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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Hao Shen
Columbia University
Title: Singular stochastic PDEs and renormalization

Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, systematic renormalization techniques with Feynman diagrams, and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs with emphasis on renormalization, and how these SPDEs arise as limits of various important physical models.



Recording: http://mm.math.cmu.edu/recordings/cna/hao_shen_small.mp4
Date: Tuesday, April 17, 2018
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  Ian Tice