KAIST Math Graduate Student Seminar (KMGS)

We uploaded photos from the 53th KMGS on Dec 04, 2025.
Thanks, Donghan Kim and all the participants!

The 53rd KMGS will be held on December 4, Thursday, at the Natural Science Building (E6-1) Room 1410. We invite a speaker Donghan Kim from the Dept. of Mathematical Sciences, KAIST.
The abstract of the talk is as follows.

[Speaker] 김동한(Donghan Kim) from Dept. of Mathematical Sciences, KAIST, supervised by  Prof. 김우진 (Woojin Kim)
[Title] Persistent Homology is Complementary to the Weisfeiler–Leman Test
[Discipline] Algebraic Topology
[Abstract]
We analyze the expressive power of persistent homology obtained purely from Vietoris–Rips filtrations on the shortest-path metric of a graph, without using any node features. We show that the verbose diagram completely determines the clique numbers in all dimensions, demonstrating that persistent homology captures rich combinatorial structure. We further construct, for every integer k, explicit graph pairs that the k-dimensional Weisfeiler–Leman test cannot distinguish but persistent homology can. These results demonstrate that persistent homology and the Weisfeiler–Leman test are fundamentally incomparable.
[Language] Korean

We uploaded photos from the 52th KMGS on Dec 04, 2025.
Thanks, Yoochan Han and all the participants!

The 52nd KMGS will be held on November 20, Thursday, at the Natural Science Building (E6-1) Room 1410. We invite a speaker Yoochan Han from the Dept. of Mathematical Sciences, KAIST.
The abstract of the talk is as follows.

[Speaker] 한유찬 (Yoochan Han) from Dept. of Mathematical Sciences, KAIST, supervised by  Prof. 이지운 (Ji Oon Lee)
[Title] Spectral Properties and Weak Detection in Stochastic Block Models
[Discipline] Probability Theory
[Abstract]
In this talk, I will introduce basic ideas from random matrix theory and explain how spectral methods are used to study random graphs. Focusing on the stochastic block model, I will present recent results showing a sharp phase transition in the extreme eigenvalues and a central limit theorem for linear spectral statistics. These results lead to a simple spectral test for detecting the presence of communities. This talk is based on the joint work with Prof. Ji Oon Lee and Dr. Wooseok Yang.
[Language] Korean

We uploaded photos from the 51th KMGS on Nov 06, 2025.
Thanks, CHANYOUNG KIM and all the participants!

The 51st KMGS will be held on November 6, Thursday, at the Natural Science Building (E6-1) Room 1410. We invite a speaker Chanyoung Kim from the Dept. of Mathematical Sciences, KAIST.
The abstract of the talk is as follows.

[Speaker] 김찬영(Chanyoung Kim) from Dept. of Mathematical Sciences, KAIST, supervised by  Prof. 하우석 (Wooseok Ha)
[Title] Quantum spectral operator learning for solving partial differential equations
[Discipline] Applied Mathematics
[Abstract]
Partial differential equations (PDEs) are central to modeling physical and engineering systems. Operator learning approximates their solution operators, enabling fast inference after training across diverse problem instances and strong generalization. While recent advances have proposed unsupervised methods that mitigate the cost of data generation, classical neural network–based approaches remain computationally expensive for high-dimensional operators and fine-resolution problems. To address these challenges, we propose a quantum–classical hybrid framework for unsupervised spectral operator learning. Our approach predicts spectral coefficients using quantum circuits, with gate parameters mapped from PDE instances (e.g., forcing functions or PDE parameters) via a classical neural network. To improve efficiency and feasibility, we introduce a training objective that requires fewer measurement repetitions than standard variational quantum linear solvers (VQLS). With this, we design shallower circuits by replacing controlled-unitary gates with direct Pauli measurements, which in turn allows grouping of commuting measurement operators for further reduction in runtime. The objective also resolves the sign ambiguity inherent in standard VQLS and guarantees recovery of the correct solution sign for PDEs. Overall, our framework reduces the computational cost and improves solution accuracy of VQLS, while also demonstrating the potential efficiency and scalability advantages of quantum operator learning over classical machine learning approaches. We validate our framework on one- and two-dimensional reaction–diffusion, Helmholtz, and convection–diffusion equations under diverse boundary conditions, achieving relative errors below 1%.
[Language] English

We uploaded photos from the 50th KMGS on Oct 02, 2025.
Thanks, Dongha Lee and all the participants!

The 50th KMGS will be held on October 2, Thursday, at the Natural Science Building (E6-1) Room 1410. We invite a speaker Dongha Lee from the Dept. of Mathematical Sciences, KAIST.
The abstract of the talk is as follows.

[Speaker] 이동하 (Dongha Lee) from Dept. of Mathematical Sciences, KAIST, supervised by  Prof. 박진성 (Jinsung Park, KIAS) and Prof. 백형렬 (Hyungryul Baik, KAIST)
[Title] Minimal Surfaces in Riemann-Cartan Geometry
[Discipline] Differential Geometry
[Abstract]
In this talk, we extend the classical theory of minimal surfaces studied in Euclidean and Riemannian geometry to a more general framework in Weitzenböck and Riemann-Cartan geometry, which incorporates torsion. After providing a gentle introduction to minimal surface theory, we present theorems that generalize classical results concerning the holomorphic nature of the Hopf differential, the conformality of the Gauss map, and the minimality of surfaces.
[Language] English

We uploaded photos from the 49th KMGS on Sep 25, 2025.
Thanks, Bowoo Kang and all the participants!

The 49th KMGS will be held on September 25, Thursday, at the Natural Science Building (E6-1) Room 1410. We invite a speaker Bowoo Kang from the Dept. of Mathematical Sciences, KAIST.
The abstract of the talk is as follows.

[Speaker] 강보우 (Bowoo Kang) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. Nguyen Ngoc Cuong
[Title] The pluripotential complex Monge-Ampère flows
[Discipline] PDE, Differential Geometry
[Abstract]
The Kahler-Ricci flow has been a main interest in the field of Kahler geometry, for its application to the construction of canonical metrics. It is a classical result that solving a Kahler-Ricci flow is equivalent to solving a parabolic PDE named complex Monge-Ampere flow. Recently, Guedj-Lu-Zeriahi (‘2021) introduced a parabolic pluripotential theory and studied the weak solutions of degenerate complex Monge-Ampere flows. In this talk, I will first explain their approach with the classical results in elliptic pluripotential theory. I will also explain my recent result on the existence and uniqueness of the solution for more general measures, which is a generalization of the result by Guedj-Lu-Zeriahi.
[Language] English