• We are planning to cover various topics in Discrete Mathematics and related fields.

• Organizer: Seunghun Lee (이승훈).

• 도움 주시는 분들: 김건욱(학부생), 변진혁(학부생), 김지안(행정).

• Place: Department of Mathematics, Baekeun Hall (백은관), Seongseo Campus (성서캠퍼스), Keimyung University (계명대학교).
  (지하철로 오실 경우, 계명대역보다 강창역으로 오시면 더 빠릅니다.)

• If you are interested in giving a talk at Keimyung, please contact Seunghun Lee (please check my personal information).

• If you are interested in subscribing our mailing list, please visit
  https://groups.google.com/g/keimyung-dm-seminar

Upcoming!

2026

Date and Time: May 12, Tuesday, 6-7 PM

Title: Denoising data reduction algorithm for Topological Data Analysis

Speaker: Semin Oh (오세민), KNU G-LAMP Project Group, Kyungpook National University (경북대학교)

Location: Room 324

Abstract: Persistent homology is a central tool in topological data analysis, but its application to large and noisy datasets is often limited by computational cost and the presence of spurious topological features. Noise not only increases data size but also obscures the underlying structure of the data.

In this talk, we propose the Refined Characteristic Lattice Algorithm (RCLA), a grid-based method that integrates data reduction with threshold-based denoising in a single procedure. By incorporating a threshold parameter k, RCLA removes noise while preserving the essential structure of the data. We further provide a theoretical guarantee by proving a stability theorem under a homogeneous Poisson noise model. This theorem bounds the bottleneck distance between the persistence diagrams of the output and the underlying shape with high probability. In addition, we introduce an automatic parameter selection method based on nearest-neighbor statistics. Experimental results show that RCLA offers advantages over existing denoising methods in both the accuracy and stability of topological feature extraction, measured by the bottleneck distance between persistence diagrams. Its effectiveness is further validated on a 3D shape classification task. For further details, we refer the reader to the preprint (arXiv:2603.29248).

Date and Time: May 19, Tuesday, 6-7 PM

Title: From One Path to Two: Full Homomorphisms and Minimal Obstructions

Speaker: Korina Ernjulie Manaloto, Kyungpook National University (경북대학교)

Location: Room 324

Abstract: Full homomorphisms are mappings between vertices of graphs that preserve both adjacency and non-adjacency. A minimal obstruction is a graph that does not admit a full homomorphism to a target graph H, but whose every induced subgraph does.

A structural description of the minimal obstructions to full homomorphisms to paths and cycles was given by Santiago Guzmán-Pro in "Full-homomorphisms to paths and cycles." In this talk, we extend this line of study to the case of two disjoint paths. We compare the similarities and differences between the single-path and two-path targets, and explore whether there is an efficient algorithm for enumerating minimal obstructions to full homomorphisms in this setting. 

Date and Time: May 26, Tuesday, 6-7 PM

Title : How much does local information determine a graph?

Speaker: Jongyook Park (박종육), Kyungpook National University (경북대학교)

Location: Room 324

Abstract: Strongly regular graphs are defined by very simple rules: every vertex has the same number of neighbors, and any two vertices share a fixed number of common neighbors. Surprisingly, these local conditions already impose strong restrictions on the global structure of the graph.

In this talk, we introduce the basic ideas of spectral graph theory, where graphs are studied using eigenvalues of matrices. We explain how eigenvalues capture global information, and how they can be used to detect hidden structure.

We also show that spectral information alone is not always sufficient, and introduce additional combinatorial methods involving cliques and cocliques. Using these tools, we present examples where certain graphs cannot exist, even though all known numerical conditions are satisfied.

Date and Time: June 4, Thursday, 6-7 PM

Title : An Invitation of Complex Geometry

Speaker: Seungjae Lee (이승재), Institute for Mathematical Convergence, Kyungpook National University (경북대학교)

Location: Room 324

Abstract: This talk introduces key concepts in complex geometry, a branch of mathematics that studies geometric objects using complex numbers rather than real numbers. Since the 19th century, complex geometry has had a profound influence on many areas of mathematics, including differential and algebraic geometry. The talk begins by highlighting the main differences between real-variables calculus, typically studied at the undergraduate level, and complex variable calculus (complex analysis). It then presents complex geometry as a natural extension of complex-variable calculus. Prerequisites are kept to minimum. The talk is intended to be accessible to those with a working knowledge of calculus and matrix algebra, along with basic familiarity with the imaginary unit $\sqrt{-1}$.

Date and Time: June 9, Tuesday, 6-7 PM

Title : TBA

Speaker: Wonwoo Kang (강원우), International Center for Mathematical Sciences - Sofia (ICMS-Sofia)

Location: Room 324

Abstract: TBA

Past presentations

2026

Date and Time: April 14, Tuesday, 6-7 PM

Title : From toric manifolds to Bier spheres (slide)

Speaker: Seonghyeon Yu (유성현), Ajou University (아주대학교)

Location: Room 324

Abstract : Toric topology is the study of topological spaces equipped with torus actions. Within this field, a topological toric manifold corresponds to a simplicial sphere and its realization as a complete fan. In this talk, we will introduce the cohomological rigidity problem, which is a fundamental topic in toric topology. Furthermore, we will discuss a specific class of simplicial spheres with nice combinatorial properties, known as Bier spheres. In particular, we focus on the full subcomplexes of Bier spheres and their combinatorial structures.

Date and Time: April 10, Friday, 4-6 PM
Title:  A special quotient extension of the polynomial ring: The Anderson ring  (slide)
Speaker: Hyungtae Baek (백형태), Kyungpook National University (경북대학교)
Location: Room 324
Abstract: Many ring theorists have studied various properties of Nagata rings and Serre's conjecture rings. In this talk, we first construct the Anderson ring as a generalization of localization at 0.

After constructing the Anderson ring, we examine the historical motivations and constructions of Nagata rings and Serre's conjecture rings, and then we compare them with the Anderson ring.

The main questions of this talk are as follows:

∙ Can we characterize the maximal spectrum of the Anderson ring?
∙ Under what conditions does the Anderson ring become a PIR?