n 2014, Beck-Flandoli-Gubinelli-Maurelli considered stochastic differential equation with inverse square drift $b(x)=c|x|^{-2}x$ and showed that if $c$ is larger than a certain critical threshold $c_\ast$, then the Brownian motion gets stuck at the singularity of the drift, and so there is no weak solution starting at the origin. Until recently, the examples of this type were used to justify the optimality of a popular condition $|b| \in L^d$. We argue, however, that the situation is more subtle and this is a counterexample to the value of $c$. Namely, using a variant of De Giorgi's method, we prove, under minimal assumptions on a general $b$, that if $c< c_\ast'$, then the corresponding SDE has a martingale solution; moreover, this solution is weak and is unique if $c$ is sufficiently small. Here $c_\ast$ and $c_\ast'$ approach each other in high dimensions, making the result essentially sharp. Joint with Yu.A.Semenov. arXiv:2110.11232

Bio: Damir Kinzebulatov is a mathematician at the Université Laval in Quebec City. He earned his doctorate at the University of Toronto in 2012 under supervision of Pierre Milman. His research mainly concerns singular SDEs and heat kernel bounds for local and non-local parabolic equations with rough coefficients.