Dear colleagues,

we are happy to announce the following talk

Damir Kinzebulatov (Université Laval) Recent progress on well-posedness of singular SDEs with critical drifts

Abstract: In the first part of the talk, I will review the basic results on SDEs with singular drifts. In the second part, I will discuss some recent progress on weak and strong existence and conditional uniqueness for SDEs with singular drifts having critical-order singularities. These drifts either (a) reach the critical strength of the singularities, i.e. multiplying such a drift by a constant even slightly greater than 1 can destroy the weak existence, or (b) are more singular (not necessarily even in L^{2}_{\loc}(R^{1+d})) and can have critical 1/\sqrt{t} singularities in time. I will be referring to De Giorgi's method in L^p with p chosen sufficiently large (in order to accommodate the strength of the singularities going up to the critical threshold), some "fractional" Duhamel series representations and an appropriate parabolic Adams-Krylov estimate, the method of Röckner-Zhao of constructing strong solutions, and a "critical" Orlicz space with gauge function \cosh - 1 that allows to treat the Kolmogorov operator with the borderline strength of the singularities in the drift where the L^p no longer exists.

Date and time: Thursday September 10, 14:00-15:00 (Rome time zone) Place: Aula Beltrami, Dip. Matematica, Univ. Di Pavia.

Zoom meeting link: https://unipv-it.zoom.us/j/96306243310?pwd=YahZ15tfGy3iF4SoCc5JoQ5UDxDiDB.1 https://unipv-it.zoom.us/j/96306243310?pwd=YahZ15tfGy3iF4SoCc5JoQ5UDxDiDB.1

ID riunione: 963 0624 3310 Codice d’accesso: 920516

These talks are part of the (PMS)^2: Pavia-Milano Seminar series on Probability and Mathematical Statistics organized jointly by the universities Milano-Bicocca, Pavia and Milano-Politecnico.

Participation is free and welcome!

Best regards The organizers (Carlo Orrieri, Maurizia Rossi, Margherita Zanella)