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

• Organizer: Seunghun Lee (이승훈).

• 도움 주시는 분들: 김건욱(학부생), 변진혁(학부생), 홍태영(학부생)

• 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 Fall

Date and Time: November 10, Tuesday, 6-7 PM
Title: Helly-type theorem for multiple piercing
Speaker: Dohyeon Lee (이도현), KAIST and IBS-DIMAG.
Location: Room 324
Abstract: A family of sets is k-pierceable if some k points meet every member, and it has property Π^k_m if every subfamily of size at most m is k-pierceable. For k=1 this is the setting of Helly's theorem from 1923, but nothing similar survives for k≥2. The question is then how far the global piercing number of a family of convex sets in R^d with property Π^k_m can exceed k. The (p,q) theorem of Alon and Kleitman keeps it finite, at the cost of very large bounds.
We will discuss new upper bounds on that number, including the planar case k=2, which is the subject of a conjecture of Katchalski and Nashtir. Fractional and approximate versions also come out of the work. So does a statement for d-collapsible and d-Leray simplicial complexes, together with a bound on small weak ε-nets in the plane that turned up along the way.

Date and Time: November 13, Friday, 16:30 PM (Korea time) = 8:30 AM UTC+1
Title: The rainbow arborescence problem on a cycle
Speaker: Tamás Király, HUN-REN-ELTE Egerváry Research Group, Eötvös Loránd University
Location: Zoom.

Link: https://kaist.zoom.us/j/81507347149?pwd=0anso73PWafgCYMGQlXi8a8sdCaGjl.1

Meeting ID: 815 0734 7149

Password: 1234

Absract: The rainbow arborescence conjecture posits that if the arcs of a directed multigraph with n vertices are colored by n-1 colors such that each color class forms a spanning arborescence, then there is a spanning arborescence that contains exactly one arc of every color. If true, this would be a rare special case of the rainbow common independent set problem where a rainbow common basis is guaranteed to exist. In this talk, I sketch the main ideas of the proof that the rainbow arborescence conjecture is true if the underlying simple undirected graph is a cycle. The result also implies a new theorem about systems of distinct representatives for intervals on a cycle. Joint work with Kristóf Bérczi, Yutaro Yamaguchi, and Yu Yokoi.

Date and Time: November 24, Tuesday, 6-7 PM
Title: Coresets for Farthest Point Problems in Hyperbolic Space
Speaker: Eunku Park (박은구), BRL AGSTA, DGIST
Location: Room 324
Abstract: How many points are needed to approximately preserve all farthest-point distances of a finite point set? A coreset is a small subset that provides this guarantee for every query point. In this talk, I will explore this question in hyperbolic space, where exponential volume growth creates challenges for familiar Euclidean discretization techniques. I will also briefly discuss ongoing work on coresets for the continuous k-center problem and the additional challenges posed by multiple centers.

Date and Time: December 1,  Tuesday, 6-7 PM
Title: Extension theorems for arrangements of pseudolines and pseudocircles
Speaker:  Hyungu Kim (김현구), KAIST and IBS-DIMAG.
Location: Room 324
Abstract: A pseudoline is a curve in the plane that need not be straight but behaves like a line in one essential way: any two pseudolines cross exactly once. A finite collection of them forms a pseudoline arrangement, a combinatorial relaxation of straight line arrangements. Peudocircles are pretty much the same, but they imitate circles instead of lines. In this talk I will introduce their non-realizability results and extension theorems to show how these curves both defy and imitate their straight and round counterparts.
Levi's extension lemma guarantees that through any two points one can always add a new pseudoline compatible with the arrangement. Snoeyink and Hershberger showed the pseudocircle counterpart of the lemma. Goodman, Pollack, Wenger, and Zamfirescu proved that every pseudoline arrangement extends to a topological plane, a geometry whose "lines" may be curved, but in which any two points still lie on exactly one. I will briefly sketch these results and prove this topological plane extension carries over to arrangements that also contain pseudocircles. This is a joint work with Andreas Holmsen.

Past presentations

2026 Fall

Date and Time: October 6, Tuesday, 6-7 PM

Title : Skein Algebras and their bases (slide)

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

Location: Room 324

Abstract: Skein algebras turn the topology of curves on a surface into algebra through local relations that resolve crossings. These relations also play a central role in cluster algebras associated with marked surfaces, connecting geometric operations on curves with algebraic identities among cluster variables. In this talk, I will explore this connection and explain how skein relations help construct natural bases. This talk is based on joint work with Esther Banaian and Elizabeth Kelley.

2026 Spring

Date and Time: June 9, Tuesday, 4:30-5:30 PM 6-7 PM

Title : Unimodality and Cluster Algebras (slide)

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

Location: Room 324

Abstract: We prove that the rank polynomial of the lattice of order ideals of a loop fence poset is unimodal. This structure arises as the poset of join-irreducibles in the lattice of good matchings of loop graphs associated with notched arcs. Such polynomials can be obtained by evaluating all coefficient variables of an $F$-polynomial at a single variable $q$. We also establish that the rank polynomial of any tagged arc, whether plain or notched, is unimodal and satisfies a symmetry condition known as almost interlacing. We conclude by conjecturing that products of these polynomials are also unimodal. This is joint work with Kyeongjun Lee and Eunsung Lim.

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: May 26, Tuesday, 6-7 PM

Title : How much does local information determine a graph? (slide)

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: 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 12, Tuesday, 6-7 PM

Title: Denoising data reduction algorithm for Topological Data Analysis (slide)

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: 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?