Wednesday, May 6, 2020

2020-05-07 / 10:00 ~ 11:40

콜로퀴엄 - 위상수학 세미나: Knots, surfaces, and 3- and 4-manifolds

by 박정환(Georgia Institute of Technology)

There are two different but closely related perspectives in low dimensional topology. Both are motivated by the fact that it is often easier to understand manifolds when broken into smaller pieces. Given a closed 3-manifold, it is natural to ask which compact 4-manifolds can it bound. More concretely, one can ask whether it bounds a compact 4-manifold with simple homology. I will talk about some recent developments in this direction including joint work with Aceto and Celoria. Another perspective is to consider knots in a 3-manifold which arises as the boundary of a 4-manifold and ask what kind of surfaces can the knots bound in the 4-manifold. A commonly studied special case is the 3-sphere and the 4-ball. I will talk about a result joint with Hom and Kang where we study the complexity of disks embedded in the 4-ball.

2020-05-11 / 16:00 ~ 17:30

콜로퀴엄 - PDE 세미나: Well-posedness theory for the compressible Euler system

by 강문진(숙명여자대학교)

In 1752, Euler first formulated the system of equations describing the dynamics of a perfect fluid. This system was complemented by Clausius in the 19th century, by introducing the concept of entropy of thermodynamics. This self-contained system is called compressible Euler system (CE). The most important feature of CE is the finite-time breakdown of smooth solutions, that is, the formation of shock as severe singularity due to irreversibility and discontinuity. Therefore, a fundamental question (since Riemann 1858) is on what happens after a shock occurs. This is the problem on well-posedness (that is, existence, uniqueness, stability) of weak solutions satisfying the 2nd law of thermodynamics, which is called entropy solution. This issue has been conjectured as follows: Well-posedness of entropy solutions for CE can be obtained in a class of vanishing viscosity limits of solutions to the Navier-Stokes system. This conjecture for the fundamental issue remains wide open even for the one-dimensional CE. My recent result (arXiv:1902.01792) provides a first answer to the conjecture in the case of the 1D isentropic CE starting from a shock. The proof crucially uses our new methodology (arXiv:1712.07348) to get the contraction of any large perturbations from viscous shock to the Navier-Stokes. This will be a main part of my talk.

2020-05-13 / 16:00 ~ 17:30

학과 세미나/콜로퀴엄 - 위상수학 세미나: Big mapping class groups acting on homology

by Federica Fanoni(CNRS)

To try and understand the group of symmetries of a surface, its mapping class group, it is useful to look at its action on the first homology of the surface. For finite-type surfaces this action is fairly well understood. I will recall what happens in this case, introduce infinite-type surfaces (surfaces whose fundamental group is not finitely generated) and discuss joint work with Sebastian Hensel and Nick Vlamis in which we describe the action on homology for these surfaces.

2020-05-06 / 16:00 ~ 17:30

학과 세미나/콜로퀴엄 - 위상수학 세미나: On Translation Lengths of Anosov Maps on Curve Graph of Torus

by Changsub Kim(KAIST)

We show that an Anosov map has a geodesic axis on the curve graph of a torus. The direct corollary of our result is the stable translation length of an Anosov map on the curve graph is always a positive integer. As the proof is constructive, we also provide an algorithm to calculate the exact translation length for any given Anosov map.

Events for the 취소된 행사 포함