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.

(information) "Introduction to Oriented Matroids" Series Thursdays 14:30-15:45

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Lecture to be recorded by KAI-X

TBA

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심사위원장: 김동수, 심사위원:안드레아스 홈슨, 엄상일, 이주영(전산학부), 서승현(강원대학교)

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.

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Zoom information will be provided a few days before the zoom talk.

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심사위원장: 박철우, 심사위원: 정연승, 전현호, 안정연(산업및시스템공학과), 전용호(연세대학교)