Xuanzhong Dai

I am currently a postdoctoral researcher at the Research Institute for Mathematical Sciences of Kyoto University in Japan. My postdoctoral mentor is Prof. Tomoyuki Arakawa. I obtained my PhD in 2020 from the Hong Kong University of Science and Technology, under the supervision of Prof. Yongchang Zhu.

Publication

On some simple orbifold affine VOAs at non-admissible level arising from rank one 4D SCFTs (with T. Arakawa, J. Fasquel, B.Li and A. Moreau), Commun. Math. Physics. 406，2025.
Simple vertex algebras arising from congruence subgroups (with B. Song), Adv. Math. 456, 109900, 2024.
Chiral de Rham Complex on the Upper Half Plane and Modular Forms, Int. Math. Res. Not. (IMRN) 2022 (24) 19258-19299.
A Construction of Representations of Loop Group and Affine Lie Algebra of sl_n (with Y. Zhu), Algebr. Represent. Theory (2022) 25:649–668.
Chiral Differential Operators on the Upper Half Plane and Modular Forms, Adv. Math. 390, 107957, 2021.
Linear Topological Modules over Vertex Algebras, to appear in RIMS Kokyuroku Bessatsu series (with Y. Zhu), arXiv:1912.12025.

Talks

Chiral differential operators on the base affine space and the Gelfand-Graev action, Nanjing University, Nanjing, China, January 2025.
Vertex algebras arising from congruence subgroups, Finite Group Theory, Algebraic Combinatorics, and Vertex Algebras, Kyoto, Japan, December 2024.
Chiral differential operators on base affine space, Kyoto Representation Theory Seminar, RIMS, Kyoto University, Kyoto, Japan, December 2024.
On a series of simple affine VOAs at non-admissible level arising from rank one 4D SCFTs, Xiamen, China, July 2024.
On recent progress of chiral de Rham complex and modular forms I & II, TU Darmstadt, Germany, June 2024.
Chiral differential operators over G/U and associated variety, Vertex algebras, geometric representation theory and quantum groups, CIRM, Luminy, France, June 2024.
A quantization of modular forms, Workshop on quantum algebras and representation, Tianyuan Mathematics Research center, Kunming, China, June 2024.
Chiral differential operators over G/N and associated variety, Vertex Algebras and Related Topics, Ningbo, April 2024.
Geometric perspective of vertex algebras and modular forms, Representation theory and number theory, National University of Singapore, Singapore, April 2024.
Simple affine VOAs at non-admissible level arising from rank one 4D SCFTs, Shanghai Jiao Tong University, Shanghai, China, March 2024.
On recent progress of chiral de Rham complex and modular forms, Mini-workshop on vertex algebras and related topics, University of Alberta，Edmonton, Canada, February 2024.
Vertex algebras arising from congruence subgroups, Mathematical Aspects of Quantum Theory, Tsinghua University, Sanya, China, January 2024.
Chiral differential operators on basic affine space and quasi-lisse vertex algebras, University of Science and technology of China, Hefei, China, July 2023.
Chiral de Rham complex and automorphic forms, REPRESENTATION THEORY XVIII, Inter-University Centre, Dubrovnik, Croatia, July 2023.
Chiral differential operators over G/N, Vertex Algebra, Hopf Algebra and Related Topics, Shanghai Jiao Tong University, Shanghai, China, June 2023.
Chiral de Rham complex on the upper half plane and modular forms, Session “Young Mathematicians’ Challenge” 2023, Tokyo, Japan, March 2023 (Poster presentation).
Invariant Global Sections of Chiral de Rham complex on the Upper Half Plane, Online Komaba Seminar, University of Tokyo, Tokyo, Japan, September 2022.
Chiral De Rham Complex on the Upper Half Plane and Modular Forms, online Algebra and Logic Seminar, University of Denver, USA, October 2021.
Chiral De Rham Complex on the Upper Half Plane and Modular Forms, online BIRS-IASM workshop "Subfactors, Vertex Operator Algebras, and Tensor Categories”, IASM, Zhejiang University, Hangzhou, China, September 2021.
Chiral De Rham Complex on the Upper Half Plane and Modular Forms, Soochow University, Suzhou, China, April 2021.
Chiral De Rham Complex on the Upper Half Plane and Modular Forms, online Kyoto Representation Theory Seminar, RIMS, Kyoto University, Kyoto, Japan, February 2021.