Several cluster interfaces in 2D critical lattice models have been proven to have conformally invariant scaling limits, which are described by SLE(Schramm-Loewner evolution) process, a family of random fractal curves. As the remarkable achie...

Since Belavin, Polyakov, and Zamolodchikov introduced conformal field theory as an operator algebra formalism which relates some conformally invariant critical clusters in two-dimensional lattice models to the representation theory of Viraso...

Brownian motion with darning (BMD) is a diffusion process obtained from Brownian motion by shorting each hole in the space into one point. In this talk, I will present a quick introduction to BMD and its basic properties including the zero p...

Anomalous diffusion phenomenon has been observed in many natural systems, from the signalling of biological cells, to the foraging behaviour of animals, to the travel times of contaminants in groundwater. In this talk, I will first discuss t...

On some nonlinear elliptic problems

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...

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...

Empirical observations have shown that for an adequate description of many random phenomena non-Gaussian processes are needed. The paths of these Markov processes necessarily have jumps. Their generators are nonlocal operators which admit a ...

In this talk, we shall discuss the semi-infinite variation of Hodge structure associated to real valued solutions of a Toda equation. First, we describe a classification of the real valued solutions of the Toda equation in terms of their par...

It has been more than thirty years since white noise analysis was launched systematically. It is now a good time to have an overview of the theory and to reflect on its advantages in order to anticipate further developments of this theory. O...

I will give a very personal overview of the evolution of mainstream applied mathematics from the early 60's onwards. This era started pre computer with mostly analytic techniques, followed by linear stability analysis for finite difference a...

In this talk I will present some results in the area of topological, low-dimensional, discrete dynamical systems.

In this talk, we will present an approach to construct the Green’s function for an initial boundary value problem with precise pointwise structure in the space-time domain. This approach is given in terms of transform variable and physical v...

In this talk I will first give a survey of recent recent results SDEs with singular coefficients. Then I will report some recent results, jointly with Longjie Xie, on critical and supercritical SDEs with singular coefficients.

A general goal of noncommutative geometry (in the sense of A. Connes) is to translate the main tools of differential geometry into the Hilbert space formalism of quantum mechanics by taking advantage of the familiar duality between spaces an...

Motivated by the analysis of the singularity of the Bergman kernel of a strictly pseudoconvex domain, Charlie Fefferman launched in the late 70s the program of determining all local biholomorphic invariants of strictly pseudoconvex domain. T...

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 ...