Robert McRae-Qiuzhen College,Tsinghua University

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Robert McRae

Assistant Professor

Yau Mathematical Science Center, Tsinghua University

Office: Ning Zhai S03

Email: rhmcrae@tsinghua.edu.cn

Research Areas

I study the representation theory of algebraic structures that arise in two-dimensional conformal quantum field theories, especially vertex operator algebras, affine Lie (super)algebras, and the Virasoro Lie algebra. More specifically, I am interested in the existence, properties, and structure of braided tensor categories of modules for these algebras.

Educational Background

2007 - 2014: Ph.D. in Mathematics, Rutgers University - New Brunswick

Work Experience

2020 - present: Assistant Professor (tenure track), Yau Mathematical Sciences Center, Tsinghua University

2016 - 2019: Assistant Professor (non-tenure track), Vanderbilt University

2014 - 2016: Postdoc, Beijing International Center for Mathematical Research, Peking University

Publications

1. On rationality for C_2-cofinite vertex operator algebras, arXiv:2108.01898.

2. A general mirror equivalence theorem for coset vertex operator algebras, arXiv:2107.06577.

3. On semisimplicity of module categories for finite non-zero index vertex operator subalgebras, arXiv:2103.07657.

4. (with J. Yang) Structure of Virasoro tensor categories at central charge 13-6p-6/p for integers p>1, arXiv:2011.02170.

5. (with T. Creutzig and J. Yang) Tensor structure on the Kazhdan-Lusztig category for affine gl(1|1), International Mathematics Research Notices 2021, rnab080, DOI: 10.1093/imrn/rnab080.

6. (with T. Creutzig and J. Yang) Direct limit completions of vertex tensor categories, Communications in Contemporary Mathematics (2021), 2150033, DOI: 10.1142/S0219199721500334.

7. (with T. Creutzig and J. Yang) On ribbon categories for singlet vertex algebras, Communications in Mathematical Physics 387 (2021), no. 2, 865-925.

8. Twisted modules and G-equivariantization in logarithmic conformal field theory, Communications in Mathematical Physics 383 (2021), no. 3, 1939-2019.

9. Vertex algebraic intertwining operators among generalized Verma modules for affine Lie algebras, Advances in Mathematics 374 (2020), 107351, 23 pp.

10. On the tensor structure of modules for compact orbifold vertex operator algebras, Mathematische Zeitschrift 296 (2020), no. 1-2, 409-452.

11. (with T. Creutzig and S. Kanade) Gluing vertex algebras, arXiv:1906.00119.

12. (with J. Yang) Vertex algebraic intertwining operators among generalized Verma modules for sl(2,C)^, Transactions of the American Mathematical Society 370 (2018), no. 4, 2351-2390.

13. (with T. Creutzig and S. Kanade) Tensor categories for vertex operator superalgebra extensions, to appear in Memoirs of the American Mathematical Society, arXiv:1705.05017.

14. (with B. Coulson, S. Kanade, J. Lepowsky, F. Qi, M. C. Russell, and C. Sadowski) A motivated proof of the Gollnitz-Gordon-Andrews identities, The Ramanujan Journal 42 (2017), no. 1, 97-129.

15. Non-negative integral level affine Lie algebra tensor categories and their associativity isomorphisms, Communications in Mathematical Physics 346 (2016), no. 1, 349-395.

16. Integral forms for tensor powers of the Virasoro vertex operator algebra L(1/2,0) and their modules, Journal of Algebra 431 (2015), 1-23.

17. Intertwining operators among modules for lattice and affine Lie algebra vertex operator algebras which respect integral forms, Journal of Pure and Applied Algebra 219 (2015), no. 10, 4757-4781.

18. On integral forms for vertex algebras associated with affine Lie algebras and lattices, Journal of Pure and Applied Algebra 219 (2015), no. 4, 1236-1257.

19. Linear automorphisms of vertex operator algebras associated with formal changes of variable and Bernoulli-type numbers, arXiv:1401.6442.

20. (with L. Carbone, S. Chung, L. Cobbs, D. Nandi, Y. Naqvi, and D. Penta) Classification of hyperbolic Dynkin diagrams, root lengths and Weyl group orbits, Journal of Physics A: Mathematical and Theoretical 43 (2010), no. 15, 155209, 30 pp.