2 papers
math.CV2023
Bounded Connected Components of Polynomial Lemniscates
Adam Kraus, Brian Simanek
We consider families of polynomial lemniscates in the complex plane and determine if they bound a Jordan domain. This allows us to find examples of regions for which we can calcula…
math.CA2023
New Perspectives on Torsional Rigidity and Polynomial Approximations of z-bar
Adam Kraus, Brian Simanek
We consider polynomial approximations of z-bar to better understand the torsional rigidity of polygons. Our main focus is on low degree approximations and associated extremal probl…