Abstract. I will review a recent progress in designing convex integration schemes to construct nonunique solutions to the Navier-Stokes and transport equation. In particular, we will discuss the use of spacial and temporal intermittency, observed in turbulent flows, and essential for producing sharp counterexamples to the known uniqueness results.

Bio. Alexey Cheskidov received his Ph.D degree from Indiana University in 2004. He has held postdoctoral positions at the University of Michigan and University of Chicago before becoming a professor at the University of Illinois at Chicago. Currently he is a member of the Institute for Advanced Study, Princeton. Cheskidov works in the area of partial differential equations and mathematical fluid mechanics, and has publications in top journals like Invent. Math., Adv. Math., ARMA, CMP, etc. His recent interests include regularity and uniqueness of solutions to the Navier-Stokes equations, global attractors, analytical approach to intermittency and the number of degrees of freedom in turbulence.