Date of Award
1-1-2023
Document Type
Thesis
Degree Name
M.S. in Mathematics
First Advisor
Samuel Lisi
Second Advisor
Rizwanur Khan
Third Advisor
Sasa Kocic
School
University of Mississippi
Relational Format
dissertation/thesis
Abstract
Symplectic capacities are a central tool from quantitative symplectic topology which act as symplectic invariants, distinguishing symplectic manifolds as different. There are a wide variety of capacities common in the literature today. The still-open Viterbo conjecture states all normalized symplectic capacities coincide on convex domains. Even upper bounds for these capacities are not completely understood, and there are many hard computational barriers. The recent work of Chaidez and Hutchings as well as that of Haim-Kislev have yielded results simplifying computation of a capacity in the case of convex polytopes. In this thesis, we prove an upper bound on normalized capacities over a rotated hypercube. We investigate a linearization of the cylinder capacity and prove results which aid in computing this linearization. Through these, we are able to investigate statistical properties of the linearized capacity with a computer and can prove a result regarding the distribution of this linearization over randomly rotated hypercubes.
Recommended Citation
Zediker, Matthew Palmer, "Bounds for Symplectic Capacities of Rotated 4-Polytopes" (2023). Electronic Theses and Dissertations. 2602.
https://egrove.olemiss.edu/etd/2602