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Bounds for Symplectic Capacities of Rotated 4-Polytopes.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Bounds for Symplectic Capacities of Rotated 4-Polytopes./
Author:	Zediker, Matthew.
Description:	1 online resource (68 pages)
Notes:	Source: Masters Abstracts International, Volume: 85-01.
Contained By:	Masters Abstracts International85-01.
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9798379847425

Bounds for Symplectic Capacities of Rotated 4-Polytopes.
Zediker, Matthew.

Bounds for Symplectic Capacities of Rotated 4-Polytopes. - 1 online resource (68 pages)

Source: Masters Abstracts International, Volume: 85-01.

Thesis (M.S.)--The University of Mississippi, 2023.

Includes bibliographical references

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.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798379847425Subjects--Topical Terms:

527692
Mathematics.
Subjects--Index Terms:

CapacityIndex Terms--Genre/Form:

554714
Electronic books.

Bounds for Symplectic Capacities of Rotated 4-Polytopes.
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500 $a Advisor: Lisi, Samuel.
502 $a Thesis (M.S.)--The University of Mississippi, 2023.
504 $a Includes bibliographical references
520 $a 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.
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538 $a Mode of access: World Wide Web
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650 4 $a Theoretical mathematics. $3 1180455
653 $a Capacity
653 $a Computational barriers
653 $a Geometry
653 $a Polytopes
653 $a Symplectic capacities
653 $a Topology
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