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NIM-representations of Tambara-Yamagami generalizations
Agustina Czenky, Emily McGovern, Melody Molander +2
We compute and classify the irreducible non-negative integer matrix (NIM-)representations of two proposed generalizations of the Tambara-Yamagami fusion ring, as studied by Jordan-…
Pivotal Brauer-Picard groupoids and graded extensions
Agustina Czenky, David Jaklitsch, Dmitri Nikshych +4
We develop pivotal and spherical versions of graded extension theory. We define the corresponding analogues of Brauer-Picard -categorical groups and realize them as fixed points…
Cochain valued TQFTs from nonsemisimple modular tensor categories
Agustina Czenky, Cris Negron
We show that a vector space valued TQFT constructed in work of De Renzi et al. [DGGPR23] extends naturally to a topological field theory which takes values in the symmetric monoida…
On extended Frobenius structures
Agustina Czenky, Jacob Kesten, Abiel Quinonez +1
A classical result in quantum topology is that oriented 2-dimensional topological quantum field theories (2-TQFTs) are fully classified by commutative Frobenius algebras. In 2006,…
On Frobenius-Schur exponent bounds
Agustina Czenky, Julia Plavnik, Andrew Schopieray
Here we study bounds on the Frobenius-Schur exponent of spherical fusion categories based on their global dimension generalizing bounds from the representation theory of finite-dim…
Diagramatics for cyclic pointed fusion categories
Agustina Czenky
We give a parametrization of cyclic pointed categories associated to the cyclic group of order in terms of -th roots of unity. We also provide a diagramatic description of t…
On modular categories with Frobenius-Perron dimension congruent to 2 modulo 4
Akshaya Chakravarthy, Agustina Czenky, Julia Plavnik
We contribute to the classification of modular categories with . We prove that such categories have group of invert…
Unoriented 2-dimensional TQFTs and the category
Agustina Czenky
We construct a family of unoriented 2-dimensional cobordism theories parametrized by certain triples of sequences. We also prove that some specializations of these sequences yield…
Classification of low-rank odd-dimensional modular categories
Agustina Czenky, William Gvozdjak, Julia Plavnik
We prove that any odd-dimensional modular category of rank at most 23 is pointed. We also show that an odd-dimensional modular category of rank 25 is either pointed, perfect, or eq…
Remarks on symmetric fusion categories of low rank in positive characteristic
Agustina Czenky
We give lower bounds for the rank of a symmetric fusion category in characteristic in terms of . We prove that the second Adams operation is not the identity for…
On odd-dimensional modular tensor categories
Agustina Czenky, Julia Plavnik
We study odd-dimensional modular tensor categories and maximally non-self dual (MNSD) modular tensor categories of low rank. We give lower bounds for the ranks of modular tensor ca…