We uploaded photos from the 9th KMGS on 2nd June 2022. Thanks, Kihoon Seong and all the participants!

## [Notice] 9th KMGS on June 2(Thu), 2022

The 9th KMGS will be held on June 2nd, Thursday, via Zoom and Gather Town.

We invite a speaker Kihoon Seong from the Dept. of Mathematical Sciences, KAIST.

The abstract of the talk is as follows.

Slot (PM 12:00~12:40)

[**Speaker**] Kihoon Seong from the Dept. of Mathematical Sciences, KAIST, supervised by Prof. Soonsik Kwon.

[**Title**] Transport properties of Gibbs and Gaussian measures under the flow of Hamiltonian PDEs

[**Discipline**] Analysis

[**Abstract**] Transport properties of Gibbs and Gaussian measures under different transformations have been studied in probability theory. In this talk, I will discuss the invariance and quasi-invariance of Gaussian type measures on functions/distributions under the flow of Hamiltonian PDEs.

[**Language**] Korean (English if it is requested)

[Zoom 링크]

https://kaist.zoom.us/j/7337200858?pwd=SjQ2ZnhDbTYrVFJIaDNneWc5MXcwUT09

회의 ID: 733 720 0858

암호: 123456

[Gather Town 링크]

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

## Photos from the 8th KMGS

We uploaded photos from the 8th KMGS on 26th May 2022. Thanks, Jaehoon Lee, Hyukpyo Hong, and all the participants!

## Photos from the 7th KMGS

We uploaded photos from the 7th KMGS on 19th May 2022. Thanks, Wonwoogn Lee and all the participants!

## [Notice] 8th KMGS on May 26(Thu), 2022

The 8th KMGS will be held on May 26th, Thursday, via Zoom and Gather Town.

We invite two speakers, Jaehoon Lee from the Dept. of Mathematical Sciences, KAIST, and Hyukpyo Hong from the Dept. of Mathematical Sciences, KAIST and IBS Biomedical Mathematics Group (BIMAG).

The abstract of the talks are as follows.

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

[**Speaker**] Jaehoon Lee (이재훈) from the Dept. of Mathematical Sciences, KAIST, supervised by Prof. Paul Jung (폴 정 교수님)

[**Title**] Spectrum of sparse random graphs and related problems

[**Discipline**] Probability

[**Abstract**]

Around early 2010, there was a huge success in understanding the spectrum of large random matrices, in other words, large random graphs. It was only for large but dense random graphs at first. However, as random matrix theory has been developed, there is some progress in sparse cases. In this short talk, I will review a series of results for spectral statistics of sparse random graphs and explain their implications.

[**Language**] Korean (English if it is requested)

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

[**Speaker**] Hyukpyo Hong (홍혁표) from the Dept. of Mathematical Sciences, KAIST and IBS Biomedical Mathematics Group (BIMAG), supervised by Prof. Jae Kyoung Kim (김재경 교수님)

[**Title**] Deriving Stationary distributions from an underlying graph structure

[**Discipline**] Mathematical Biology

[**Abstract**]

Randomness of biochemical reactions is inherent in various biological systems, from DNA to organs and the human body. These stochastic dynamics are frequently modeled using a continuous-time Markov chain (CTMC). Its long-term behavior is described by a stationary distribution, corresponding to its deterministic counterpart called a steady state. Stationary distribution can be derived analytically only in limited systems such as linear or finite-state systems. In this talk, I will introduce a recent result by Anderson, Craciun, and Kurtz deriving stationary distribution from the underlying graph structure of a reaction network and how we can extend it. For those who are first told the word ‘Mathematical Biology,’ I will briefly introduce mathematical biology before going into the detailed topic.

[**Language**] Korean (English if it is requested)

[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

## [Notice] 7th KMGS on May 19(Thu), 2022

The 7th KMGS will be held on May 19th, Thursday, via Zoom and Gather Town.

We invite a speaker Wonwoong Lee from Dept. of Mathematical Sciences, KAIST.

The abstract of the talk is as follows.

Slot (PM 12:00~12:40)

[**Speaker**] Wonwoong Lee (이원웅) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. Bo-Hae Im (임보해 교수님)

[**Title**] Modular forms and transcendental questions

[**Discipline**] Number Theory

[**Abstract**]

Modular curves for Hecke congruence groups, or more generally, for Fuchsian groups of the first kind can be seen as the moduli spaces of the isomorphism classes of elliptic curves with torsion data in some sense. In this talk, I will introduce the notion of modular curves and modular forms. If time permits, I will also introduce their applications to some transcendental questions.

[**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

## Photos from the 6th KMGS

We uploaded photos from the 6th KMGS on 26th April, 2022. We apologize for forgeting to take a group photo. Thank you Doosung Choi and all the participants!

## [Notice] 6th KMGS on Apr. 26(Tue), 2022

The 6th KMGS will be held on April 26th, **Tuesday**, via Zoom and Gather Town.

We invite a speaker Doosung Choi from Dept. of Mathematical Sciences, KAIST.

The abstract of the talk is as follows.

Slot (PM 12:00~12:40)

[**Speaker**] Doosung Choi (최두성) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. Mikyoung Lim (임미경 교수님)

[**Title**] 해외 수학과 포닥 지원은 어떻게 하는가 / Finding a postdoc position

[**Discipline**] General Topic

[**Abstract**]

한국의 수학과 박사과정 대학원생이 해외로 포닥을 지원하는 방법에 대해 발표합니다. 기본적으로 포닥을 지원하기위해 필요한 서류인 CV, 추천서, 연구소개서, 강의소개서 등을 어떻게 준비하는 지에 대해 설명드립니다. 또한 미국과 유럽은 한국과 달리 후기로 뽑기 때문에 지원 시기 및 절차가 많이 다릅니다. 어느 시기에, 어디서, 그리고 누구에게서 포닥 포지션을 구할 수 있는 지에 대한 다방면의 정보를 공유합니다.

I will present how to apply for the abroad postdoc position. Basically, I will explain how to prepare the CV, recommendation letters, research statement, teaching statement, diversity statement, etc., which are necessary documents to apply postdoc. The timelines for the postdoc application of the universities in the U.S. and Europe are very different from Korean universities. I will share a variety of information about when, where, and who you can apply for the postdoc position.

[**Language**] Korean (English if it is requested)

[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

## [Notice] 5th KMGS on Apr. 7(Thu), 2022

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

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

ID: 265 572 8482

Password: 2AHRKr

[Gather Town link]

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

## [Notice] 4th KMGS on Mar. 24(Thu), 2022

The 4th KMGS will be held on March 24th, Thursday, via Zoom and Gather Town.

We invite two speakers Jeong-Seop Kim from Dept. of Mathematical Sciences, KAIST and IBS Center for Complex Geometry (CCG), and Jaehyeon Seo from Dept. of Mathematical Sciences, KAIST.

The abstracts of two talks are as follows.

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

[**Speaker**] Jeong-Seop Kim (김정섭) from Dept. of Mathematical Sciences, KAIST and IBS Center for Complex Geometry (CCG), supervised by Prof. Yongnam Lee (이용남 교수님)

[**Title**] Curves on ruled surfaces

[**Discipline**] Algebraic Geometry

[**Abstract**]

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.

[**Language**] Korean (English if it is requested)

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

[**Speaker**] Jaehyeon Seo (서재현) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. Jaehoon Kim (김재훈 교수님)

[**Title**] How can we find a ‘rainbow’ subgraph?

[**Discipline**] Graph Theory

[**Abstract**]

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.

[**Language**] Korean (English if it is requested)

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

ID: 265 572 8482

Password: 2AHRKr

[Gather Town link]

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