In this talk, we briefly introduce how a combinatorial object, Integer partition, is related with number theoretic subjects : q-series and modular forms. In particular, we will focus on (1) combinatorial proof for q-series identities (2) ari...
A knot is a smooth embedding of an oriented circle into the three-sphere, and two knots are concordant if they cobound a smoothly embedded annulus in the three-sphere times the interval. Concordance gives an equivalence relation, and the se...
Ill-posedness for incompressible Euler equations at critical regularit
We obtain a quantitative and robust proof that incompressible fluid models are strongly ill-posed in critical Sobolev spaces, in the sense that norm inflation and even nonexistence occur for critical initial data. We then show how to use th...
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
Hybrid discontinuous Galerkin methods in computational science and engineering
Computation facilitates to understand phenomena and processes from science and engineering; we no longer need to depend only on theory and experiment. Computational Science and Engineering (CSE) is a rapidly developing multidisciplinary area...
There are basically two approaches for solving linear systems: one is to exactly solve the linear sytem such as Gaussian-elimination. The other approximates the solution in the Krylov spaces; Conjugate-gradient and General minimum residual m...
Heavy-tailed large deviations and deep learning's generalization mystery
Abstract: While the typical behaviors of stochastic systems are often deceptively oblivious to the tail distributions of the underlying uncertainties, the ways rare events arise are vastly different depending on whether the underlying tail ...
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...
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...
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...