I'll describe my thesis results beginning to characterize finite
and infinite time blowup in four- dimensional yang-mills flow.

We will continue discussing the paper "Bivariate Polynomials Modulo Composites and their Applications" by Dan Boneh and Henry Corrigan-Gibbs  
https://eprint.iacr.org/2014/719.pdf

More than 30,000 papers are published each year
in which modern density functional calculations are performed.
However, there is presently no systematic route to finding useful
approximations. Over 40 years ago, Lieb and Simon demonstrated
that the original version of density functional theory, Thomas-Fermi
theory, becomes relatively exact in a very particular
non-relativistic limit of large electron number. I will explain why I believe this
holds the key to a systematic treatment of such approximations, and
what my group has done in the last 8 years to use this insight.

Metastable transitions are rare events, such as bistable switching, that occur under weak noise conditions, causing dramatic shifts in the expression of a gene. Within a gene circuit, one or more genes randomly switch between regulatory states, each having a different mRNA transcription rate. The circuit is self regulating when the proteins it produces affect the rate of switching between gene regulatory states. Under weak noise conditions, the deterministic forces are much stronger than fluctuations from gene switching and protein synthesis. A general tool used to describe metastability is the quasi stationary analysis (QSA). A large deviation principle is derived so that the QSA can explicitly account for random gene switching without using an adiabatic limit or diffusion approximation, which are unreliable and inaccurate for metastable events.This allows the existing asymptotic and numerical methods that have been developed for continuous Markov processes to be used to analyze the full model.