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 ...
Category수학강연회소속University of Bielefeld강연자Walter Hoh
Harmonic bundles and Toda lattices with opposite sign
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...
<학부생을 위한 ε 강연> What mathematics can do for the real and even fake world
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...
Green’s function for initial-boundary value problem
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...
Category수학강연회소속National Univ. of Singapore강연자Shih-Hsien Yu
Weak and strong well-posedness of critical and supercritical SDEs with singular coefficients
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.
Category수학강연회소속University of Illinois강연자Renming Song
Noncommutative Geometry. Quantum Space-Time and Diffeomorphism Invariant Geometry
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...
Fefferman's program and Green functions in conformal geometry
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 ...
Category특별강연소속Collège de France강연자Pierre-Louis Lions
We survey work on a class of nonlinear elliptic PDEs that was initiated by Moser. Methods from PDE, dynamical systems, and geometry set in the framework of the calculus of variations are used to construct a rich collection of solutions.
Category수학강연회소속Univ. of Wisconsin/포항공대강연자Paul Rabinowitz
In this talk, I will talk about the definition Q-curvature and some of its properties. Then I will talk about the problem of prescribing Q-curvature, especially I will explain the ideas of studying the problem using flow approach.
In this talk, we discuss recent work with Albers, Cieliebak, Fish, Frauenfelder, Hofer and Paternain on several aspects of the three body problem. The ultimate goal of this project is to use modern, holomorphic curve techniques to investigat...
<학부생을 위한 ɛ 강연> Symplectic geometry and the three-body problem
We describe some of the history of the three-body problem and how it lead to symplectic geometry. We start by sketching Poincare’s prize-winning work, and discuss how it lead to the birth of the fields of dynamical systems and symplec...
A classical theorem of Jacobs, de Leeuw and Glicksberg shows that a representation of a group on a reflexive Banach space may be decomposed into a returning subspace and a weakly mixing subspace. This may be realized as arising from the idem...
Category수학강연회소속University of Waterloo강연자Nico Spronk