In the search for possible blow-up of the incompressible Navier-Stokes equations, there has been much recent attention on the class of axisymmetric solutions with swirl. Several interesting structures of this system have led to regularity criteria...

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School of Mathematics

### Symplectic Capacities of Domains Close to the Ball and Banach-Mazur Geodesics in the Space of Contact Forms

An old open question in symplectic topology is whether all normalized capacities coincide on convex bounded domains in the standard symplectic vector space. I will discuss this question for domains which are close to the Euclidean ball and its...

I will present a new theory of motivic cohomology for general (qcqs) schemes. It is related to non-connective algebraic K-theory via an Atiyah-Hirzebruch spectral sequence. In particular, it is non-A1

-invariant in general, but it recovers classical...

Consider the process where a signal propagates downward an infinite rooted tree. On every edge some independent noise is applied to the signal. The reconstruction problem asks whether it is possible to reconstruct the original signal given...

The problem of control of large multi-agent systems, such as vehicular traffic, poses many challenges both for the development of mathematical models and their analysis and the application to real systems. First, we discuss how conservation laws can...

I will give a construction of certain Q-valued deformation invariants of (in particular) complete non-positively curved Riemannian manifolds. These are obtained as certain elliptic Gromov-Witten curve counts. As one immediate application we give the...

Consider an oracle which takes a point x

and returns the minimizer of a convex function f in an ℓ2

ball of radius r around x. While it is straightforward to show that ≈r−1 queries to this oracle suffice to minimize f

to high accuracy in a unit ball...

In 1982, S. T. Yau conjectured that there exists at least four embedded minimal 2-spheres in the 3-sphere with an arbitrary metric. In this talk, we will show that this conjecture holds true for bumpy metrics and metrics with positive Ricci curvature...

I will discuss the relationship between positive loops of contactomorphisms of a fillable contact manifold and the symplectic cohomology (SH) of the filling. The main result is that the existence of a positive loop which is "extensible" implies SH...

In this talk, I will first describe how classical Dieudonne module of finite flat group schemes and p-divisible groups can be recovered from crystalline cohomology of classifying stacks. Then, I will explain how in mixed characteristics, using...