31 citations · 33 across the 8 of their papers we have counts for
9 papers
A Solution to the Periodic Square Peg Problem
Cole Hugelmeyer
We resolve the periodic square peg problem using a simple Lagrangian Floer homology argument. Inscribed squares are interpreted as intersections between two non-displaceable Lagran…
Diagram Systems and Generalized Finite Type Theories
Cole Hugelmeyer
We present a category theoretical generalization of the Goussarov theorem for finite type invariants, relating generating sets for generalized finite type theories with diagrams sy…
Inscribed Squares and Relation Avoiding Paths
Cole Hugelmeyer
We develop a connection between the inscribed square problem and the question of understanding relation avoiding paths in a complex vector space. Our main theorem is that a Jordan…
What's knot to like? Observation of a linked loop quantum state
Ilya Belopolski, Guoqing Chang, Tyler A. Cochran +22
Quantum phases can be classified by topological invariants, which take on discrete values capturing global information about the quantum state. Over the past decades, these invaria…
Inscribed rectangles in a smooth Jordan curve attain at least one third of all aspect ratios
Cole Hugelmeyer
We prove that for every smooth Jordan curve , if is the set of all so that there is an inscribed rectangle in of aspect ratio , then the…
A Representation Theorem for Knots and a Generalization of the Fundamental Theorem of Finite Type Invariants
Cole Hugelmeyer
We provide a way to produce knots in from signed chord diagrams, and prove that every knot can be produced in this way. Using these diagrams, we generalize the fundamental th…
Inscribed Trefoil Knots
Cole Hugelmeyer
Let be a knot type for which the quadratic term of the Conway polynomial is nontrivial, and let be an analytic -periodic function wi…
Every smooth Jordan curve has an inscribed rectangle with aspect ratio equal to
Cole Hugelmeyer
We use Batson's lower bound on the nonorientable slice genus of -torus knots to prove that for any , every smooth Jordan curve has an inscribed rectangle of of…
A Construction on Operads Applicable to Homology Operations and the Minimal Model
Cole Hugelmeyer
We define a construction on operads which yields a new description of the minimal model. The construction also allows us to define algebraic structures on the homology of chain com…