1. 금본위제, 달러, 비트코인 등 돈의 흐름으로 보는 세계사 2. 사람은 어떻게 생각하고 행동하는가 ? (행동경제학, 비선형성) 3. 돈에 대한 생각, 행동, 습관을 바꾸어보자. (부자들은 무엇이 다른가 ? 지금부터 준비해보자.) 4. 주식, 부동산 등 자산관리 [...
We will introduce the behavior of zeros of linear combinations of zeta functions. Those linear combinations are related to the Riemann zeta function, the Eisenstein series, Periods, etc.
I will introduce the basic notions of model theory, a branch of mathematical logic, and survey its applications to other areas of mathematics such as analysis, algebra, combinatorics and number theory. If time permits I will present recent w...
Black holes are perhaps the most celebrated predictions of general relativity. Miraculously, these complicated spacetimes arise as explicit (i.e., exact expression can be written down!) solutions to the vacuum Einstein equation. Looking thes...
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...
Weyl character formula and Kac-Wakimoto conjecture
The character of the finite-dimensional irreducible modules over a finite-dimensional simple Lie algebra is given by the celebrated Weyl character formula. However, such a formula does not hold in general for finite-dimensional irreducible m...
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
A W-algebra is introduced as a symmetry algebra in 2-dimensional conformal field theory. Mathematical realization of a W-algebra was introduced by the theory of vertex algebras. Especially, W-algebras related to Lie superalgebras have been s...
Volume entropy of a compact manifold is the exponential growth rate of balls in the universal cover. This seemingly coarse invariant contains a lot of geometric information of the manifold. We will discuss some relations to other invariants,...
Vlasov-Maxwell equations and the Dynamics of Plasmas
In this colloquium talk, we study the Vlasov-Maxwell equations, a collisionless model in the field of kinetic theory. The model is a fundamental model for the dynamics of plasmas and was introduced in 1938 by Vlasov. Due to the hyperbolic n...
If a problem has an approximate solution, we try to get some information of the linearized kernel of the problem at the approximate solution to find a real solution. In this talk, I would like to introduce a different approach which is purel...
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
A feature of log-correlation naturally appears in diverse objects such as random matrices, random discrete geometries and Riemann zeta function. In this talk, I will give an overview on the theory of log-correlated fields and talk about rec...
Trends to equilibrium in collisional rarefied gas theory
Dynamics of many particle system can be described by PDE of probability density function. The Boltzmann equation in kinetic theory is one of the most famous equation which describes rarefied gas dynamics. One of main property of the Boltzman...
Towards Trustworthy Scientific Machine Learning: Theory, Algorithms, and Applications
Machine learning (ML) has achieved unprecedented empirical success in diverse applications. It now has been applied to solve scientific problems, which has become an emerging field, Scientific Machine Learning (SciML). Many ML techniques, h...
Toward bridging a connection between machine learning and applied mathematics
This lecture explores the topics and areas that have guided my research in computational mathematics and deep learning in recent years. Numerical methods in computational science are essential for comprehending real-world phenomena, and dee...