Welcome to my homepage.

About me

I am a 4-th year Ph.D student at Tsinghua University, Yau Mathematical Sciences Center. Here is my google scholar and CV.

E-mail:
h-zhang21(at)mails(dot)tsinghua(dot)edu(dot)cn
zhanghao1999math(at)gmail(dot)com

Research Descriptions

I am interested in vertex operator algebras and their applications in conformal field theory. Recently, I proved the sewing-factorization theorem on finite logarithmic chiral CFTs with Bin Gui.

My SLIDES at Rocky Mountain Representation Theory Seminar describe the relation between sewing-factorization theorem and coend.

Bin Gui’s SLIDES at SJTU describe the relation between sewing-factorization theorem and pseudo-traces.

If you have any questions, feel free to send me an e-mail.

Publications

• (Joint with Bin Gui) How are pseudo-q-traces related to (co)ends? to appear soon

  In this paper, under the C_2-cofinite condition, we prove that the pseudo-q-trace construction gives an isomorphism between the space of vacuum torus conformal blocks and the space of symmetric linear functionals of , where G is a projective generator of Mod(V). This is a conjecture by Gainutdinov-Runkel. With the help of pseudotrace reciprocity in our previous paper, we prove this conjecture by showing that the end

  

  is an AUF algebra and constructing a linear isomorphism between Mod(V) and the category of coherent left module of this AUF algebra.

• (Joint with Bin Gui) Almost Unital and Finite Dimensional Algebras, to appear soon

  In this paper, we introduce almost unital and finite dimensional algebras (AUF algebras) and prove pseudotrace reciprocity.

• (Joint with Bin Gui) Analytic Conformal Blocks of C_2-cofinite Vertex Operator Algebras III: The Sewing-Factorization Theorems, arXiv:2503.23995 Preprint

  In this paper, we prove several equivalent versions of sewing-factorization theorem for finite logarithmic chiral CFTs. One of our versions takes the form of horizontal composition of profunctors—defined via coends—which aligns with the framework proposed in the paper Modular Functors from Non-Semisimple 3D TFTs by Hofer-Runkel. In particular, our result naturally connects with the topological modular functors in the sense of Lyubashenko and Fuchs-Schweigert.

• (Joint with Bin Gui) Analytic Conformal Blocks of C_2-cofinite Vertex Operator Algebras II: Convergence of Sewing and Higher Genus Pseudo-q-traces, arXiv:2411.07707 Preprint

  In this paper, we prove the higher genus convergence of sewing for finite logarithmic chiral CFTs, which aligns with the convergence of pseudo-q-traces in the sense of Fiordalisi’s work. This type of sewing is the correct one to build the sewing-factorization property.

• (Joint with Bin Gui) Analytic Conformal Blocks of C_2-cofinite Vertex Operator Algebras I: Propagation and Dual Fusion Products, arXiv:2305.10180 Preprint

  In this paper, we construct higher genus (dual) fusion products using propagation of partial conformal blocks. We also formulate the sewing-factorization theorem in terms of (dual) fusion products.

Upcoming Travel

• July 21 - 25, 2025, Recent Developments in Logarithmic Conformal Field Theory, BIRS, Canada.
• September 29 - October 10, 2025, CFT: Algebraic, Topological and probabilistic approaches in Conformal Field Theory, Institut Pascal, France.

Talks

• 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”, China, April 24, 2025
• The sewing-factorization theorem and pseudotraces for C_2-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.
• The sewing-factorization theorem and pseudotraces for C_2-cofinite VOAs, Algebra and Logic Seminar (online), University of Denver, USA, November 1, 2024
• Conformal blocks and a Verlinde formula for self-dual C_2-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 C_2 cofinite vertex operator algebras, Tsinghua Sanya International Mathematics Forum, China, January 17, 2024
• Conformal blocks of C_2-cofinite vertex operator algebras, Tsinghua University, China, April 14, 2023