Month: March 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

[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