Fokker-Planck and Kolmogorov (backward) equations can be interpreted as linearisations of the underlying stochastic differential equations (SDE). It turns out that, in particular, on infinite dimensional spaces (i.e. for example if the SDE i...

Counting circles in Apollonian circle packings and beyond

We consider different growth rates associated with the geometry (distance, volume, heat kernel) on a cover of a compact Riemannian manifold. We present general inequalities. We discuss the rigidity results and questions in the case of negati...

In this talk, we shall first present several examples of numerical simulations of complex industrial systems. All these simulations rely upon some mathematical models involving Partial Differential Equations and we shall briefly explain the ...

There are some phenomena called "regularization by noise" in nonlinear evolution equations. This means that if you add a noise to the system, the system would have a better property than without noise. As one of examples, I will explain this...

The talk will review a new approach to the limits of the quantum N-body dynamics leading to the Hartree equation (in the large N limit) and to the Liouville equation (in the small Planck constant limit). This new strategy for studying both l...

150902_HYKE.pdf

The goal of this lecture is to explain and motivate the connection between AubryMather theory (Dynamical Systems), and viscosity solutions of the Hamilton-Jacobi equation (PDE). This connection is the content of weak KAM Theory. The talk sho...

After a review of various types of tilings and aperiodic materials, the notion of tiling space (or Hull) will be defined. The action of the translation group makes it a dynamical system. Various local properties, such as the notion of "Finit...

Modern mathematics with axiomatic systems has been developed to create a complete reasoning system. This was one of the most exciting mathematical experiments. However, even after the failure of the experiment, mathematical research is still...

In this talk, we discuss some results of convex and non-convex optimization methods in image processing. Examples including image colorization, blind decovolution and impulse noise removal are presented to demonstrate these methods. Their a...

In many applications such as X-ray Crystallography, imaging, communication and others, one must construct a function/signal from only the magnitude of the measurements. These measurements can be, for example, the Fourier transform of the den...

Gromov introduced the analytic method of pseudoholomorphic curves into the study of symplectic topology in the mid 80's and then Floer broke the conformal symmetry of the equation by twisting the equation by Hamiltonian vector fields. We sur...