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Robert McRae

Associate Professor, Yau Mathematical Sciences Center, Tsinghua University

Basic Information

Email
rhmcrae (at) tsinghua.edu.cn
Office
Shuangqing Complex Building B622

Research Areas

Vertex operator algebras, tensor categories, and mathematical physics.

Education

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

Employment

  • 2026-present, Associate Professor, Yau Mathematical Sciences Center, Tsinghua University.
  • 2019-2026, Assistant Professor, Yau Mathematical Sciences Center, Tsinghua University.
  • 2016-2019, Assistant Professor, Vanderbilt University.
  • 2014-2016, Postdoctoral Fellow, Beijing International Center for Mathematical Research, Peking University.

Research Summary

Robert McRae studies vertex operator algebras and tensor-category structures in logarithmic and rational conformal field theory. His recent work builds tensor and ribbon categories for Virasoro, affine sl2, singlet, triplet, and W-(super)algebra representation categories, while also developing Deligne tensor products and rationality criteria for VOA module categories. The broader goal is to understand when representation categories of conformal field theories carry enough rigidity and braided structure to support modular, logarithmic, and orbifold constructions.

Representative Publications

  • R. McRae, J. Yang, “Structure of Virasoro tensor categories at central charge 13-6p-6/p for integers p > 1,” arXiv:2011.02170.
  • R. McRae, “Vertex algebraic intertwining operators among generalized Verma modules for affine Lie algebras,” Adv. Math. 374 (2020) 107351.
  • R. McRae, “On semisimplicity of module categories for finite non-zero index vertex operator subalgebras,” arXiv:2103.07657.
  • T. Creutzig, R. McRae, J. Yang, “Tensor structure on the Kazhdan-Lusztig category for affine gl(1|1),” Int. Math. Res. Not. IMRN (2021).
  • T. Creutzig, R. McRae, J. Yang, “On ribbon categories for singlet vertex algebras,” Comm. Math. Phys. 387 (2021) 865-925.
  • R. McRae, “Twisted modules and G-equivariantization in logarithmic conformal field theory,” Comm. Math. Phys. 383 (2021) 1939-2019.
  • R. McRae, “A general mirror equivalence theorem for coset vertex operator algebras,” arXiv:2107.06577.
  • R. McRae, “On rationality for C_2-cofinite vertex operator algebras,” arXiv:2108.01898.

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