UNIST Mathematical Physics and AI - Group Workshop 2026

Talks

Talk 1

Machine Learning Toric Duality in Brane Tilings

Benjamin Suzzoni (UNIST)
Tuesday, January 13, 2026
108-320, 09:30 - 10:30

The space of brane tilings comes equipped with infrared dualities, known as Seiberg dualities. Given two brane tilings, one may ask "are these Seiberg dual?". In general, the answer isn't obvious and finding the set of Seiberg dualities that takes us from one to the other is non-trivial. We present here a first stepping stone in this direction, by making use of machine learning's effectiveness in classifying objects with relations. We focus on the the simplest case of Z_m x Z_n orbifolds of the conifold. In the first part of this talk, we will present arguments as to why the Kasteleyn matrices are good representative data for machine learning. From those, we will outline how to build a dataset suitable for training purposes. We will then introduce a couple of different neural network architectures and display their strengths and weaknesses in this classification problem. We will conclude with a detailed description of what should be done next. This talk is based on my paper 2409.15251.

Talk 2

Abelian Orbifolds of Brane Brick Models

Juno Kwon (UNIST)
Tuesday, January 13, 2026
108-320, 11:00 - 12:00

Brane brick models provide a combinatorial description of a family of 2d N=(0,2) quiver gauge theories. In this talk, I will discuss the construction of brane brick models that realize abelian orbifolds of toric Calabi–Yau 4-folds as mesonic moduli spaces. As examples, I will present the general formulas of J- and E-term for abelian orbifolds of Q^{1,1,1} and D_3 models.

Talk 3

Dimer Integrable Systems and Birational Transformations

Minsung Kho (UNIST)
Tuesday, January 13, 2026
108-320, 14:00 - 15:00

The dimer integrable system proposed by Goncharov and Kenyon has been actively studied in mathematics and theoretical physics due to its many interesting properties. In this talk, I will discuss how birational transformations arise in the context of dimer integrable systems and how these transformations can be interpreted from the perspective of integrable systems. The talk will begin with a brief introduction to integrable systems, followed by an explanation of how the combinatorial structures of the dimer model give rise to an integrable system. Birational transformations on the of dimer integrable systems will then be introduced, and it will be shown that if two integrable systems are related by a birational transformation, then they are equivalent as integrable systems.

Talk 4

Futaki Invariants and Reflexive Polygons in 4d N=1 Gauge Theories

Eugene Choi (UNIST)
Tuesday, January 13, 2026
108-320, 15:30 - 16:30

This talk discusses Futaki invariants in 4d N=1 supersymmetric gauge theories whose mesonic moduli spaces are toric Calabi–Yau threefolds. We review how the notion of K-stability arises in Kähler geometry and explain its physical interpretation in relation to the existence of superconformal fixed points and Sasaki–Einstein metrics. Building on this perspective, we introduce Futaki invariants for test configurations of the moduli space and describe how they can be captured by deformations of the Hilbert series by trial symmetries. We then outline how volumes, divisor data, Chern numbers, Euler characteristics, and integrated curvature invariants enter the framework, clarifying the role of Futaki invariants in K-stability and in constraining the infrared dynamics.