TopMath Talk with Gideon Chiusole: Singular SPDEs and Renormalization

„Partial differential equations describe a vast range of natural phenomena, and their stochastic counterparts (SPDEs) extend these models to systems subject to noise. A naïve reading suggests that noise merely blurs the deterministic solution, reducing its regularity without altering its qualitative behaviour. In reality, the noise interacts with the nonlinearity, producing genuine corrections to the dynamics — corrections that, in the physically central singular regime, are infinite in a precise sense and cause the equation to collapse to an object admitting only degenerate solutions. The non-trivial behaviour one set out to model is lost. The procedure that restores it is called renormalization. In this talk, I will make the above precise and illustrate it on some concrete examples.“

TopMath Talks

As part of the TopMath talks, TopMath doctoral students present parts of their research. They provide an understandable insight into their current area of interest, enabling students and staff from different research fields to broaden their mathematical background knowledge. The talks are open to the public and last about an hour, followed by discussion. You are cordially invited!