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GKZ Hypergeometric Systems and Toric...

Han, Zengrui,

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GKZ Hypergeometric Systems and Toric Mirror Symmetry /

Record Type:	Electronic resources : Monograph/item
Title/Author:	GKZ Hypergeometric Systems and Toric Mirror Symmetry // Zengrui Han.
Author:	Han, Zengrui,
Description:	1 electronic resource (96 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 87-01, Section: B.
Contained By:	Dissertations Abstracts International87-01B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31932324
ISBN:	9798288803352

GKZ Hypergeometric Systems and Toric Mirror Symmetry /
Han, Zengrui,

GKZ Hypergeometric Systems and Toric Mirror Symmetry /Zengrui Han. - 1 electronic resource (96 pages)

Source: Dissertations Abstracts International, Volume: 87-01, Section: B.

In this dissertation, we study questions related to the Gel'fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems and toric mirror symmetry. Such systems are conjecturally the de-categorification of an isotrivial family of triangulated categories over the stringy Kahler moduli space associated to a toric Gorenstein singularity, which underlies the derived equivalences between different crepant resolutions of this singularity.The two main results of this dissertation are the following:(1) We study the relationship between solutions to such systems near different large radius limit points, and their geometric counterparts given by the K-groups of the corresponding crepant resolutions. We prove that analytic continuation transformations of solutions are realized by the natural Fourier-Mukai transforms associated to the toric wall-crossings. This settles a conjecture of Borisov and Horja.(2) We apply such systems to study toric Calabi-Yau Deligne-Mumford stacks and their Hori-Vafa mirrors. We verify that A- and B-model integral structures coincide by establishing the equality between A-brane and B-brane central charges, in terms of period integrals and Gamma series respectively. This settles a (variation of a) conjecture of Hosono.This dissertation builds upon the papers [17] and [16] of the author.

English

ISBN: 9798288803352Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

GKZ hypergeometric systems

GKZ Hypergeometric Systems and Toric Mirror Symmetry /
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100 1 $a Han, Zengrui, $e author. $0 (orcid)0009-0006-7691-4986 $3 3823020
245 1 0 $a GKZ Hypergeometric Systems and Toric Mirror Symmetry / $c Zengrui Han.
264 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2025
300 $a 1 electronic resource (96 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 87-01, Section: B.
500 $a Advisors: Borisov, Lev Committee members: Buch, Anders; Woodward, Christopher; Liu, Chiu-Chu Melissa.
502 $b Ph.D. $c Rutgers The State University of New Jersey, School of Graduate Studies $d 2025.
520 $a In this dissertation, we study questions related to the Gel'fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems and toric mirror symmetry. Such systems are conjecturally the de-categorification of an isotrivial family of triangulated categories over the stringy Kahler moduli space associated to a toric Gorenstein singularity, which underlies the derived equivalences between different crepant resolutions of this singularity.The two main results of this dissertation are the following:(1) We study the relationship between solutions to such systems near different large radius limit points, and their geometric counterparts given by the K-groups of the corresponding crepant resolutions. We prove that analytic continuation transformations of solutions are realized by the natural Fourier-Mukai transforms associated to the toric wall-crossings. This settles a conjecture of Borisov and Horja.(2) We apply such systems to study toric Calabi-Yau Deligne-Mumford stacks and their Hori-Vafa mirrors. We verify that A- and B-model integral structures coincide by establishing the equality between A-brane and B-brane central charges, in terms of period integrals and Gamma series respectively. This settles a (variation of a) conjecture of Hosono.This dissertation builds upon the papers [17] and [16] of the author.
546 $a English
590 $a School code: 0190
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a GKZ hypergeometric systems
653 $a Mellin-Barnes integrals
653 $a Mirror symmetry
653 $a Toric geometry
653 $a Tropical geometry
690 $a 0405
690 $a 0642
710 2 $a Rutgers The State University of New Jersey, School of Graduate Studies. $b Mathematics. $e degree granting institution. $3 3823021
720 1 $a Borisov, Lev $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 87-01B.
790 $a 0190
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31932324