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Bounds for Symplectic Capacities of ...

Zediker, Matthew.

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Bounds for Symplectic Capacities of Rotated 4-Polytopes.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Bounds for Symplectic Capacities of Rotated 4-Polytopes./
Author:	Zediker, Matthew.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2023,
Description:	68 p.
Notes:	Source: Masters Abstracts International, Volume: 85-01.
Contained By:	Masters Abstracts International85-01.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30485463
ISBN:	9798379847425

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

Bounds for Symplectic Capacities of Rotated 4-Polytopes. - Ann Arbor : ProQuest Dissertations & Theses, 2023 - 68 p.

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

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

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.

ISBN: 9798379847425Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Capacity

Bounds for Symplectic Capacities of Rotated 4-Polytopes.
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100 1 $a Zediker, Matthew. $3 3769880
245 1 0 $a Bounds for Symplectic Capacities of Rotated 4-Polytopes.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2023
300 $a 68 p.
500 $a Source: Masters Abstracts International, Volume: 85-01.
500 $a Advisor: Lisi, Samuel.
502 $a Thesis (M.S.)--The University of Mississippi, 2023.
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.
590 $a School code: 0131.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Capacity
653 $a Computational barriers
653 $a Geometry
653 $a Polytopes
653 $a Symplectic capacities
653 $a Topology
690 $a 0405
690 $a 0642
710 2 $a The University of Mississippi. $b Mathematics. $3 3279473
773 0 $t Masters Abstracts International $g 85-01.
790 $a 0131
791 $a M.S.
792 $a 2023
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30485463