[Notice] 10th KMGS on Sep. 15(Thu), 2022

The 10th KMGS will be held on September 15th, Thursday, at Natural Science Building (E6-1) Room 1501.
We invite two speakers Sungho Han (한성호) and Hoil Lee (이호일) from the Dept. of Mathematical Sciences, KAIST.
The abstracts of the talks are as follows.

1st slot (AM 11:50~PM 12:10)
[Speaker] Sungho Han (한성호) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. Moon-Jin Kang (강문진 교수님)
[Title] Large time behavior of one-dimensional barotropic compressible Navier-Stokes equations
[Discipline] Analysis (PDE)
[Abstract]
We will discuss on large time behavior of the one dimensional barotropic compressible Navier-Stokes equations with initial data connecting two different constant states. When the two constant states are prescribed by the Riemann data of the associated Euler equations, the Navier-Stokes flow would converge to a viscous counterpart of Riemann solution. This talk will present the latest result on the cases where the Riemann solution consist of two shocks, and introduce the main idea for using to prove.
[Language] Korean

2nd slot (PM 12:15~12:35)
[Speaker] Hoil Lee (이호일) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. Ji Oon Lee (이지운 교수님)
[Title] On infinitely wide deep neural networks
[Discipline] Probability theory, Deep learning
[Abstract]
Deep neural networks have proven to work very well on many complicated tasks. However, theoretical explanations on why deep networks are very good at such tasks are yet to come. To give a satisfactory mathematical explanation, one recently developed theory considers an idealized network where it has infinitely many nodes on each layer and an infinitesimal learning rate. This simplifies the stochastic behavior of the whole network at initialization and during the training. This way, it is possible to answer, at least partly, why the initialization and training of such a network is good at particular tasks, in terms of other statistical tools that have been previously developed. In this talk, we consider the limiting behavior of a deep feed-forward network and its training dynamics, under the setting where the width tends to infinity. Then we see that the limiting behaviors can be related to Bayesian posterior inference and kernel methods. If time allows, we will also introduce a particular way to encode heavy-tailed behaviors into the network, as there are some empirical evidences that some neural networks exhibit heavy-tailed distributions.
[Language] Korean (English if it is requested)

[Notice] 2022 Fall KMGS

We are informing you of the schedule of the KAIST Math Graduate student Seminar(KMGS) 2022 Fall. We look forward to your attention and participation!

In this seminar, 6 talks will be held on Thursday from 11:50 to 12:40 in Room 1501 on the first floor of the Natural Science Building(E6-1).

Lunch will be provided after each talk.

2022 Fall KMGS Poster

[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!

Speaker: Jaehoon Lee
Speaker: Hyukpyo Hong
Group Photo
Gather Town

[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)
[SpeakerHyukpyo 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

[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