Fano varieties are fundamental objects in algebraic geometry. These can be considered as the unique output of the -K -minimal model program on the varieties with effective anticanonical divisors. Thus the initial models should encode the in...

We introduce a conformally invariant nonlinear sigma model on the bulk of contact manifolds with boundary condition on the Legendrian links in any odd dimension. We call any finite energy solution a contact instanton. We also explain its Ha...

In recent years, artificial intelligence has made remarkable progress in developing algorithms that can learn from vast amounts of carefully labeled data. This paradigm of supervised learning has made great success in training specialist mo...

It is a fascinating and challenging problem to count number fields with bounded discriminant. It has so many applications in number theory. We give two examples. First, we compute the average of the smallest primes belonging to a conjugacy ...

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...

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...

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...

※ 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...

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...

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...

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...

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...

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...