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 ...
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...
I will tell two interrelated stories illustrating fruitful interactions between combinatorics and Hodge theory. The first is that of Lorentzian polynomials, based on my joint work with Petter Brändén. They link continuous convex...
<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...
