KAIST Math Graduate Student Seminar (KMGS)

The 19th KMGS will be held on May 11th, Thursday, at Natural Science Building (E6-1) Room 1501.
We invite a speaker Doyoung Choi from the Dept. of Mathematical Sciences, KAIST.
The abstract of the talk is as follows.

Slot (AM 11:50~PM 12:30)
[Speaker] Doyoung Choi(최도영) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. Yongnam Lee (이용남 교수님)
[Title] Degree of the 3-secant variety
[Discipline] Algebraic geometry
[Abstract] 
In this talk, we present a formula for the degree of the 3-secant variety of a nonsingular projective variety embedded by a 3-very ample line bundle. The formula is provided in terms of Segre classes of the tangent bundle of a given variety. We use the generalized version of double point formula to reduce the calculation into the case of the 2-secant variety. Due to the singularity of the 2-secant variety, we use secant bundle as a nonsingular birational model and compute multiplications of desired algebraic cycles.
[Language] Korean

The 18th KMGS will be held on April 6th, Thursday, at Natural Science Building (E6-1) Room 1501.
We invite a speaker Kyunghan Choi from the Dept. of Mathematical Sciences, KAIST.
The abstract of the talk is as follows.

Slot (AM 11:50~PM 12:30)
[Speaker] Kyunghan Choi(최경한) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. Yongjung Kim (김용정 교수님)
[Title] Pattern formations by biological diffusion : chemotaxis model 
[Discipline] Analysis 
[Abstract]
In this seminar, we will talk about the chemotaxis model, which is a diffusion model for biological dispersion. Chemotaxis is the movement of biological organisms in response to chemical stimuli. The chemotaxis model has nonlinear diffusion with no reaction term and has been extensively studied in the sense of a diffusion model for heterogeneous media. The nonlinear diffusion alone makes it possible to allow us to observe various spatial patterns. We will see what kind of pattern formation the model provides and what mathematical problems this model can be applied to. 
[Language] Korean but English if it is requested 

The 17th KMGS will be held on March 23th, Thursday, at Natural Science Building (E6-1) Room 1501.
We invite a speaker Byeongsu Sim from the Dept. of Mathematical Sciences, KAIST.
The abstract of the talk is as follows.

Slot (AM 11:50~PM 12:30)
[Speaker] Byeongsu Sim(심병수) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. Jong Chul Ye (예종철 교수님)
[Title] Improved diffusion generative models for inverse problems respecting the geometry of high-dimensional data
[Discipline] Applied math, deep learning 
[Abstract] In this seminar, I will provide an overview of diffusion generative models, inverse problems, and their applications in solving such problems. Furthermore, I will present a novel interpretation of diffusion generative models and their translation to inverse problems.In collaboration with Hyungjin Chung and Dohoon Ryu, we propose that when data lies in a low-dimensional structure, the set of data with intermediate noise represents the interpolating manifold between the data manifold and the hypersphere of pure noise. Our new method, which respects this geometry, outperforms previous methods, and we provide experimental results as proof of concept.
[Language] Korean but English if it is requested 

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

Slot (AM 11:50~PM 12:30)
[Speaker] Wonyong Jang(장원용) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. Hyungryul Baik (백형렬 교수님)
[Title] On the freeness of groups generated by two parabolic matrices
[Discipline] Geometric Group Theory
[Abstract]
For complex number $\alpha$, let $ A = \begin{bmatrix}
1 & 1 \ 0 & 1
\end{bmatrix}$ and
$B = \begin{bmatrix}
1 & 0 \ \alpha & 1
\end{bmatrix} $
be two parabolic matrices and let $G_\alpha$ be the group generated by these two matrices.
Determining whether $G_\alpha$ is the free group rank 2 or not, is one of the important problems.
In this talk, I will introduce a geometric aspect of the group $G_\alpha$ and give previous results of the problem.
Next, I will introduce my work joint with KyeongRo Kim.
[Language] Korean

We are informing you of the schedule of the KAIST Math Graduate student Seminar(KMGS) 2023 Spring. 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.
Please apply through the QR code on the poster.