I consider myself a mathematician, as I try to prove theorems in my papers. However, a big part of my motivation comes from quantum field theories (QFT), particularly twists of supersymmetric gauge theories. In QFT, one is interested in various observables and how they act on the state spaces. Colliding observables (or operator product expansions, OPEs) endow the set of observables with algebraic structures and state spaces form representations of these algebraic structures. Thus, the subject of QFTs is intimately related to that of representation theory.
Traditionally, physicists apply representation theory to study QFTs. In recent decades, however, QFT methods, particularly that of duality, have become integral to modern representation theory. This connection enriches both subjects. On the one hand, physical methods can lead to deep conjectures in representation theory; on the other hand, representation-theoretic developments are crucial to a rigorous definition of quantum field theories. This dynamic is what I am passionate about.
In my research, I consider certain classes of QFTs, and apply methods from algebraic geometry and representation theory to give rigorous definitions to the set of observables, thereby turning physical conjectures into mathematical statements. Recently, I have been focusing on holomorphic-topological field theories, and the categorical aspects of these theories. Mathematically, I study chiral categories and meromorphic tensor categories, and my work is related to geometry of algebraic loop spaces, enumerative invariants and integrable systems.
Elliptic Coulomb Branches (joint with S. Dehority, M. Semenyakin and M. Yamashita). In progress.
Cohomological Hall Algebras and Meromorphic Braidings (joint with S. Dehority and A. Latyntsev). In progress.
Dynamical R-matrices over Higher-Genus Curves (joint with R. Abedin and F. Moosavian). To appear.
Chiral rings and Chiral Categories (joint with J. Hilburn). To appear.
Double Yangian, Factorization, and qKZ-equation for Cotangent Lie Algebras (joint with R. Abedin). arXiv:2512.16996.
Higgs Branches in the Omega-background via the Category of Line Operators (joint with T. Karabela). arXiv:2511.14943.
Line Operators in 3d Holomorphic QFT: Meromorphic Tensor Categories and dg-Shifted Yangians (joint with T. Dimofte and V. Py), 2025, arXiv.
D-convolution categories and Hopf algebras, 2025, arXiv.
1-shifted Lie bialgebras and their quantizations (joint with V. Py), 2025, arXiv.
Quantum groupoids from moduli spaces of G-bundles (joint with R. Abedin), 2024, arXiv.
Quantum groups and symplectic reductions, 2024, arXiv.
Tannakian QFT: from spark algebras to quantum groups (joint with T. Dimofte), 2024, arXiv.
Yangian for cotangent Lie algebras and spectral R-matrices (joint with R. Abedin), 2024, arXiv.
Kazhdan-Lusztig Correspondence for Vertex Operator Superalgebras from Abelian Gauge Theories (joint with T. Creutzig), 2024, arXiv.
Line Operators in U(1|1) Chern-Simons Theory (joint with N. Garner), 2023, arXiv.
3d mirror symmetry of braided tensor categories (joint with A. Ballin, T. Creutzig and T. Dimofte), 2023, arxiv.
3d Mirror Symmetry and the Beta-gamma VOA (joint with A. Ballin), 2022, arXiv. Communications in Contemporary Mathematics, 2024. https:///dx.doi.org/10.1142/S0219199722500699.
Local Operators of 4d N=2 Gauge Theories From the Affine Grassmannian, 2022, arXiv. Advances in Theoretical and Mathematical Physics, 2022. https://dx.doi.org/10.4310/ATMP.2022.v26.n9.a10.
On Behaviors of Maximal Dimension, 2018, arXiv.