Jaehoon Kim (KAIST)
Title: An introduction to extremal graph theory
Abstract: Graph theory is one of the most dynamic areas of modern mathematics, studying the structure and properties of graphs—networks of vertices and edges that model relationships between objects. In this talk, we begin with a gentle introduction to the basic concepts of graph theory. We then move on to extremal graph theory, a central branch of combinatorics that asks fundamental quantitative questions: How large/dense can a graph be without containing a particular subgraph? We will introduce classical results such as Turán’s theorem and Ramsey’s theorem.
Eunjung Lee (Chungbuk National University)
Title: An invitation to toric manifolds
Abstract: Toric manifolds are smooth manifolds equipped with nice torus actions. Since they have lots of symmetries, the topology and geometry of a toric manifold are closely intertwined with combinatorics and representation theory. In this talk, I will introduce toric manifolds and present explicit examples that demonstrate these connections.
Jaeseong Oh (Sungkyunkwan University)
Title: Sign-reversing involutions in algebraic combinatorics
Abstract: Sign-reversing involutions play a central role in algebraic combinatorics. The Lindström–Gessel–Viennot (LGV) lemma provides one of the most powerful frameworks for employing such techniques. In this talk, we will present several applications of the LGV lemma, highlighting its connections to Schur functions, shuffle theorems, and knot homology.
Priyam Patel (University of Utah)
Title: From Foundations to Frontiers: How Point Set Topology and Combinatorics Shape Modern Research in Geometry
Abstract: Undergraduate courses in point set topology and combinatorics introduce students to ideas that often feel abstract, technical, or disconnected from the mathematics they encounter elsewhere. Yet these subjects quietly provide the language and tools that underpin vast areas of contemporary research. In this talk, I will explore how foundational concepts—such as separation axioms, compactness, connectedness, and combinatorial structure—play an essential role in my own research on infinite-type surfaces. These surfaces can be studied as Polish topological spaces and through graphs that capture their geometric and topological features. By tracing this thread from undergraduate definitions to open research problems, I aim to highlight how ideas first encountered in foundational courses continue to shape the frontiers of modern mathematics.