By Stochastic Evolution Equations, do you mean infinite-dimensional equations & SPDE?
Below are a few names to get you started, I would recommend looking at their papers to see if you can find something that interests you, then making a choice on the school. It's more about who you work with and less about the school name.
In no particular order (and non-exhaustive):
- Jan Van Neerven, TU Delft
- Mark Veraar, TU Delft
- Giuseppe Da Prato,
- Zdzislaw Brzezniak, University of York
- Jerzy Zabczyk, Polish Academy of Sciences
- Giuseppe Da Prato, Scuola Normale Superiore di Pisa
- Michael Röckner
- Franco Flandoli
- István Gyöngy
- Nicolai V. Krylov
- Bohdan Maslowski
- Szymon Peszat
- Anna Chojnowska-Michalik
- Benjiamin Goldys
- Jan Seidler
- Davar Khoshnevisan
- Robert Dalang
- Carl Mueller
- Martin Hairer
- J. C. Mattingly
- L. Zambotti
- F. Russo