KAIST Math Graduate Student Seminar (KMGS)

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

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

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

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

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)

[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

The 3rd KMGS will be held on March 17th, Thursday, via Zoom and Gather Town.
We invite Junghyun Lee who graduated from Dept. of Mathematical Sciences, KAIST and is now a graduate student in Kim Jaechul Graduate School of AI, KAIST.
In this seminar, we have one talk which will last for 40 minutes with 10 minutes discussion session, after the talk.
The abstract is as follows.

Slot (PM 12:00~12:40)
[Speaker] Junghyun Lee (이정현) from Kim Jaechul Graduate School of AI, KAIST, supervised by Prof. Se-Young Yun (윤세영 교수님)
[Title] Fast and efficient MMD-based fair PCA via optimization over Stiefel manifold
[Discipline] Machine Learning, Optimization
[Abstract]
This paper defines fair principal component analysis (PCA) as minimizing the maximum mean discrepancy (MMD) between dimensionality-reduced conditional distributions of different protected classes. The incorporation of MMD naturally leads to an exact and tractable mathematical formulation of fairness with good statistical properties. We formulate the problem of fair PCA subject to MMD constraints as a non-convex optimization over the Stiefel manifold and solve it using the Riemannian Exact Penalty Method with Smoothing (REPMS; Liu and Boumal, 2019). Importantly, we provide local optimality guarantees and explicitly show the theoretical effect of each hyperparameter in practical settings, extending previous results. Experimental comparisons based on synthetic and UCI datasets show that our approach outperforms prior work in explained variance, fairness, and runtime.
This paper is accepted to the 36th AAAI Conference on Artificial Intelligence (AAAI 2022).
[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