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Hao Zhang

Postdoctoral researcher in Mathematics · BICMR, Peking University

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About

Beginning in September 2026, I will join the Beijing International Center for Mathematical Research (BICMR) at Peking University as a postdoctoral researcher in mathematics, under the mentorship of Xin Sun. I received my PhD in mathematics from Tsinghua University in June 2026, under the supervision of Bin Gui and Zhengwei Liu.

Research

My recent work studies the analytic and categorical structures behind logarithmic conformal field theory. In particular, I am interested in the geometry of conformal blocks in the non-semisimple setting.

• sewing-factorization theorems and their connection with coends;
• pseudo-traces and associative algebras in logarithmic CFT;
• modular functors from conformal blocks in logarithmic CFT.

Selected slides.

• Université Paris-Saclay slides on smooth and nodal conformal blocks in logarithmic CFT.
• Rocky Mountain Representation Theory Seminar slides on sewing-factorization and coends.
• Bin Gui's Orsay slides on pseudo-traces and (co)ends.

Publications

Non-Equivalence of Smooth and Nodal Conformal Block Functors in Logarithmic CFT

Preprint · arXiv:2509.07720

Preprint

How are pseudo-q-traces related to (co)ends?

Joint with Bin Gui · Preprint · arXiv:2508.04532

Preprint

Under the C₂-cofinite condition, we prove that the pseudo-q-trace construction gives an isomorphism between vacuum torus conformal blocks and symmetric linear functionals, resolving a conjecture of Gainutdinov and Runkel.

Pseudotraces on Almost Unital and Finite-Dimensional Algebras

Joint with Bin Gui · J. Algebra 704C (2026) pp. 220-254 · arXiv:2508.00431

Journal Preprint

Analytic Conformal Blocks of C₂-cofinite Vertex Operator Algebras III: The Sewing-Factorization Theorems

Joint with Bin Gui · Proc. Lond. Math. Soc., 132 (2026), no. 2, Paper No. e70130 · arXiv:2503.23995

Journal Preprint Errata

We prove several equivalent versions of the sewing-factorization theorem for finite logarithmic chiral CFTs and connect them to topological modular-functor ideas in the non-semisimple setting.

Analytic Conformal Blocks of C₂-cofinite Vertex Operator Algebras II: Convergence of Sewing and Higher Genus Pseudo-q-traces

Joint with Bin Gui · Commun. Contemp. Math., Vol. 28, No. 09 (2026) · arXiv:2411.07707

Journal Preprint

Analytic Conformal Blocks of C₂-cofinite Vertex Operator Algebras I: Propagation and Dual Fusion Products

Joint with Bin Gui · New York J. Math. 32 (2026) 859–942. · arXiv:2305.10180

Journal Preprint

Upcoming Travel

Jan 11–15, 2027 Mathematical Aspects of Quantum Theory · TSIMF, China.

Talks

2026

• Conformal Blocks and the Sewing-Factorization Theorem in Logarithmic CFT, Algebra Seminar, East China Normal University, China, Sep 2, 2026.
• Conformal Blocks and the Sewing-Factorization Theorem in Logarithmic CFT, Seminar on Mathematical Physics (online), Aalto University, Finland, Jan 26, 2026.
• Sewing and Factorization of Smooth and Nodal Conformal Blocks in Logarithmic CFT, Geometric and Category-Theoretic approaches to CFT, Chennai, India, Jan 7, 2026.

2025

• Sewing and Factorization of Smooth and Nodal Conformal Blocks in Logarithmic CFT, Quantum Symmetry Seminar, BIMSA, China, Oct 15, 2025.
• Sewing and Factorization of Smooth and Nodal Conformal Blocks in Logarithmic CFT, Algebraic, Topological and Probabilistic approaches in CFT, Institut Pascal, France, Oct 6, 2025.
• Sewing-factorization theorem and coends, Rocky Mountain Representation Theory Seminar (online), May 23, 2025.
• Sewing-factorization theorem and coends, Nanjing University, China, May 23, 2025.
• Conformal blocks and coends, Shenzhen Thematic Program “Representation Theory”, SUSTech, China, April 24, 2025.
• The sewing-factorization theorem and pseudotraces for C₂-cofinite VOAs, Mathematical Physics Seminar, Perimeter Institute, Canada, March 20, 2025.
• Vertex operator algebras and conformal blocks, Mathematical Physics Seminar, Perimeter Institute, Canada, March 17, 2025.
• Conformal blocks and coends, Quantum groups, tensor categories and quantum field theory, University of Oslo, Norway, Jan 13, 2025.

2024

• The sewing-factorization theorem and pseudotraces for C₂-cofinite VOAs, Algebra and Logic Seminar (online), University of Denver, USA, Nov 1, 2024.
• Conformal blocks and a Verlinde formula for self-dual C₂-cofinite non-rational vertex operator algebras, Vertex Algebras, Tensor Category and Related Topics, Shanghai Jiao Tong University, China, June 24, 2024.
• Logarithmic conformal field theory: sewing and factorization, Lie Group/Quantum Mathematics Seminar, Rutgers University, USA, April 19, 2024.
• Conformal blocks of C₂-cofinite vertex operator algebras, Tsinghua Sanya International Mathematics Forum, China, Jan 17, 2024.

2023

• Conformal blocks of C₂-cofinite vertex operator algebras, Tsinghua University, China, April 14, 2023.

Contact

Please feel free to contact me by email.

zhanghao1999math at gmail dot com