#### Contact Information

SC 1529(32)2-2802

robert.h.mcrae

#### Education

Ph.D., Rutgers University, 2014

Employed at Vanderbilt Since: 2016

# Robert McRae

Assistant Professor (NTT) [AY ’16-19]

#### Research Interests

Vertex operator algebras, affine Lie algebras, mathematics related to conformal field theory

#### Publications

(with J. Yang) Vertex algebraic intertwining operators among generalized Verma modules for sl(2, C)^, to appear in *Trans. Amer. Math. Soc.*

(with B. Coulson, S. Kanade, J. Lepowsky, F. Qi, M. C. Russell, and C. Sadowski) A motivated proof of the Göllnitz-Gordon-Andrews identities, *Ramanujan J.* **42** (2017), 97-129.* *

Non-negative integral level affine Lie algebra tensor categories and their associativity isomorphisms, *Comm. Math. Phys. ***346 **(2016), 349-395.

Integral forms for tensor powers of the Virasoro vertex operator algebra L(½, 0) and their modules, *J. Algebra ***431 **(2015), 1-23.

Intertwining operators among modules for affine Lie algebra and lattice vertex operator algebras which respect integral forms, *J. Pure Appl. Algebra* **219** (2015), 4757-4781.

On integral forms for vertex algebras associated with affine Lie algebras and lattices, *J. Pure Appl. Algebra ***219** (2015), 1236-1257.

(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, *J. Phys. A: Math. Theor.* **43** 155209 (2010).

#### Conference Talks

Tensor categories for vertex operator superalgebra extensions, at *Quantum Symmetries: Subfactors and Planar Algebras*, Maui, Hawaii, July 2017.

Tensor categories for vertex operator algebra extensions: Theory, at *AMS Fall Western Sectional Meeting, Special Session on Vertex Algebras and Geometry*, University of Denver, Denver, October 2016.

On the associativity isomorphisms in affine Lie algebra tensor categories, at *Lie Algebras, Vertex Operator Algebras, and Related Topics*, University of Notre Dame, August 2015.

Vertex algebraic structure in integral forms of standard affine Lie algebra modules, at *AMS Fall Eastern Sectional Meeting*, *Special Session on Representation Theory, Combinatorics and Categorification*, Temple University, Philadelphia, October 2013.

Vertex algebraic structure in integral forms of standard affine Lie algebra modules, at *Representation Theory XIII*, Dubrovnik, Croatia, June 2013.

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