Research Interests

I am currently interested in problems involving representation theory of vertex operator algebras,
tensor categories and integer partition identities.

Articles

[E]: Expository [C]: Conference Proceedings

Principal subspaces of basic modules for twisted affine Lie algebras, \(q\)-series multisums, and Nandi's identities

+ K. Baker, M. C. Russell, C. Sadowski

Coloured \(\mathfrak{sl}_r\) invariants of torus knots and characters of \(\mathcal{W}_r\) algebras

Submitted.

[C]
Searching for modular companions

Meh.

On certain identities involving Nahm-type sums with double poles

+ A. Milas and M. C. Russell

Adv. in Appl. Math. (Accepted)

Completing the \(\mathrm{A}_2\) Andrews-Schilling-Warnaar identities

+ M. C. Russell

Int. Math. Res. Not. IMRN (Accepted)

\(A_{2l}^{(2)}\) at level \(-l-\frac{1}{2}\)

J. Algebra (2022)

On \(q\)-series for principal characters of standard \(A_2^{(2)}\)-modules

+ M. C. Russell

Adv. Math. (2022)

Gluing vertex algebras

+ T. Creutzig and R. McRae

Adv. Math. (2022)

Braided Tensor Categories related to \(\mathcal{B}_p\) Vertex Algebras

+ J. Auger, T. Creutzig and M. Rupert

Commun. Math. Phys. (2020)

[C]
A variant of IdentityFinder and some new identities of Rogers-Ramanujan-MacMahon type

+ D. Nandi, M. C. Russell

Ann. Comb., Combinatory Analysis 2018: In Honor of George Andrewsâ€™ 80th Birthday

[E, C]
NGK and HLZ: Fusion for Physicists and Mathematicians

+ D. Ridout

Springer INdAM Series: Affine, Vertex and W-algebras (2020)

Cosets, characters and fusion for admissible-level \(\mathfrak{osp}(1|2)\) minimal models

+ T. Creutzig, T. Liu, D. Ridout

Nucl. Phys. B. (2019)

Universal two-parameter even spin \(\mathcal{W}_\infty\)-algebra

+ A. R. Linshaw

Adv. Math. (2019)

Staircases to analytic sum-sides for many new integer partition identities of Rogers-Ramanujan type

+ M. C. Russell

Electron. J. Combin. (2019)

Representation theory of \(L_k(\mathfrak{osp}(1|2))\) from vertex tensor categories and Jacobi forms

+ T. Creutzig and J. Frohlich

Proc. Amer. Math. Soc. (2018)

Tensor categories for vertex operator superalgebra extensions

+ T. Creutzig and R. McRae

Mem. Amer. Math. Soc. (Accepted)

Schur-Weyl Duality for Heisenberg cosets

+ T. Creutzig, A. R. Linshaw and D. Ridout

Transf. Groups. (2019)

Simple current extensions beyond semi-simplicity

+ T. Creutzig and A. R. Linshaw

Commun. Contemp. Math. (2020)

On a Koszul complex related to the principal subspace of the basic vacuum module for \(A^{(1)}_1\)

J. Pure and Appl. Alg. (2018)

Structure of certain level \(2\) standard modules for \(A_5^{(2)}\) and the Göllnitz-Gordon identities

Ramanujan J. (2018)

IdentityFinder and some new identities of Rogers-Ramanujan type

+ M. C. Russell

Exp. Math. (2015)

Ghost series and a motivated proof of the Andrews-Bressoud identities

+ J. Lepowsky, M. C. Russell and A. V. Sills

J. Combin. Theory Ser. A. (2017)

A motivated proof of the Göllnitz-Gordon-Andrews identities

+ B. Coulson, J. Lepowsky, R. McRae, F. Qi, M. C. Russell and C. Sadowski

Ramanujan J. (2017)