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Title: Exploring Bifurcations of Stochastic Partial Differential Equations

Abstract: In this talk, I shall introduce several classical models of SPDEs of reaction-diffusion type. We shall see that local existence theory is quite well-understood by now for relatively large classes of noise arising in applications but that analyzing pattern formation in the context of noise is still a massive challenge. In particular, I shall explain recent results on trying to understand local bifurcations of SPDEs for small noise. The results include analytical proofs for stochastic fluctuations near bifurcations utilizing projections as well as numerical techniques to efficiently compute these fluctuations over large ranges of parameters via numerical continuation.