Tuesday, November 19, 2024

2024-11-25 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 박사논문심사: 에너지 임계성 비균질 비선형 슈뢰딩거 방정식의 해의 전역적 존재성 및 분산성

by 박동진()

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.

2024-11-25 / 17:00 ~ 18:00

학과 세미나/콜로퀴엄 - 대수기하학:

by ()

Given two relatively prime positive integers, p < q, Kunz and Waldi defined a class of numerical semigroups which we denote by KW(p, q) consisting of semigroups of embedding dimension n and type n−1 and multiplicity p by filling in the gaps of the semigroup < a, b >. We study these semigroups, give a criterion for these in terms of principal matrices or their critical binomials and generalize the notion to KW(p, q, w) and prove some results and questions. We will discuss their resolutions and Betti Numbers. Most of this is a joint work with Srishti Singh.

2024-11-25 / 15:30 ~ 16:30

학과 세미나/콜로퀴엄 - 대수기하학:

by ()

In this talk, we consider a finite rational map determined by a linear system with base locus. The degree of such map has been studied in many situation, for instance, the degree of Gauss map of theta divisors. In principal, this degree can be computed by Segre class of the base locus. In practice, one can use Vogel's cycle to give an estimation. Associated to the base locus, one can define distinguished subvarieties, which has been used to the study of geometric Nullstellensatz by Ein-Lazarsfeld. We discuss how distinguished subvarieties and their coefficients can be used to estimate the degree of finite rational map. This is a joint work with Yilong Zhang.

2024-11-25 / 14:00 ~ 15:00

학과 세미나/콜로퀴엄 - 대수기하학:

by ()

Let (R,m_R) be a d-dimensional, excellent, normal local ring. A divisorial filtration {I_n} is determined by a divisor D on a normal scheme X determined by blowing up an ideal on R, so that I_n are the global sections of nD. Associated to an m_R-primary divisorial filtration, we have the Hilbert function f(n)=\lambda_R(R/I_n), where \lambda_R is the length of an R-module. We discuss how close or far this function is from being a polynomial, focusing on examples which are constructed and analyzed geometrically.

2024-11-26 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Graphon branching processes and fractional isomorphism

by Eng Keat Hng(IBS 극단 조합 및 확률 그룹)

In 2005, Bollobás, Janson and Riordan introduced and extensively studied a general model of inhomogeneous random graphs parametrised by graphons. In particular, they studied the emergence of a giant component in these inhomogeneous random graphs by relating them to a broad collection of inhomogeneous Galton-Watson branching processes. Fractional isomorphism of finite graphs is an important and well-studied concept at the intersection of graph theory and combinatorial optimisation. It has many different characterizations that involve a range of very different and seemingly unrelated properties of graphs. Recently, Grebík and Rocha developed a theory of fractional isomorphism for graphons. In our work, we characterise inhomogeneous random graphs that yield the same inhomogeneous Galton-Watson branching process (and hence have a similar component structure). This is joint work with Jan Hladký and Anna Margarethe Limbach.

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