### [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

ID: 265 572 8482

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

### Photos from the 3rd KMGS

We uploaded photos from the 3rd KMGS on 17th March, 2022. Thank you Junghyun Lee and the participants!

### [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)

ID: 265 572 8482

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

### [Notice] 3rd KMGS on Mar. 17(Thu), 2022

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)

ID: 265 572 8482

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

### Photos from the 2nd KMGS

We uploaded photos from the 2nd KMGS on November 25th. Thanks to Wooyoung, Donggyu, and all other participants!

### Photos from the 1st KMGS

We have successfully completed our first KMGS! Thanks to the speakers Ho-youn Kim and Doyoung Choi and other attendees. Here are photos from the seminar. See you soon in the 2nd KMGS, the next week.

### [Notice] 2nd KMGS on Nov. 25(Thu), 2021

Our second KMGS will be held on November 25th, Thursday, via Zoom and Gather Town.
We invite Wooyoung Chin from Dept. of Mathematical Sciences, KAIST and Donggyu Kim from Dept. of Mathematical Sciences, KAIST and IBS Discrete Mathematics Group (DIMAG).
The abstracts of two talks are as follows.

1st slot (PM 12:00~12:20)
Speaker: Wooyoung Chin (진우영) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. Paul Jung (폴 정 교수님)
Title: A new elementary proof of the central limit theorem
Discipline: Probability
Abstract: The proof of the central limit theorem (CLT) is often deferred to a graduate course in probability because the notion of characteristic functions is sometimes considered too advanced. I’ll start the talk by reviewing the past efforts to provide an elementary proof of the CLT which is not based on characteristic functions. Then I will explain a new proof of the CLT that derives it from the de Moivre-Laplace theorem, which is the CLT for Bernoulli random variables. The de Moivre-Laplace theorem is the first instance of the CLT in the history, and can be proved directly by computation.
Language: Korean (English if it is requested)

2nd slot (PM: 12:25~12:45)
Speaker: Donggyu Kim (김동규) from Dept. of Mathematical Sciences, KAIST and IBS Discrete Mathematics Group (DIMAG), supervised by Prof. Sang-il Oum (엄상일 교수님)
Title: Eigenvalues and parity factors in graphs
Discipline: Graph Theory
Abstract: Let $G$ be a graph and let $g, f$ be nonnegative integer-valued functions defined on $V(G)$ such that $g(v) \le f(v)$ and $g(v) \equiv f(v) \pmod{2}$ for all $v \in V(G)$.A $(g,f)$-parity factor of $G$ is a spanning subgraph $H$ such that for each vertex $v \in V(G)$, $g(v) \le d_H(v) \le f(v)$ and $f(v)\equiv d_H(v) \pmod{2}$.In this paper, we prove sharp upper bounds for certain eigenvalues in an $h$-edge-connected graph $G$ with given minimum degree to guarantee the existence of a $(g,f)$-parity factor; we provide graphs showing that the bounds are optimal. This is a joint work with Suil O.
Language: Korean (English if it is requested)

### [Notice] 1st KMGS on Nov. 18(Thu), 2021

We are glad to inform you that our first KMGS will start on November 18th, Thursday, via Zoom and Gather Town.
We invite Ho-Youn Kim from Dept. of Mathematical Sciences, KAIST and Doyoung Choi from Dept. of Mathematical Sciences, KAIST and IBS Center for Complex Geometry (CCG).
The abstracts of two talks are as follows.

1st slot (PM 12:00~12:20)
Speaker: Ho-youn Kim (김호연) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. Yong Jung Kim (김용정 교수님)
Title: What is the correct diffusion equation in heterogeneous mediums
Discipline: PDE
Abstract: In the classical diffusion theory, the diffusivity has been regarded as an intrinsic property of particles. However, it can’t explain diffusion phenomena in heterogeneous medium, one of the most famous example is Soret effect. The diffusivity can be changed along different mediums and it arises a question: how can we express heterogeneous diffusion. In this talk, I’ll introduce the heterogeneous diffusion equation we found and give some experimental data verifying this work.
Language: Korean

2nd slot (PM 12:25~12:45)
Speaker: Doyoung Choi (최도영) from Dept. of Mathematical Sciences, KAIST and IBS Center for Complex Geometry (CCG), supervised by Prof. Yongnam Lee (이용남 교수님)
Title: Chern classes of tautological sheaves on Hilbert schemes of points on surface
Discipline: Algebraic Geometry
Abstract: I will introduce some concepts of Chern classes, Hilbert schemes and tautological sheaves on Hilbert scheme of points which is associated to a line bundle on surfaces. Also, I will provide a brief description of Lehn’s work which gives an algorithmic approach of the action of the Chern classes of tautological bundles on the cohomology of Hilbert schemes of points on a smooth surface. His work is based on the framework of Nakajima’s oscillator algebra. At the end, I will present the computation of the top Segre classes of tautological bundles associated to line bundles on $Hilb^n$ up to $n \leq 7$, extending computations of Severi, LeBarz, Tikhomirov and Troshina.
Language: Korean

### We are looking for abstracts!

On November 18th and 25th, dates with colloquiums, we would like to start our first and second seminar.
For our friendly KAIST graduate students in the department of mathematical sciences, if you are interested in delivering a short talk, feel free to send us your abstract via the below email.
On each date, we would organize two slots each of which consists of 20 min talk and 5 min QnA session.
After these slots, there would be a “coffee break” for discussing and communicating with other attendees.

Contact :
Jungho Ahn – junghoahn(at)kaist(dot)ac(dot)kr
Yeongjong Kim – kimyj(at)kaist(dot)ac(dot)kr

The email format is as follows.

Email title: KMGS abstract submission – (NAME)
Email content should contain the following.

• Your name, including English version