KAIST Math Graduate Student Seminar (KMGS)

The 41th KMGS will be held on December 05, Thursday, at the Natural Science Building (E6-1) Room 3438. We invite a speaker Woojoo Lee from the Dept. of Mathematical Sciences, KAIST.
The abstract of the talk is as follows.

[Speaker] 이우주 (Woojoo Lee) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. 임미경, Mikyoung Lim

[Title] Inverse scattering problems for moving targets: tracking of location and orientation

[Discipline] Inverse problems (Applied mathematics)

[Abstract]Inverse scattering problems aim to identify geometric and material properties of scatterers from measurements. For moving targets, the problems extend to estimating their trajectories; these problems are inherently nonlinear, ill-posed, and further complicated by the unpredictable motion of the targets. In this talk, I address the inverse scattering problem for moving targets using far-field data. Specifically, I focus on identifying both the location and orientation of targets from a single incident field, assuming the target’s movement is modeled as a rigid motion. We derive the translation and rotation formulas for far-field data and establish their local Lipschitz property with respect to the rotation angle. By integrating these results with Bayesian optimization and machine learning, we recover the trajectory of the moving target and estimate its shape with accurate orientation at each time point. Numerical simulations with randomly generated targets and trajectories demonstrate the robustness and effectiveness of the proposed method.

[Language] Korean but English if it is requested

The 40th KMGS will be held on November 21, Thursday, at the Natural Science Building (E6-1) Room 3438. We invite a speaker Minseong Kwon from the Dept. of Mathematical Sciences, KAIST.
The abstract of the talk is as follows.

[Speaker] 권민성 (Minseong Kwon) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. 황준묵, Jun-Muk Hwang from IBS CCG

[Title] Isotropy Irreducible Varieties and Complex Contact Geometry

[Discipline] Geometry

[Abstract]Isotropy irreducible spaces are first introduced by Riemannian geometers, as homogeneous real manifolds carrying a canonical invariant metric. Such spaces are classified by Manturov (1960s), Wolf (1968) and Krämer (1975), and their classification provides a number of interesting new examples, for example satisfying the Einstein condition. In this talk, I will introduce a complexified version of isotropy irreducible space, which is called isotropy irreducible variety. In the first half, I will explain geometric properties of isotropy irreducible varieties, and give several non-classical examples belonging to algebraic geometry. Next, I will present a connection between isotropy irreducible varieties and complex contact geometry, which has not been observed in the real setting.

[Language] Korean but English if it is requested

The 39th KMGS will be held on November 7, Thursday, at the Natural Science Building (E6-1) Room 3438.We invite a speaker Junseok Kim from the Dept. of Mathematical Sciences, KAIST.
The abstract of the talk is as follows.

[Speaker] 김준석 (Junseok Kim) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. 백형렬, Hyungryul Baik

[Title] Right-angled Artin groups and their automorphism groups

[Discipline] Group Theory

[Abstract]Right-angled Artin groups are fascinating objects in geometric topology and geometric group theory. They play a central role in Ian Agol’s proof of Thurston’s virtual fibering and virtual Haken conjectures, providing numerous examples in the field of geometric group theory. In this talk, we will focus on their automorphism groups and outer automorphism groups. I will introduce these groups from a group-theoretic perspective, covering aspects such as finite generation and the standard representation. If time permits, we will also explore the relationship between Gromov-hyperbolicity and the outer automorphism groups.

[Language] Korean but English if it is requested

The 38th KMGS will be held on October 31, Thursday, at the Natural Science Building (E6-1) Room 3438.We invite a speaker Yun Min Song from the Dept. of Mathematical Sciences, KAIST.
The abstract of the talk is as follows.

[Speaker] 송윤민 (Yun Min Song) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. 김재경, Jae Kyoung Kim

[Title] Personalized Digital Medicine for Mood & Sleep disorders using mathematical models

[Discipline] Mathematical Biology

[Abstract]
Mood and sleep disorders are common in today’s society, often linked to irregular sleep patterns and disrupted circadian rhythms. However, it is difficult to measure circadian rhythms directly, making the relationship between these factors unclear. In this talk, we show how mathematical models, applied to data from wearable devices, can help predict changes in circadian rhythms and clarify the connection between sleep patterns and mood. We also discuss the potential for using these models to develop personalized digital treatments for mood and sleep disorders.[Language] Korean but English if it is requested

The 37th KMGS will be held on October 10, Thursday, at the Natural Science Building (E6-1) Room 3438.We invite a speaker Dohyeon Lee from the Dept. of Mathematical Sciences, KAIST.
The abstract of the talk is as follows.

[Speaker] 이도현 (Dohyeon Lee) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. Andreas Holmsen
[Title] Colorful intersecting patterns of convex sets
[Discipline] Combinatorics
[Abstract]
In d-dimensional Euclidean space R^d, any set of d+1 points is linearly dependent, meaning they can be partitioned into two parts, say A and B, such that the subspace spanned by A and B intersect nontrivially. Similarly, d+2 points in R^d have affine dependency, and Radon’s theorem asserts that this dependency gives a partition that their convex hull intersect. In this talk, we will see fundamental results in combinatorial geometry including Tverberg’s, Caratheodory’s, and Helly’s theorem in a linear algebraic point of view. We will also discuss various generalizations of these theorems, including colorful and fractional versions.
[Language] Korean but English if it is requested

The 36th KMGS will be held on September 26th, Thursday, at the Natural Science Building (E6-1) Room 3438.
We invite a speaker Namhyun Eun from the Dept. of Mathematical Sciences, KAIST.
The abstract of the talk is as follows.

[Speaker] 은남현 (Namhyun Eun) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. 강문진, Moon-Jin Kang
[Title] Uniqueness and Stability of Riemann shocks to compressible Euler system in a class of inviscid limits
[Discipline] Analysis (of PDEs)
[Abstract]
In this talk, we will discuss the uniqueness and stability of a Riemann shock solution to the compressible Euler system, which is a self-similar entropy solution connecting two different constant states, in a physical vanishing viscosity limits. We focus on the one dimensional compressible full Euler system and consider the Brenner-Navier-Stokes-Fourier system, which is an amendment of the Navier-Stokes-Fourier system, to describe the physical perturbation class. (This is a joint work with Moon-Jin Kang (KAIST) and Saehoon Eo (Stanford University).
[Language] Korean

The 35th KMGS will be held on September 12th, Thursday, at the Natural Science Building (E6-1) Room 3438.
We invite a speaker Daehee Cho from the Dept. of Mathematical Sciences, KAIST.
The abstract of the talk is as follows.

[Speaker] 조대희 (Daehee Cho) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. 임미경, Mikyoung Lim
[Title] Analytic shape recovery of an elastic inclusion from elastic moment tensors
[Discipline] Inverse problem (Applied mathematics)
[Abstract]
In this presentation, I will present an analytic non-iterative approach for recovering a planar isotropic elastic inclusion embedded in an unbounded medium from the elastic moment tensors (EMTs), which are coefficients for the multipole expansion of field perturbation caused by the inclusion. EMTs contain information about the inclusion’s material and geometric properties and, as is well known, the inclusion can be approximated by a disk from leading-order EMTs. We define the complex contracted EMTs as the linear combinations of EMTs where the expansion coefficients are given from complex-valued background polynomial solutions. By using the layer potential technique for the Lamé system and the theory of conformal mapping, we derive explicit asymptotic formulas in terms of the complex contracted EMTs for the shape of the inclusion, treating the inclusion as a perturbed disk. These formulas lead us to an analytic non-iterative algorithm for elastic inclusion reconstruction using EMTs. We perform numerical experiments to demonstrate the validity and limitations of our proposed method.
[Language] Korean

We are informing you of the schedule of the KAIST Math Graduate student Seminar(KMGS) 2024 Fall. We look forward to your attention and participation!

In this seminar, 7 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.
Please apply through the QR code on the poster.

The 34th KMGS will be held on May 16th, Thursday, at Natural Science Building (E6-1) Room 1501.
We invite a speaker Seungyeol Park from the Dept. of Mathematical Sciences, KAIST.
The abstract of the talk is as follows.

[Speaker] 박승열 (Seungyeol Park) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. 최서영, Suhyoung Choi
[Title] Deformations of Coxeter orbifolds
[Discipline] Geometric Topology
[Abstract]
Given a smooth manifold or orbifold M and a Lie group G acting transitively on a space X, we consider the space of all (G, X)-structures on M up to an appropriate equivalence relation. This space, known as the deformation space of (G, X)-structures on M, encodes information about how one can “deform” the (G, X)-manifold M. In this talk, I will provide a general definition of deformation spaces and character varieties, which capture the local structure of the deformation space. Additionally, I will introduce a class of orbifolds called the Coxeter orbifolds, for which deformation spaces can be computed using an approach due to the foundational work of E. Vinberg.
[Language] Korean but English if it is requested