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Hao Zhang

PhD Candidate in Mathematics · Yau Mathematical Sciences Center, Tsinghua University

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About

I am a fifth-year PhD student in mathematics at Tsinghua University, Yau Mathematical Sciences Center.

Research interests Vertex operator algebras, logarithmic conformal field theory, conformal blocks, modular functors, and related topics in mathematical physics.

Current collaboration I am currently working with Bin Gui on logarithmic CFT for a C₂-cofinite VOA.

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 · Preprint · arXiv:2508.00431

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

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 · to appear in Commun. Contemp. Math. · arXiv:2411.07707

Journal Preprint

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

Joint with Bin Gui · to appear in New York J. Math. · arXiv:2305.10180

Preprint

Upcoming Travel

July 1–17, 2026 · University of Hamburg, Germany.

Talks

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.

Primary: zhanghao1999math (at) gmail (dot) com

Secondary: h-zhang21 (at) mails (dot) tsinghua (dot) edu (dot) cn