Research

I have been studying the mathematical aspects of 3d and 4d SUSY QFTs, and their relation to representation theory. My focus has been the study of the category of line operators in these theories under topological or holomorphic-topological twists. These categories are closely related to the moduli space of triples in the work of Braverman-Finkelberg-Nakajima. I am interested in understanding the precise mathematical structure of these categories, the relations between them under dimensional reduction, and the roles they play in the study of Coulomb branches and their resolutions. 

• 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.

• Kazhdan-Lusztig Correspondence for a class of Lie superalgebras. Categorical Global Symmetry Colloquium, November 2023.

• Quantum supergroups associated to 3d N=4 abelian gauge theories. Algebra Seminar, University of Southern California, March 2023. 

• Quantum-supergroup extension of $\overline{U}_i^H(\mathfrak{sl}(2))$. Informal string math seminar, UC Berkeley, January 2023. 

• Boundary VOA and BTC from 3d N=4 abelian gauge theories. Algebra Seminar, University of Southern California, November 2022. 

• Matrix factorizations in 3d N=4 gauge theories. Student run research seminars, UC Davis, 2022

• Mirror symmetry of 3d N=4 abelian gauge theories. EGRET seminar, Edinburgh, April 2022.

• Beta-gamma VOA and 3d mirror symmetry. Rocky mountain representation theory seminar, April 2022. 

• Local operators of 4d N=2 gauge theories from the affine grassmannian. Oxford junior physics and geometry seminar, Oxford, 2022. 

• Line operators and the affine grassmannians. Student run research seminars, UC Davis, 2019

• Geometric Satake equivalence, AIM research seminar, 2021.