The 5th KMGS will be held on April 7th, Thursday, via Zoom and Gather Town.

We invite two speakers Ho Bin Lee and Juhun Baik from Dept. of Mathematical Sciences, KAIST.

The abstracts of two talks are as follows.

1st slot (PM 12:00~12:20)

[**Speaker**] Ho Bin Lee (이호빈) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. Moon-Jin Kang (강문진 교수님)

[**Title**] The time-asymptotic stability of composite wave for the 1-d compressible barotropic Navier-Stokes Equation

[**Discipline**] Analysis (PDE)

[**Abstract**]

We prove the time-asymptotic stability of composite wave consisting of superposition of a viscous shock and a rarefaction for the 1-dimensional compressible barotropic Navier Stokes equations. This problem first mentioned in 1986 by Matsumura and Nishihara. This problem has unsolved between 1986 and 2021. The main difficulty is due to the incompatibility of the standard anti-derivative method, often used to study this area. In 2021, MOON-JIN KANG, ALEXIS F. VASSEUR, and YI WANG solve this problem using ground-breaking technic. But this has a little limits which make generalization to difficult. So, HO BIN LEE and SUNG-HO HAN little change the proof.

[**Language**] Korean

2nd slot (PM 12:25~12:45)

[**Speaker**] Juhun Baik (백주헌) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. Hyungryul Baik (백형렬 교수님)

[**Title**] Mapping class groups and Topological entropy

[**Discipline**] Geometric Topology

[**Abstract**]

Let $S := S_{g, n}$ be a surface of genus $g$ with $n$ punctures. We collect all isotopy classes of homeomorphisms of $S$, call it as a “Mapping class group” and denote it as $Mod(S)$ or $MCG(S)$. In this talk I will introduce (1) classification of elements in $Mod(S)$, (2) Actions on some spaces such as moduli space or Teichmuller space, (3) Topological entropy followed by my recent work. This is a joint work with my advisor Harry Hyungryul Baik, Changsub Kim, and Philippe Tranchida.

[**Language**] Korean

[Zoom link]

https://kaist.zoom.us/j/2655728482?pwd=OXpJeFdDcWliSG51WUp0N1Nad2JHdz09

ID: 265 572 8482

Password: 2AHRKr

[Gather Town link]

https://gather.town/app/ffr2PVibAWRIyXWO/kaistmath