Mathematical physics, quantum fields and machine learning

Research

We conduct research at the interface of mathematics and theoretical physics, with a particular emphasis on the mathematical structures that arise in quantum field theory and string theory.

We also pioneered the introduction of machine learning tools in order to study the dynamics and moduli spaces of supersymmetric gauge theories realized in string theory.

Our research group also works on applied problems that appear in industry, where we use fundamental concepts from geometry, topology and machine learning to solve optimization and automation problems.

Selected work

Research Highlights

Phase diagrams for supersymmetric gauge theories obtained using machine learning

Phase diagrams for supersymmetric gauge theories obtained using machine learning

Unsupervised machine learning techniques let us construct phase diagrams for 4-dimensional supersymmetric gauge theories related to toric Calabi-Yau 3-folds. These phase diagrams help us study gauge theory phenomena such as Seiberg duality.

Unsupervised Machine Learning Techniques for Exploring Tropical Coamoeba, Brane Tilings and Seiberg Duality
Rak-Kyeong Seong
Physical Review D 108, 106009 (2023)

arXiv:2309.05702 DOI
New brane configurations realizing supersymmetric gauge theories

New brane configurations realizing supersymmetric gauge theories

Brane brick models are Type IIA brane configurations that encode 2d supersymmetric gauge theories corresponding to toric Calabi-Yau 4-folds. They can be used to study gauge theory phenomena such as Gadde-Gukov-Putrov triality.

Brane Brick Models, Toric Calabi-Yau 4-Folds and 2d (0,2) Quivers
Sebastian Franco, Sangmin Lee, Rak-Kyeong Seong
Journal of High Energy Physics (JHEP) 02, 047 (2016)

arXiv:1510.01744 DOI
Geometric unification of gauge theories across spacetime dimensions

Geometric unification of gauge theories across spacetime dimensions

Calabi-Yau mirror symmetry leads to a geometric unification of dualities in different spacetime dimensions. It is a powerful tool that helped us discover new gauge theory phenomena across dimensions.

Brane Brick Models in the Mirror
Sebastian Franco, Sangmin Lee, Rak-Kyeong Seong, Cumrun Vafa
Journal of High Energy Physics (JHEP) 02, 106 (2017)

arXiv:1609.01723 DOI
Hidden mathematical structures with physical implications

Hidden mathematical structures with physical implications

By studying geometrical quantities for non-compact toric Calabi-Yau n-folds defined as cones over Gorenstein Fano varieties, we were able to conjecture new bounds for the volume of the associated Sasaki-Einstein base manifolds.

Calabi-Yau Volumes and Reflexive Polytopes
Yang-Hui He, Rak-Kyeong Seong, Shing-Tung Yau
Communications in Mathematical Physics, 361, 155–204 (2018)

arXiv:1704.03462 DOI

Worldwide

Research Collaborators

  • Jiakang BaoUniversity of Tokyo, Japan
  • Massimo BianchiUniversity of Rome, Italy
  • Cyril ClossetBirmingham University, UK
  • Stefano CremonesiDurham University, UK
  • Anindya DeyJohns Hopkins University, USA
  • Sebastian FrancoCUNY, New York, USA
  • Dongwook GhimRIKEN, Tokyo, Japan
  • Georgios P. GoulasCUNY, New York, USA
  • Sergei GukovCalifornia Institute of Technology, USA
  • Amihay HananyImperial College London, UK
  • Yang-Hui HeLondon Institute for Mathematical Sciences, UK
  • Kazuo HosomichiNational Defence Academy, Japan
  • Chiung HwangUSTC, Hefei, China
  • Vishnu JejjalaUniversity of Witwatersrand, South Africa
  • Daniel KreflUniversity of Lausanne, Switzerland
  • Chang Hyeong LeeUNIST, Korea
  • Kimyeong LeeBIMSA, China
  • Norton LeeIBS-CGP, Korea
  • Sangmin LeeSeoul National University, Korea
  • Noppadol MekareeyaMilano-Bicocca, Italy
  • Jose Francisco MoralesUniversity of Rome, Italy
  • Jaemo ParkPOSTECH, Korea
  • Sanjaye RamgoolamQueen Mary, University of London, UK
  • Diego Rodriguez-GomezUniversity of Oviedo, Spain
  • James SparksUniversity of Oxford, UK
  • Seiji TerashimaKyoto University, Japan
  • Cumrun VafaHarvard University, Boston, USA
  • Masahito YamazakiUniversity of Tokyo, Japan
  • Jaeho YangSamsung SDS, Korea
  • Shing-Tung YauHarvard University, USA / Tsinghua University, China
  • Daisuke YokoyamaMeiji University, Japan

Elsewhere

Profiles and Repositories