Tuesday, November 26, 2024

2024-11-29 / 11:00 ~ 12:00

by 정윤모(성균관대학교)

Dimensionality reduction represents the process of generating a low dimensional representation of high dimensional data. In this talk, I explain what dimensionality reduction is and shortly mention formation control. After that, I will introduce a nonlinear dynamical system designed for dimensionality reduction. I briefly discuss mathematical properties of the model and demonstrate numerical experiments on both synthetic and real datasets.

2024-11-29 / 14:00 ~ 15:00

SAARC 세미나 - SAARC 세미나:

by ()

We discuss on fractional weighted Sobolev spaces with degenerate weights and related weighted nonlocal integrodifferential equations. We provide embeddings and Poincare inequalities for these spaces and show robust convergence when the parameter of fractional differentiability goes to $1$. Moreover, we prove local H\"older continuity and Harnack inequalities for solutions to the corresponding nonlocal equations. The regularity results naturally extend those for degenerate linear elliptic equations presented in [Comm. Partial Differential Equations 7 (1982); no. 1; 77?116] by Fabes, Kenig, and Serapioni to the nonlocal setting. This is a joint work with Linus Behn, Lars Diening and Julian Rolfes from Bielefeld.

2024-12-03 / 14:00 ~ 15:00

학과 세미나/콜로퀴엄 - 박사논문심사: 물리지식기반 인공신경망의 학습을 개선하는 방법

by 오재민()

2024-11-27 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 박사논문심사: 분자 및 행동 수준의 동적 생명현상 이해를 위한 수리모델의 개선 및 응용

by 송윤민()

2024-12-03 / 15:30 ~ 18:00

편미분방정식 통합연구실 세미나 - 편미분방정식:

by ()

Ist lecture: Understanding material microstructure Abstract Under temperature changes or loading, alloys can form beautiful patterns of microstructure that largely determine their macroscopic behaviour. These patterns result from phase transformations involving a change of shape of the underlying crystal lattice, together with the requirement that such changes in different parts of the crystal fit together geometrically. Similar considerations apply to plastic slip. The lecture will explain both successes in explaining such microstructure mathematically, and how resolving deep open questions of the calculus of variations could lead to a better understanding. 2nd lecture: Monodromy and nondegeneracy conditions in viscoelasticity Abstract For certain models of one-dimensional viscoelasticity, there are infinitely many equilibria representing phase mixtures. In order to prove convergence as time tends to infinity of solutions to a single equilibrium, it is necessary to impose a nondegeneracy condition on the constitutive equation for the stress, which has been shown in interesting recent work of Park and Pego to be necessary. The talk will explain this, and show how in some cases the nondegeneracy condition can be proved using the monodromy group of a holomorphic function. This is joint work with Inna Capdeboscq and Yasemin Şengül.

2024-12-03 / 15:30 ~ 18:00

SAARC 세미나 - SAARC 세미나:

by ()

2024-12-03 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Pairwise disjoint perfect matchings in regular graphs

by Yulai Ma(Paderborn University)

An $r$-graph is an $r$-regular graph in which every odd set of vertices is connected to its complement by at least $r$ edges. A central question regarding $r$-graphs is determining the maximum number of pairwise disjoint perfect matchings they can contain. This talk explores how edge connectivity influences this parameter. For ${0 \leq \lambda \leq r}$, let $m(\lambda,r)$ denote the maximum number $s$ such that every $\lambda$-edge-connected $r$-graph contains $s$ pairwise disjoint perfect matchings. The values of $m(\lambda,r)$ are known only in limited cases; for example, $m(3,3)=m(4,r)=1$, and $m(r,r) \leq r-2$ for all $r \not = 5$, with $m(r,r) \leq r-3$ when $r$ is a multiple of $4$. In this talk, we present new upper bounds for $m(\lambda,r)$ and examine connections between $m(5,5)$ and several well-known conjectures for cubic graphs. This is joint work with Davide Mattiolo, Eckhard Steffen, and Isaak H. Wolf.

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.

2024-11-29 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 박사논문심사: 계수가 주어진 델타매트로이드와 쌍선형 형식이 주어진 선형공간

by 김동규()

2024-11-28 / 16:00 ~ 18:00

학과 세미나/콜로퀴엄 - 기타: About birational classification of smooth projective surfaces III

by 김재홍(KAIST)

This is a reading seminar to be given by Mr. Jaehong Kim (a graduate student in the department) on foundations of the intersection theory and the classification theory of complex algebraic surfaces. He will give three 2-hour long talks.

2024-12-02 / 16:00 ~ 17:00

편미분방정식 통합연구실 세미나 - 편미분방정식: Absence of anomalous dissipation in the 2D Navier Stokes equations.

by (연세대학교)

In this talk, we will discuss Leray-Hopf solutions to the two-dimensional Navier-Stokes equations with vanishing viscosity. We aim to demonstrate that when the initial vorticity is only integrable, the Leray-Hopf solutions in the vanishing viscosity limit do not exhibit anomalous dissipation. Moreover, we extend this result to the case where the initial vorticity is merely a Radon measure, assuming its singular part maintains a fixed sign. Our proof draws on several key observations from the work of J. Delort (1991) on constructing global weak solutions to the Euler equation. This is a joint work with Luigi De Rosa (University of Basel).

2024-11-29 / 11:00 ~ 12:00

IBS-KAIST 세미나 - IBS-KAIST 세미나:

by ()

Malignant gliomas are highly invasive brain tumors. Recent attention has focused on their capacity for network-driven invasion, whereby mitotic events can be followed by the migration of nuclei along long thin cellular protrusions, termed tumour microtubes (TM). Here I develop a mathematical model that describes this microtube-driven invasion of gliomas. I show that scaling limits lead to well known glioma models as special cases such as go-or-grow models, the PI model of Swanson, and the anisotropic model of Swan. I compute the invasion speed and I use the model to fit experiments of cancer resection and regrowth in the mouse brain. (Joint work with N. Loy, K.J. Painter, R. Thiessen, A. Shyntar).

Events for the 취소된 행사 포함