Month: March 2023

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