We proved the codimension three conjecture that says the micro-local perverse sheaves extend if it is defined outside odimension three (counting from Lagrangian subvarity). It is a joint work with Kari Vilonen.
Categorical representation theory, Categorification and Khovanov-Lauda-Rouquier algebras
Representation theory is to study the actions of groups or algebras on vector spaces. Recently, its categorical version, categorical representation theory, attracts researchers in representation theory. In this theory we replace "vector spac...
Riemann-Hilbert correspondence for irregular holonomic D-modules
The original Riemann-Hilbert problem is to construct a liner ordinary differential equation with regular singularities whose solutions have a given monodromy. Nowadays, it is formulated as a categorical equivalence of the category of regular...
Convex and non-convex optimization methods in image processing
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...
CategoryMath ColloquiaDept.Hong Kong Baptist UniversityLecturerMichael Ng
A new view of Fokker-Planck equations in finite and Infinite dimensional spaces
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...
Unprojection or "constructing bigger Gorenstein ideals from smaller one" is an algebraic device for constructing Gorenstein varieties in codimension 4, 5, ..., beyond the range of standard structure theorems; it has a large number of fairly ...
CategoryMath ColloquiaDept.University of Warwick / 서강대LecturerMiles Reid
I will talk on Cannes's Embedding Conjecture, which is considered as one of the most important open problems in the field of operator algebras. It asserts that every finite von Neumann algebra is approximable by matrix algebras in suitable s...
Recent progress on the Brascamp-Lieb inequality and applications
In his survey paper in the Bulletin of the AMS from 2002, R. J. Gardner discussed the Brunn-Minkowski inequality, stating that it deserves to be better known and painted a beautiful picture of its relationship with other inequalities in anal...
CategoryMath ColloquiaDept.Saitama UniversityLecturerNeal Bez
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...
CategoryMath ColloquiaDept.University of WaterlooLecturerNico Spronk
<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...
CategoryMath ColloquiaDept.서울대학교LecturerOtto van Koert
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.
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.
CategoryMath ColloquiaDept.Univ. of Wisconsin/포항공대LecturerPaul Rabinowitz
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...
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.
CategoryMath ColloquiaDept.University of IllinoisLecturerRenming Song
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...
CategoryMath ColloquiaDept.National Univ. of SingaporeLecturerShih-Hsien Yu