological algebra is put
to use to compute the derived braided Hochschild cohomology of $R$;
moreover, its action on $\mathrm{Ext}_R(M,N)$ is shown to be
noetherian for any pair of finitely generated color $R$-modules $M$
and $N$. When the parameters defining $R$ are roots of unity we use
these cohomology operators to define the support variety for a pair of
color $R$-modules. Applications include a proof of the Generalized
Auslander-Reiten Conjecture and that $R$ possesses symmetric
complexity when the defining parameters of $R$ are roots of unity.
Join Zoom Meeting https://zoom.us/j/96217128540?pwd=NjU5dzE2RjZvV0prejhOOWVjVENadz09
Meeting ID: 962 1712 8540
Passcode: 474170
The rapid development of single-cell experimental technologies provides unprecedented resolutions to study the dynamical process in the cell-fate decision. Mathematically, the cell-fate decision can be modeled as a (stochastic) dynamical system with multiscale structure. In this talk, we will introduce some recent efforts to combine the techniques of dynamical system models into the single-cell data analysis.
We begin with exploring energy landscape theory for stochastic dynamics, which serves as the mathematical realization of the famous Waddington metaphor of cell-fate decision in developmental biology. Next, we will introduce the experimental evidence for the “barrier-crossing” process on energy landscape in real biology, based on the single-cell trajectory data analysis of S-phase checkpoint in budding yeast cells. Motivated by such a picture, we then propose a new algorithm to dissect the multiscale structure of state-transitions underlying scRNA-seq datasets. Lastly, in the context of dynamical system analysis, we will provide some theoretical results and mathematical insights about RNA velocity -- a recent and popular proposal in biology, to infer dynamics underlying scRNA-seq datasets with the spliced/unspliced RNA abundance.
Please virtually attend this seminar via this zoom link Wednesday the 3rd at 4 PM.