Friday, March 18, 2022

2022-03-25 / 16:00 ~ 17:00

SAARC 세미나 - SAARC 세미나: Sparse graphs based on exchangeable random measures: properties, models and examples

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.

2022-03-25 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 콜로퀴엄:

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.

2022-03-24 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by 김진수()

When a biological system is modeled using a mathematical procedure, the following step is normally to estimate the system parameters. Despite the numerous computational and statistical techniques, estimating parameters for complex systems can be a difficult task. As a result, one can think of revealing parameter-independent dynamical properties of a system. More precisely, rather than estimating parameters, one can focus on the underlying structure of a biochemical system to derive the qualitative behavior of the associated mathematical process. In this talk, we will discuss introduce reaction network theory. A reaction network is a graphical configuration of a biochemical system. One of the most important problems in this field is to relate dynamical properties and the underlying reaction network structure. When abundances of biochemical species (variables) in the system are small, then the randomness inherent in the molecular interactions is crucial to the system dynamics, and the abundances are modeled stochastically as a jump by jump fashion continuous-time Markov chain. The goal of this talk is to 1. walk you through the basic modeling aspect of the stochastically modeled reaction networks, and 2. to show how to derive stability (ergodicity) of the associated Markov process solely based on the underlying network structure.

2022-03-21 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Ramsey numbers of cycles versus general graphs

by 김재훈(KAIST)

The Ramsey number $R(F,H)$ is the minimum number $N$ such that any $N$-vertex graph either contains a copy of $F$ or its complement contains $H$. Burr in 1981 proved a pleasingly general result that for any graph $H$, provided $n$ is sufficiently large, a natural lower bound construction gives the correct Ramsey number involving cycles: $R(C_n,H)=(n-1)(\chi(H)-1)+\sigma(H)$, where $\sigma(H)$ is the minimum possible size of a colour class in a $\chi(H)$-colouring of $H$. Allen, Brightwell and Skokan conjectured that the same should be true already when $n\geq |H|\chi(H)$. We improve this 40-year-old result of Burr by giving quantitative bounds of the form $n\geq C|H|\log^4\chi(H)$, which is optimal up to the logarithmic factor. In particular, this proves a strengthening of the Allen-Brightwell-Skokan conjecture for all graphs $H$ with large chromatic number. This is joint work with John Haslegrave, Joseph Hyde and Hong Liu

2022-03-24 / 12:25 ~ 12:50

대학원생 세미나 - 대학원생 세미나: How can we find a rainbow subgraph?

by 서재현(KAIST)

Finding a given graph in a large host graph is a very essential problem in graph theory. One main variant of this is coloring edges of a host graph with many colors and trying to find a 'rainbow' subgraph, whose edges have distinct colors. I will explain some history, and introduce my recent result which searches for a rainbow color-critical graph.

2022-03-24 / 12:00 ~ 12:25

대학원생 세미나 - 대학원생 세미나: Curves on ruled surfaces

by 김정섭(KAIST / IBS 복소기하연구단)

A ruled surface is a fibration over a smooth curve with fibers being isomorphic to the projective line. If a ruled surface is assumed to not have any section with negative self-intersection, then it is known that there is no curve with negative self-intersection on the ruled surface. Moreover, if the ruled surface is “sufficiently” general in its moduli, then the surface does not admit a curve with zero self-intersection. So, it is natural to ask the questions of which ruled surface admits a curve with zero self-intersection, and how many such ruled surfaces exist in the moduli. In this talk, I will introduce some answers to the questions.

2022-03-25 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - PDE 세미나:

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.

2022-03-18 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - PDE 세미나:

by ()

We prove global Holder gradient estimates for bounded positive weak solutions of fast diffusion equations in smooth bounded domains with homogeneous Dirichlet boundary condition, which then leads us to establish their optimal global regularity. It solves a problem raised by Berryman and Holland in 1980. This is joint work with Jingang Xiong.

2022-03-24 / 11:00 ~ 12:00

IBS-KAIST 세미나 - 수리생물학:

by ()

From the venation patterns of leaves to spider webs, roads in cities, social networks, and the spread of COVID-19 infections and vaccinations, the structure of many systems is influenced significantly by space. In this talk, I will discuss the application of topological data analysis (specifically, persistent homology) to spatial systems. I will present a few examples, such as voting in presidential elections, city street networks, spatiotemporal dynamics of COVID-19 infections and vaccinations, and webs that were spun by spiders under the influence of various drugs.

2022-03-24 / 10:30 ~ 10:55

IBS-KAIST 세미나 - 수리생물학:

by ()

I will give an introduction to topological data analysis (TDA), in which one uses ideas from algebraic topology to study the “shape” of data. I will focus on persistent homology (PH), which is the most common approach in TDA.

2022-03-25 / 10:30 ~ 11:45

학과 세미나/콜로퀴엄 - 대수기하학: An introductory guide to mixed Hodge modules #7

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.

2022-03-18 / 10:30 ~ 11:45

학과 세미나/콜로퀴엄 - 대수기하학: An introductory guide to mixed Hodge modules #6

by 정승조(전북대학교)

2022-03-22 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 대수기하학: Hochschild homology of matrix factorization categories of Deligne-Mumford Stacks

by Bhamidi Sreedhar(IBS Center for Geometry and Physics)

In this talk we will discuss a Hirzebruch-Riemann-Roch (HRR) type theorem for matrix factorization categories of Deligne-Mumford stacks. We will first discuss a proof of a Hochschild-Kostant-Rosenberg type isomorphism and show how it can be used to define a Chern character formula which allows us to prove the HRR type theorem. This talk is based on a joint work with Dongwook Choa and Bumsig Kim.

Events for the 취소된 행사 포함