※ 강연 뒷부분이 녹화되지 않았습니다. A symplectic manifold is a space with a global structure on which Hamiltonian equations are defined. A classical result by Darboux says that every symplectic manifold locally looks standard, so it has be...
Study stochastic biochemical systems via their underlying network structures
When a biological system is modeled using a mathematical process, the following step is normally to estimate the system parameters. Despite the numerous computational and statistical techniques, estimating parameters for complex systems can...
A dissipative effect on some PDEs with physical singularity
초록: In this lecture, we study various dissipative effect in a phase space from either entropy dissipation or boundary. We see how this effect leads mathematical studies on long time behavior and scale-uniform estimate of kinetic PDEs in g...
Category수학강연회소속University of Wisconsin-Madison강연자김찬우
Concordance is a relation which classifies knots in 3-space via surfaces in 4-space, and it is closely related with low dimensional topology. Satellite operators are one of the main tools in the study of knot concordance, and it has been wi...
In late 1970's John McKay discovered the astonishing identity 196884=196883+1, which lead Conway and Norton to formulate the famous Monstrous Moonshine conjectures about the Monster group, the largest sporadic finite simple group. The simple...
행렬, 행렬함수 그리고 행렬방정식 (Matrix, Matrix Functions and Matrix Equations)
In this presentation, we introduce how matrices appeared in the history of mathematics and how they are used in today's fields. Also, we consider the necessary mathematics concepts to define the matrix functions. and the existence and conver...
The thirteen books "Elements" were written or collected by Euclid of Alexandria about 300 BCE. Many think that "Elements" is the most important example of deductive mathematics. In fact, the Common Notions and the Postulates of Elements are...
WGAN with an Infinitely wide generator has no spurious stationary points
Generative adversarial networks (GAN) are a widely used class of deep generative models, but their minimax training dynamics are not understood very well. In this work, we show that GANs with a 2-layer infinite-width generator and a 2-layer...
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...
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...
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...
