Thursday, March 25, 2021

2021-04-01 / 10:30 ~ 12:00

by 이진엽()

Bose-Einstein condensation (BEC) is one of the most famous phenomena, which cannot be explained by classical mechanics. Here, we discuss the time evolution of BEC in the mean-field limit. First, we review quantum mechanics briefly, and we understand the problem in a mathematically rigorous way. Then, we taste the idea of proof by using coherent state and the Fock space. Finally, some recent developments will be provided.

2021-03-26 / 10:00 ~ 12:00

학과 세미나/콜로퀴엄 - SAARC 세미나:

by 김경훈(고려대학교)

Many types of diffusion equations have been used to describe diverse natural phenomena. The classical heat equation describes the heat propagation in homogeneous media, and the heat equation with fractional time derivative describes anomalous diffusion, especially sub-diffusion, caused by particle sticking and trapping effects. On the other hand, space-fractional diffusion equations are related to diffusion of particles with long range jumps. In this talk, I will introduce the following: 1. Elementary notion of stochastic parabolic equations 2. Stochastic processes with jumps and their related PDEs and Stochastic PDEs 3. Some regularity results of PDEs and Stochastic PDEs with non-local operators

2021-04-01 / 13:00 ~ 14:30

학과 세미나/콜로퀴엄 - 대수기하학:

by 한강진()

Introduction: In this lecture series, we'll discuss algebro-geometric study on fundamental problems concerning tensors via higher secant varieties. We start by recalling definition of tensors, basic properties and small examples and proceed to discussion on tensor rank, decomposition, and X-rank for any nondegenerate variety $X$ in a projective space. Higher secant varieties of Segre (resp. Veronese) embeddings will be regarded as a natural parameter space of general (resp. symmetric) tensors in the lectures. We also review known results on dimensions of secants of Segre and Veronese, and consider various techniques to provide equations on the secants. In the end, we'll finish the lectures by introducing some open problems related to the theme such as syzygy structures and singularities of higher secant varieties.

2021-03-26 / 14:00 ~ 15:30

학과 세미나/콜로퀴엄 - 대수기하학:

by 한강진()

2021-03-25 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 수리생물학:

by ()

Abstract: Millions of individuals track their steps, heart rate, and other physiological signals through wearables. This data scale is unprecedented; I will describe several of our apps and ongoing studies, each of which collects wearable and mobile data from thousands of users, even in > 100 countries. This data is so noisy that it often seems unusable and in desperate need of new mathematical techniques to extract key signals used in the (ode) mathematical modeling typically done in mathematical biology. I will describe several techniques we have developed to analyze this data and simulate models, including gap orthogonalized least squares, a new ansatz for coupled oscillators, which is similar to the popular ansatz by Ott and Antonsen, but which gives better fits to biological data and a new level-set Kalman Filter that can be used to simulate population densities. My focus applications will be determining the phase of circadian rhythms, the scoring of sleep and the detection of COVID with wearables.

2021-04-01 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄: WGAN with an Infinitely Wide Generator Has No Spurious Stationary Points

by 류경석(서울대학교)

Generative adversarial networks (GAN) are a widely used class of deep generative models, but their minimax training dynamics are not understood very well. In this work, we show that GANs with a 2-layer infinite-width generator and a 2-layer finite-width discriminator trained with stochastic gradient ascent-descent have no spurious stationary points. We then show that when the width of the generator is finite but wide, there are no spurious stationary points within a ball whose radius becomes arbitrarily large (to cover the entire parameter space) as the width goes to infinity.

Events for the 취소된 행사 포함