Hamiltonian dynamics, Floer theory and symplectic topology
In this lecture, I will convey subtle interplay between dynamics of Hamiltonian flows and La-grangian intersection theory via the analytic theory of Floer homology in symplectic geometry. I will explain how Floer homology theory (`closed str...
Gromov-Witten-Floer theory and Lagrangian intersections in symplectic topology
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...
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
Global result for multiple positive radial solutions of p-Laplacian system on exterior domain
Global result for multiple positive radial solutions of p-Laplacian system on exterior domain In this talk, we consider p-Laplacian systems with singular indefinite weights. Exploiting Amann type three solutions theorem for the singular syst...
Geometry, algebra and computation in moduli theory
I will explain the basic concepts of moduli and how moduli spaces can be constructed in algebraic geometry. Exploring the moduli spaces and issues arising from their construction lead to interesting interplay of geometry, algebra and computa...
초록: Let X be a homogeneous space for a Lie group G. A (G,X)-structure on a manifold M is an atlas of coordinate charts valued in X, such that the changes of coordinates locally lie in G. It is a fundamental question to ask how many ways o...
Geometric Langlands theory: A bridge between number theory and physics
※ 강연 앞 부분이 잘렸습니다. (강연자료 다운: Geometric Langlands Theory [A Bridge between Number Theory and Physics] (2022.04.28).pdf ) 초록: The Langlands program consists of a tantalizing collection of surprising results and conjectures w...
Ward's identities and the related concept of the stress-energy tensor are standard tools in conformal field theory. I will present a mathematical overview of these concepts and outline relations between conformal field theory and Schramm-Loe...
There have been at least two surprising events to geometers in 80-90s that they had to admit physics really helps to solve classical problems in geometry. Donaldson proved the existence of exotic 4-dimensional Euclidean space using gauge th...
2000년 국제수학교육위원회( International Commission on Mathematical Instruction)는 수학교육연구에 탁월한 업적을 이룬 학자에게 수여하는 Freudenthal 메달과 Klein메달을 제정하여, 2003년 부터 홀수 해에 수상하고 있다. 이 강연에서는 2012년 서울에...
Free boundary problems arising from mathematical finance
Many problems in financial mathematics are closely related to the stochastic optimization problem because the optimal decision must be made under the uncertainty. In particular, optimal stopping, singular control, and optimal switching prob...
Fixed points of symplectic/Hamiltonian circle actions
A circle action on a manifold can be thought of as a periodic flow on a manifold (periodic dynamical system), or roughly a rotation of a manifold. During this talk, we consider symplectic/Hamiltonian circle actions on compact symplectic mani...
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...
The notion of essential dimension was introduced by Buhler and Reichstein in the late 90s. Roughly speaking, the essential dimension of an algebraic object is the minimal number of algebraically independent parameters one needs to define the...
Equations defining algebraic curves and their tangent and secant varieties
It is a fundamental problem in algebraic geometry to study equations defining algebraic curves. In 1984, Mark Green formulated a famous conjecture on equations defining canonical curves and their syzygies. In early 2000's, Claire Voisin...