Department Seminars & Colloquia
When you're logged in, you can subscribe seminars via e-mail
산업경영학동(E2-1) 세미나실 (2216)
ACM Seminars
Dohyun Kwon (Dept. of Mathematics, University of Seoul)
Applications of De Giorgi\'s Minimizing Movements and Optimal Transport
산업경영학동(E2-1) 세미나실 (2216)
ACM Seminars
The study of gradient flows has been extensive in the fields of partial differential equations, optimization, and machine learning. In this talk, we aim to explore the relationship between gradient flows and their discretized formulations, known as De Giorgi's minimizing movements, in various spaces. Our discussion begins with examining the backward Euler method in Euclidean space, and mean curvature flow in the space of sets. Then, we investigate gradient flows in the space of probability measures equipped with the distance arising in the Monge-Kantorovich optimal transport problem. Subsequently, we provide a theoretical understanding of score-based generative models, demonstrating their convergence in the Wasserstein distance.
Abstract: In 1993, Demeyer and Ford computed the Brauer group of a smooth toric variety over an algebraically closed field of
characteristic zero. One may pose the same question to the toric varieties over any field of positive characteristic. Another
interesting question is what will happen if we replace the base field by a discrete valuation ring, thereby replacing smooth toric varieties by smooth toric schemes over a discrete valuation ring in the sense of Kempf-Knudsen-Mumford-Saint-Donat. In this talk. I am going to discuss the answers to these questions. This is joint work with Roy Joshua.
Zoom information will be provided a few days before the zoom talk.
Zoom information will be provided a few days before the zoom talk.