[Notice] 12th KMGS on Oct. 6(Thu), 2022

The 12th KMGS will be held on October 6th, Thursday, at Natural Science Building (E6-1) Room 1501.
We invite a speaker Juhun Baik (백주헌) from the Dept. of Mathematical Sciences, KAIST.
The abstract of the talk is as follows.

Slot (AM 11:50~PM 12:30)
[Speaker] Juhun Baik (백주헌) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. Hyungryul Baik (백형렬 교수님)
[Title] Shift locus of cubic polynomial
[Discipline] Topology
[Abstract]This talk is about the complex dynamics, which cares the iteration of holomorphic map (usually a rational map on the Riemann sphere), and the shift locus is a nice set of polynomials that all critical points escape to infinity under iteration.Understanding the shape and topology of shift locus is a challenge for decades, and accumulated works are done by Blanchard, Branner, Hubbard, Keen, McMullen, and recently Calegari introduce a nice lamination model.In this talk I will explain the basic complex dynamics and introduce the topology of the shift locus of cubic polynomials done by Calegari’s paper ‘Sausages and Butcher paper’ and if time allows, I will end this talk with the connection to the Big mapping class group, the MCG of Sphere – Cantor set.
[Language] Korean (English if it is requested)

[Notice] 11th KMGS on Sep. 29(Thu), 2022

The 11th KMGS will be held on September 29th, Thursday, at Natural Science Building (E6-1) Room 1501.
We invite a speaker Junyoung Park (박준영) from the Dept. of Mathematical Sciences, KAIST.
The abstract of the talk is as follows.

Slot (AM 11:50~PM 12:30)
[Speaker] Junyoung Park (박준영) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. Cheolwoo Park (박철우 교수님), Prof. Jeongyoun Ahn (안정연 교수님)
[Title] Kernel methods for radial transformed compositional data with many zeros
[Discipline] Statistics
[Abstract]
Compositional data analysis with a high proportion of zeros has gained increasing popularity, especially in chemometrics and human gut microbiomes research. Statistical analyses of this type of data are typically carried out via a log-ratio transformation after replacing zeros with small positive values. We should note, however, that this procedure is geometrically improper, as it causes anomalous distortions through the transformation. We propose a radial transformation that does not require zero substitutions and more importantly results in essential equivalence between domains before and after the transformation. We show that a rich class of kernels on hyperspheres can successfully define a kernel embedding for compositional data based on this equivalence. The applicability of the proposed approach is demonstrated with kernel principal component analysis.
[Language] Korean (English if it is requested)

[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