27 citations · 61 across the 8 of their papers we have counts for
10 papers
Stably unactivated neurons in ReLU neural networks
Natalie Brownlowe, Christopher R. Cornwell, Ethan Montes +3
The choice of architecture of a neural network influences which functions will be realizable by that neural network and, as a result, studying the expressiveness of a chosen archit…
Links and the Diaconis-Graham Inequality
Christopher Cornwell, Nathan McNew
In 1977 Diaconis and Graham proved two inequalities relating different measures of disarray in permutations, and asked for a characterization of those permutations for which equali…
Unknotted cycles
Christopher R. Cornwell, Nathan McNew
Noting that cycle diagrams of permutations visually resemble grid diagrams used to depict knots and links in topology, we consider the knot (or link) obtained from the cycle diagra…
Character varieties of knot complements and branched double-covers via the cord ring
Christopher R. Cornwell
We study the relationship between Ng's abelian cord ring and SL(2,C) characters of the two-fold branched cover . Augmentations, and their corresponding rank, play a central r…
Berge duals and universally tight contact structures
Christopher R. Cornwell
Dehn surgery on a knot determines a dual knot in the surgered manifold, the core of the filling torus. We consider duals of knots in that have a lens space surgery. Each dual…
Obstructions to Lagrangian concordance
Christopher R. Cornwell, Lenhard Ng, Steven Sivek
We investigate the question of the existence of a Lagrangian concordance between two Legendrian knots in . In particular, we give obstructions to a concordance from a…
Augmentation Rank of Satellites with Braid Pattern
Christopher R. Cornwell, David R. Hemminger
Given a knot in , a question raised by Cappell and Shaneson asks if the meridional rank of equals the bridge number of . Using augmentations in knot contact homolog…
KCH representations, augmentations, and -polynomials
Christopher Cornwell
We describe a correspondence between augmentations and certain representations of the knot group. The correspondence makes the 2-variable augmentation polynomial into a generalizat…
Bennequin type inequalities in lens spaces
Christopher R. Cornwell
We give criteria for an invariant of lens space links to bound the maximal self-linking number in certain tight contact lens spaces. As a corollary we extend the Franks-Williams-Mo…
A polynomial invariant for links in lens spaces
Christopher Cornwell
We prove the existence of a polynomial invariant that satisfies the HOMFLY skein relation for links in a lens space. In the process we also develop a skein theory of toroidal grid…