RESEARCH / ACTIVE PROGRAM
Structures behind
quantum systems.
My research seeks structural descriptions of quantum systems: algebraic objects that organize observables and states, geometric constructions that make those objects computable, and field theories that explain why the structures appear.
R/01
Quantum algebras, integrability & QFT
I study how Yangians, affine Yangians, R-matrices, and related representation-theoretic structures emerge from holomorphic-topological quantum field theories, branes, line operators, and defects.
Questions
- How do line and surface operators construct representations of quantum algebras?
- How can localization and perturbative field theory compute R-matrices and other integrable data?
- Which string-theoretic constructions unify supersymmetric field theories and integrable systems?
Methods / language
- Holomorphic-topological field theory
- Supersymmetric localization
- Brane constructions
- Representation theory
Selected work
-
2026
Refined Invariants and Quantum Curves from Supersymmetric Localization
-
2024
R-matrices and Miura operators in 5d Chern-Simons theory
-
2023
Elliptic Stable Envelopes for Certain Non-Symplectic Varieties and Dynamical R-Matrices for Superspin Chains from The Bethe/Gauge Correspondence
-
2022
Line Operators in 4d Chern-Simons Theory and Cherkis Bows
-
2021
Superspin chains from superstring theory
R/02
Topological phases & quantum information
I am developing a field-theoretic approach to topological quantum codes, especially their finite-temperature behavior, dualities, and the statistical-mechanical structures controlling stability.
Questions
- How do topology and generalized symmetry constrain quantum memories?
- What polymer and cluster expansions control finite-temperature homological codes?
- How do electric-magnetic and Kramers-Wannier dualities reorganize error sectors?
Methods / language
- Topological order
- Polymer gases
- Cluster expansions
- Higher-form duality
Selected work
-
2026
An exact spacetime polymer gas for finite-temperature \(\mathbb Z_N\) homological quantum code
-
2024
Symmetry topological field theory and non-abelian Kramers-Wannier dualities of generalised Ising models
R/03
Field theory, learning & inference
I am interested in mathematical learning theory where probability, statistical mechanics, diffusion, and renormalization provide a common language for approximation and learning dynamics.
Questions
- Which conditional probability laws can diffusion architectures represent?
- Can renormalization and thermalization describe learning flows on structured spaces?
- How do geometry and information loss govern effective models?
Methods / language
- Conditional diffusion
- Information geometry
- Stochastic dynamics
- Renormalization
Selected work
-
2026
Universality of Gaussian-Mixture Reverse Kernels in Conditional Diffusion