Welcome to my homepage.

## About me

I am now a Ph.D student at Tsinghua University, Yau Mathematical Sciences Center.

E-mail:

h-zhang21@mails.tsinghua.edu.cn

zhanghao1999math@gmail.com

## Academic Experiences

- (2021.9-) Ph.D student, Yau Mathematical Sciences Center, Tsinghua University. Advisor: Zhengwei Liu
- (2017.9-2021.6) B.S., Department of Mathematics, Nanjing University

## Research Interests

I am interested in vertex operator algebras and their applications in conformal field theory. Recently, I am working on the conformal block theory for C_2 cofinite vertex operator algebras with Bin Gui.

## Publications

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

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

## Talks

- April 14, 2023, Conformal blocks of C_2-cofinite vertex operator algebras, YMSC, Tsinghua University, Beijing, China.
- January 17, 2024, Conformal blocks of C_2 cofinite vertex operator algebras, Tsinghua Sanya International Mathematics Forum, Sanya, China.
- April 19, 2024, Logarithmic conformal field theory:sewing and factorization , Department of Mathematics, Rutgers University, New Jersey, USA.
- June 24, 2024, Conformal blocks and a Verlinde formula for self-dual C_2-cofinite non-rational vertex operator algebras, School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China.
- November 1, 2024, The sewing-factorization theorem and pseudotraces for C_2-cofinite VOAs, Department of Mathematics, University of Denver, Colorado, USA.

## Notes

- Hodge theory and Serre duality
This note mainly covers Hodge theory on real or complex manifolds. With Hodge theory, we can interpret de Rham cohomology and Dolbeault cohomology as some kind of ‘harmonic forms’, which in particular gives the well-known Poincare and Serre duality.

- Cohomology theory of complex geometry
This note mainly covers some basic tools to study cohomology theory of compact Riemann surface (or more generally, compact Kähler manifold), including Riemann-Roch theorem, Serre and Kodaira vanishing theorem.

## Teaching Experiences

- (2024 Spring) Teaching assistant for Calculus
- (2023 Fall) Teaching assistant for Calculus
- (2023 Spring) Teaching assistant for Calculus
- (2022 Fall) Teaching assistant for Linear Algebra
- (2022 Spring) Teaching assistant for Calculus
- (2021 Fall) Teaching assistant for Linear Algebra