Introduction to Stochastic Partial Differential Equations

After a presentation of white noise and stochastic calculus in infinite dimension, I will explain how to solve classical SPDEs with white noise. I will focus on the stochastic Burgers and  reaction-diffusion equations which will be first solved with spatially  smooth noise and then with space time white noise. The case of the reaction-diffusion equation in dimension 2 is already not so obvious since the solutions are not expected to be function valued processes.  The case of dimension 3 is much more difficult and has been solved  only recently by Martin Hairer. I will not explain in details his theory  on regularity structure, this would take too much time. However, I will  explain why the problem is so difficult and give few hints on this difficult  theory. No prerequisite on stochastic calculus is expected from the audience.

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