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...
Contact topology of singularities and symplectic fillings
For an isolated singularity, the intersection with a small sphere forms a smooth manifold, called the link of a singularity. It admits a canonical contact structure, and this turns out to be a fine invariant of singularities and provides an...
<2020년도 젊은 과학자상 수상 기념강연> Metastability of stochastic systems
Metastability란 random process가 여러 개의 안정된 상태를 가질 때 반드시 나타나는 현상으로, 수리물리학이나 화학의 여러 모형들은 물론 딥러닝의 알고리즘 등 다양한 곳에서 공통적으로 나타나는 현상이다. 본 강연에서는 이 Metastability를 수학적으로...
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...
Noise-induced phenomena in stochastic heat equations
Stochastic heat equations (SHE) usually refer to heat equations perturbed by noise and can be a model for the density of diffusing particles under a random potential. When the irregularity of noise is dominating the diffusion, SHE exhibits ...
※ 강연 앞 부분이 잘렸습니다. (강연자료 다운: Mirror symmetry of pairings.pdf ) 초록: Mirror symmetry has served as a rich source of striking coincidences of various kinds. In this talk we will first review two kinds of mirror symmetry statem...
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...
CategoryMath ColloquiaDept.University of Wisconsin-MadisonLecturer김찬우
<학부생을 위한 ɛ 강연> Secure computation: Promise and challenges
This talk discusses modern cryptographic techniques, such as zero-knowledge proof, multi-party computation and homomorphic encryption, which provide advanced functionality and security guarantees beyond data privacy and authenticity. I will...
CategoryMath ColloquiaDept.송용수Lecturer<학부생을 위한 ɛ 강연> Secure computation: Promise and challenges
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...
Sufficient conditions for the Jensen polynomials of the derivatives of a real entire function to be hyperbolic are obtained. The conditions are given in terms of the growth rate and zero distribution of the function. As a consequence some r...
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...
Free probability is a young mathematical theory that started in the theory of operator algebras. One of the main features of free probability theory is its connection with random matrices. Indeed, free probability provides operator algebrai...
Symplectic topology and mirror symmetry of partial flag manifolds
Soon after Gromov’s applications of pseudo-holomorphic curves to symplectic topology, Floer invented an infinite-dimensional Morse theory by analyzing moduli spaces of pseudo-holomorphic curves to make substantial progress on Arnold&r...
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 [...
<학부생을 위한 ɛ 강연> Mathematics and music: Pythagoras, Bach, Fibonacci and AI
In this talk, I will introduce the audience to the original beauty that leads to exploring the mathematical elements in music. I will cover the following topics on the connection between music and mathematics. - Harmonics & equations - ...
Topological surgery through singularity in mean curvature flow
The mean curvature flow is an evolution of hypersurfaces satisfying a geometric heat equation. The flow naturally develops singularities and changes the topology of the hypersurfaces at singularities, Therefore, one can study topological pr...
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 ...
Diophantine equations and moduli spaces with nonlinear symmetry
A fundamental result in number theory is that, under certain linear actions of arithmetic groups on homogeneous varieties, the integral points of the varieties decompose into finitely many orbits. For a classical example, the set of integra...