Saturday, November 16, 2024

2024-11-22 / 15:00 ~ 17:00

학과 세미나/콜로퀴엄 - 기타: Key properties and theorems on compact Riemann surfaces

by 우태윤(KAIST)

This is a presentation by Mr. Taeyoon Woo, a graduate student in the department, after his reading course on basics on compact Riemann surfaces. He will concentrate on topics such as degree theory of holomorphic maps, Riemann-Roch theorem, residue theorem, Serre duality, Riemann-Hurtiwz theorem, Hodge decomposition, etc. on the compact Riemann surfaces. If time permits, he will discuss its connections to smooth manifolds and algebraic curves.

2024-11-21 / 11:50 ~ 12:40

대학원생 세미나 - 대학원생 세미나:

by 권민성()

Isotropy irreducible spaces are first introduced by Riemannian geometers, as homogeneous real manifolds carrying a canonical invariant metric. Such spaces are classified by Manturov (1960s), Wolf (1968) and Krämer (1975), and their classification provides a number of interesting new examples, for example satisfying the Einstein condition. In this talk, I will introduce a complexified version of isotropy irreducible space, which is called isotropy irreducible variety. In the first half, I will explain geometric properties of isotropy irreducible varieties, and give several non-classical examples belonging to algebraic geometry. Next, I will present a connection between isotropy irreducible varieties and complex contact geometry, which has not been observed in the real setting.

2024-11-19 / 16:00 ~ 17:00

SAARC 세미나 - SAARC 세미나:

by 박대한(강원대학교)

This presentation will consider the Sobolev regularity for solutions to space-time non-local equations. Spatial non-local operators in this presentation are the infinitesimal generator of Levy processes. The relation between the fundamental solution and the transition density of corresponding processes which generates the operator allows one to obtain the estimation of solutions in Lp-spaces. Several results will be introduced with assumptions. The main ingredients are a representation of solutions, heat kernel estimations, and some properties of (singular) integral operators.

2024-11-21 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by 하우석(KAIST 수리과학과)

Modern datasets are often characterized by high-dimensionality and heterogenous environments under distribution shifts, posing significant challenges in terms of signal recovery, robustness, and interpretability. In this talk, I will present three research contributions to address these challenges. First, I will introduce the notion of local concavity coefficients, a novel tool for quantifying the concavity of a set. I will demonstrate its effectiveness in analyzing optimization problems for signal recovery in high-dimensional settings. Second, I will discuss recent advancements in machine learning to handle distribution shifts and emphasize the critical role of invariant features in achieving robust predictions. Finally, I will show how wavelets allow for interpreting feature spaces learned by deep neural networks. Motivated by applications in cosmology, I'll showcase how this tool can be applied to the problem of cosmological parameter inference.

Events for the 취소된 행사 포함