KCL2026.09

It is a triannual (three-times-a-year) seminar organized by academic genealogy from Professor Dongsu Kim in KAIST Combinatorics Laboratory, which KCL stands for. The aim of this seminar is to bring together active combinatorialists to discuss recent and prospective advances in algebraic and enumerative combinatorics and related areas. The style of talk tends to be less formal.

Program

• September 19 (tentatively)

  • 10:30 - 11:00 Registration

  • 11:00 - 12:00 Invited Talk

    • Speaker Joonkyung Lee

    • Title Computer-assisted research in combinatorics

    • Abstract Recent advances in artificial intelligence and computational technology have begun to reshape the landscape of mathematical research. In this talk, I will discuss how modern computational techniques—including large language models, machine learning, reinforcement learning, local search algorithms, and gradient descent—can be applied to problems in extremal combinatorics, while reflecting on both the opportunities and limitations of these emerging computational approaches to mathematical discovery.
      First, I will discuss a joint project that applies implicit neural representations to graphons in order to study asymptotic extremal problems in graph theory. In this approach, limits of dense graph sequences, the so-called graphons, are represented by neural networks and extremal graph problems are reformulated as continuous optimisation problems that can be tackled using gradient-based methods, allowing the system to rediscover known extremal structures and suggest candidate solutions to open problems.
      I will also describe recent work on lower bounds for multivariate independence polynomials, which arise as partition functions of the hard-core model in statistical physics. In this work, we establish new inequalities that extend earlier lower bounds for independence polynomials to the multivariate case and propose further generalisations to antiferromagnetic spin models. Some of the key ideas in the proof were discovered with the assistance of Aletheia, a mathematical research agent built on top of Gemini Deep Think.
      This talk is based on joint work with Jineon Baek, Taeyoung Kim, Jaehyeon Seo, and Hongseok Yang.

  • 12:00 - 14:00 Lunch

  • 14:00 - 16:00 Lightning Talks (Up to 10 minutes each for all participants)

  • 16:00 - Closing Remarks

Organizer

• Ringi Kim, Inha University

• Heesung Shin, Inha University