Saturday, November 30, 2024

2024-12-04 / 15:00 ~ 16:30

by 최인혁()

Recently, Bowden-Hensel-Webb introduced the notion of fine curve graph as an analogue of the classical curve graph. They used this to construct nontrivial quasi-morphisms (in fact, infinitely many independent ones) on Homeo_0(S). Their method crucially uses independent pseudo-Anosov conjugacy classes, whose existence follows from the WPD-ness of pseudo-Anosov mapping classes on the curve graph. Meanwhile, the WPD-ness of pseudo-Anosov maps on the fine curve graph is not achievable, as Homeo_0(S) is a simple group. In this talk, I will explain my ongoing regarding an analogue of WPD-ness for point-pushing pseudo-Anosov maps on the fine curve graph. If time allows, I will explain how this is related to the construction of independent pseudo-Anosov conjugacy classes in Homeo_0(S).

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

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

by 오재민()

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.

2024-12-05 / 11:50 ~ 12:40

대학원생 세미나 - 대학원생 세미나:

by 이우주()

TBA

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).

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