The inception of the theory of regularity structures transformed the study of singular SPDE by generalizing the notion of "taylor expansion" and classical notions of regularity in a way flexible enough to accommodate the renormalization. In the years since then our understanding of how to implement renormalization in regularity structures has developed rapidly. I will sketch the overall framework of the theory of regularity structures and then summarize these recent developments in order to give an idea of the current state of the theory.
Ajay Chandra is a Leverhulme Early Career Fellow at Imperial College London. He graduated from the University of California, Santa Barbara before going to the University of Virginia to complete a Ph.D. in mathematics and then taking up a postdoctoral position at the University of Warwick. His research interests include singular stochastic partial differential equations, the Wilson renormalization group, statistical mechanics, and constructive quantum field theory.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
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