A website for my math(s).
A website for my math(s).
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Hello! I'm Daniel Tan (usually shortened to Dan Tan by those who admire symmetry). I'm doing my PhD in Mathematics at Rutgers University. My advisors are Yi-Zhi Huang and James Lepowsky.
I'm interested in vertex operator algebras, their representations, and structures you can build out of their representation theory (for example tensor categories and conformal field theories).
My thesis problem is on the convergence of correlation functions in orbifold conformal field theory. This mostly involves playing around with "twisted modules" of vertex operator algebras and "twisted intertwining operators" among them.
My current work forms part of Yi-Zhi Huang's program to develop mathematical orbifold conformal field theory with the representation theory of vertex operator algebras. Also working on the program, is my academic brother Jishen Du.
I expect to complete my degree in May of 2026. Then I'll hopefully have a postdoc to continue my research.
(Fall 2025)
Office 626 Hill Center, Busch Campus, Rutgers University - New Brunswick
This site is intended to be used as a bit of a digital desk drawer for collecting my stuff:
Preprints:
"Differential equations for intertwining operators among untwisted and twisted modules" - arXiv: 2510.14860 [math.QA]
"The structure of non-Fricke Monstrous Lie algebras" - arXiv: 2507.17854 [math.RT] (To appear Contemporary Math)
"C_n-cofinite twisted modules for C_2-cofinite vertex operator algebras" - arXiv: 2510.26657 [math.QA]
My master's thesis "Vertex Operator Algebras, Modular Tensor Categories and a Kazhdan-Lusztig Correspondence at a Non-negative Integral Level", from Melbourne University, supervised by David Ridout.
The syllabus for my oral qualifying exam. Committee: James Lepowsky (Chair), Yi-Zhi Huang, Lisa Carbone, Siddartha Sahi
(you get to see some nice colours if you work in the office late enough at night)
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