Friday, March 25, 2022

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2022-03-25 / 16:00 ~ 17:00
SAARC 세미나 - SAARC 세미나: Sparse graphs based on exchangeable random measures: properties, models and examples 인쇄
by François Caron(University of Oxford)
Random simple and multigraph models based on exchangeable random measures, sometimes named graphex processes or generalised graphon models, have recently been proposed as a flexible class of sparse random graph models. This class of models can be seen as a generalisation of the popular graphon models. I will present this class of models, discuss some of their asymptotic properties, in particular the asymptotic behaviour of the degree distribution and of the clustering coefficients. I will also present some particular parametric models within this class and their use for discovering latent communities in sparse real-world networks.
2022-04-01 / 16:30 ~ 18:00
학과 세미나/콜로퀴엄 - 박사논문심사: 대수 곡선 상의 차수가 2인 벡터 번들의 대칭 거듭제곱의 안정성 인쇄
by 김정섭(KAIST)
심사위원장: 이용남, 심사위원 : 곽시종, 백상훈, 최영욱(영남대 수학교육과), 최인송(건국대 수학과)
2022-04-01 / 10:30 ~ 11:45
학과 세미나/콜로퀴엄 - 대수기하학: An introductory guide to mixed Hodge modules #8 인쇄
by 정승조(전북대학교)
Morihiko Saito's theory of mixed Hodge modules is a far generalisation of classical Hodge theory, which is based on the theory of perverse sheaves, D-modules, variations of Hodge structures. One can think of mixed Hodge modules as a certain class of D-modules with Hodge structures. Naturally they are accompanied by perverse sheaves via the Riemann–Hilbert correspondence. This guide consists of about 8 talks, which may cover: review of classical Hodge theory, D-modules and filtered D-modules, nearby and vanishing cycles, etc. The main goal is to understand the notion of mixed Hodge modules and to explain two important theorems: the structure theorem and the direct image theorem. If time permits, we discuss recent applications of the theory in algebraic geometry.
2022-03-25 / 16:00 ~ 17:00
학과 세미나/콜로퀴엄 - 콜로퀴엄: 인쇄
by ()
Random simple and multigraph models based on exchangeable random measures, sometimes named graphexprocesses or generalisedgraphonmodels, have recently been proposed as a flexible class of sparse random graph models. This class of models can be seen as a generalisationof the popular graphonmodels. I will present this class of models, discuss some of their asymptotic properties, in particular the asymptotic behaviourof the degree distribution and of the clustering coefficients. I will also present some particular parametric models within this class and their use for discovering latent communities in sparse real-world networks.
2022-03-30 / 16:00 ~ 17:00
IBS-KAIST 세미나 - IBS-KAIST 세미나: 인쇄
by ()
We investigate in depth the behaviour of Monge-Ampère volumes of quasi-psh functions on a given compact hermitian manifold. We prove that the property for these Monge-Ampère volumes to stay bounded away from zero or infinity is a bimeromorphic invariant. We show in particular that a conjecture of Demailly-Paun holds true if and only if such Monge-Ampère volumes stay bounded away from infinity. This is a joint work with Vincent Guedj.
2022-03-28 / 16:30 ~ 17:30
IBS-KAIST 세미나 - 이산수학: Thresholds for incidence properties in finite vector spaces 인쇄
by Ben Lund(IBS 이산수학그룹)
Suppose that $E$ is a subset of $\mathbb{F}_q^n$, so that each point is contained in $E$ with probability $\theta$, independently of all other points. Then, what is the probability that there is an $m$-dimensional affine subspace that contains at least $\ell$ points of $E$? What is the probability that $E$ intersects all $m$-dimensional affine subspaces? We give Erdős-Renyi threshold functions for these properties, in some cases sharp thresholds. Our results improve previous work of Chen and Greenhill. This is joint work with Jeong Han Kim, Thang Pham, and Semin Yoo.
2022-03-25 / 16:00 ~ 17:00
학과 세미나/콜로퀴엄 - PDE 세미나: 인쇄
by 김일두(고려대학교)
In this talk, we present a short history of L^p-theories for partial differential equations. In particular, we introduce recent developments handling fractional derivatives and degenerate estimates in weighted spaces.
2022-03-31 / 11:00 ~ 12:00
IBS-KAIST 세미나 - 수리생물학: 인쇄
by ()
We will discuss hormone circuits and their dynamics using new models that take into account timescales of weeks due to growth of the hormone glands. This explains some mysteries in diabetes and autoimmune disease.
2022-03-25 / 10:30 ~ 11:45
학과 세미나/콜로퀴엄 - 대수기하학: An introductory guide to mixed Hodge modules #7 인쇄
by 정승조(전북대학교)
Morihiko Saito's theory of mixed Hodge modules is a far generalisation of classical Hodge theory, which is based on the theory of perverse sheaves, D-modules, variations of Hodge structures. One can think of mixed Hodge modules as a certain class of D-modules with Hodge structures. Naturally they are accompanied by perverse sheaves via the Riemann–Hilbert correspondence. This guide consists of about 8 talks, which may cover: review of classical Hodge theory, D-modules and filtered D-modules, nearby and vanishing cycles, etc. The main goal is to understand the notion of mixed Hodge modules and to explain two important theorems: the structure theorem and the direct image theorem. If time permits, we discuss recent applications of the theory in algebraic geometry.
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