141 citations · 408 across the 13 of their papers we have counts for
16 papers
Hypergraph Characterization of Fusion Rings
Paul Bruillard, Kathleen Nowak, Stephen J. Young
We present a correspondence between multiplicity-free, self-dual, fusion rings and a digraph, hypergraph pair . This correspondence is used to provide a complete characteriz…
Classification of super-modular categories
Paul Bruillard, Julia Yael Plavnik, Eric C. Rowell +1
We develop categorical and number theoretical tools for the classification of super-modular categories. We apply these tools to obtain a partial classification of super-modular cat…
Ramanujan Graphs and the Spectral Gap of Supercomputing Topologies
Sinan G. Aksoy, Paul Bruillard, Stephen J. Young +1
Graph eigenvalues play a fundamental role in controlling structural properties, such as bisection bandwidth, diameter, and fault tolerance, which are critical considerations in the…
Dimension as a quantum statistic and the classification of metaplectic categories
Paul Bruillard, Paul Gustafson, Julia Yael Plavnik +1
We discuss several useful interpretations of the categorical dimension of objects in a braided fusion category, as well as some conjectures demonstrating the value of quantum dimen…
Classification of super-modular categories by rank
Paul Bruillard, César Galindo, Siu-Hung Ng +3
We pursue a classification of low-rank super-modular categories parallel to that of modular categories. We classify all super-modular categories up to rank=, and spin modular ca…
Classification of Rank 5 Premodular Categories
Paul Bruillard, Carlos M. Ortiz
We survey a number of classification tools developed in recent years and employ them to classify pseudo-unitary rank 5 premodular categories up to equivalence.
Modular Categories of Dimension with Square-Free
Paul Bruillard, Julia Yael Plavnik, Eric C. Rowell
We give a complete classification of modular categories of dimension where is prime and is a square-free integer. When is odd, all such categories are pointed. F…
Fermionic Modular Categories and the 16-fold Way
Paul Bruillard, Cesar Galindo, Tobias Hagge +4
We study spin and super-modular categories systematically as inspired by fermionic topological phases of matter, which are always fermion parity enriched and modelled by spin TQFTs…
Low-dimensional representations of the three component loop braid group
Paul Bruillard, Liang Chang, Seung-Moon Hong +3
Motivated by physical and topological applications, we study representations of the group of motions of unlinked oriented circles in . Our point…
On classification of modular categories by rank
Paul Bruillard, Siu-Hung Ng, Eric C. Rowell +1
The feasibility of a classification-by-rank program for modular categories follows from the Rank-Finiteness Theorem. We develop arithmetic, representation theoretic and algebraic m…
On the Classification of Weakly Integral Modular Categories
Paul Bruillard, César Galindo, Siu-Hung Ng +3
We classify all modular categories of dimension , where is an odd square-free integer, and all ranks and weakly integral modular categories. This completes the clas…
Rank-finiteness for modular categories
Paul Bruillard, Siu-Hung Ng, Eric C. Rowell +1
We prove a rank-finiteness conjecture for modular categories: up to equivalence, there are only finitely many modular categories of any fixed rank. Our technical advance is a gener…
Classification of integral modular categories of Frobenius-Perron dimension pq^4 and p^2q^2
Paul Bruillard, César Galindo, Seung-Moon Hong +5
We classify integral modular categories of dimension pq^4 and p^2q^2 where p and q are distinct primes. We show that such categories are always group-theoretical except for categor…
Rank 4 Premodular Categories
Paul Bruillard
We consider the classification problem for rank 4 premodular categories. We uncover a formula for the 2nd Frobenius-Schur indicator of a premodular category, and complete the class…
Modular categories, integrality and Egyptian fractions
Paul Bruillard, Eric C. Rowell
It is a well-known result of Etingof, Nikshych and Ostrik that there are finitely many inequivalent integral modular categories of any fixed rank . This follows from a double-ex…
Chiral Supergravity
Melanie Becker, Paul Bruillard, Sean Downes
We study the linearized approximation of N=1 topologically massive supergravity around AdS3. Linearized gravitino fields are explicitly constructed. For appropriate boundary condit…