Remarkable martensitic microstructures are observed in the
alloy Ti76Nb22Al2 , which undergoes a cubic to orthorhombic
transformation with six martensitic variants Ui=UTi greater than 0
having middle eigenvalue λ2(Ui) very close to 1. Assuming
that...
This talk is concerned with solutions of the 3D incompressible
Navier-Stokes equations that are bounded in a critical space. From
small initial data, these solutions are known to be globally
well-posed due to classical work of Fujita-Kato and others...
The compressible Euler equation can lead to the emergence of
shock discontinuities in finite time, notably observed behind
supersonic planes. A very natural way to justify these
singularities involves studying solutions as inviscid limits of
Navier...
The Hopf-Tsuji-Sullivan theorem states that the geodesic flow on
(an infinite) Riemann surface is ergodic iff the Poincare series is
divergent iff the Brownian motion is recurrent. Infinite Riemann
surfaces can be built by gluing infinitely many...
Let Ω be an open set in a Euclidean space X of dimension (n+1)
and ϕ be a uniformly convex smooth norm on X. Consider an
n-dimensional unit-density varifold V in Ω, whose generalised mean
curvature vector, computed with respect to ϕ, is bounded...
The mathematical core of deep learning is function approximation
by neural networks trained on data using stochastic gradient
descent. I will present a collection of sharp results on training
dynamics for the deep linear network (DLN), a...
Several recent groundbreaking results in geometric measure
theory, homogeneous dynamics and number theory ultimately rely on a
key result of Bourgain known as Bourgain's Projection Theorem (of
course, each of these results require many other tools...
We use the min-max construction to find closed hypersurfaces
which are stationary with respect to anisotropic elliptic
integrands in any closed n-dimensional manifold . These surfaces
are regular outside a closed set of zero n-3 dimension. The...
