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The Attractor Conjecture.

Record Type:	Electronic resources : Monograph/item
Title/Author:	The Attractor Conjecture./
Author:	Lam, Yeuk Hay Joshua.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
Description:	116 p.
Notes:	Source: Dissertations Abstracts International, Volume: 83-02, Section: B.
Contained By:	Dissertations Abstracts International83-02B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28499096
ISBN:	9798534671001

The Attractor Conjecture.
Lam, Yeuk Hay Joshua.

The Attractor Conjecture. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 116 p.

Source: Dissertations Abstracts International, Volume: 83-02, Section: B.

Thesis (Ph.D.)--Harvard University, 2021.

This item must not be sold to any third party vendors.

This thesis studies the Attractor Conjecture due to Moore, which aims to produce arithmetic Calabi-Yau varieties using the attractor mechanism studied in string theory. The first part of this thesis gives counterexamples to the Attractor Conjecture in all odd dimensions except for a few small exceptions, assuming a standard conjecture in unlikely intersection theory. Our counterexamples come from a family of Calabi-Yau varieties first studied by Dolgachev, and we use crucially a transcendence result of Shiga-Wolfart. For this family of Dolgachev varieties, the conjecture holds if and only if the moduli space is a Shimura variety. The second part of this thesis proves the Attractor Conjecture in many cases of Calabi-Yau variations of Hodge structures (CYVHS) on Shimura varieties. More precisely, we study the canonical CYVHS on Shimura varieties constructed by Gross, and prove that attractor points are CM points.

ISBN: 9798534671001Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Attractor Conjecture

The Attractor Conjecture.
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100 1 $a Lam, Yeuk Hay Joshua. $0 (orcid)0000-0001-5475-2396 $3 3686074
245 1 4 $a The Attractor Conjecture.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2021
300 $a 116 p.
500 $a Source: Dissertations Abstracts International, Volume: 83-02, Section: B.
500 $a Advisor: Kisin, Mark.
502 $a Thesis (Ph.D.)--Harvard University, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a This thesis studies the Attractor Conjecture due to Moore, which aims to produce arithmetic Calabi-Yau varieties using the attractor mechanism studied in string theory. The first part of this thesis gives counterexamples to the Attractor Conjecture in all odd dimensions except for a few small exceptions, assuming a standard conjecture in unlikely intersection theory. Our counterexamples come from a family of Calabi-Yau varieties first studied by Dolgachev, and we use crucially a transcendence result of Shiga-Wolfart. For this family of Dolgachev varieties, the conjecture holds if and only if the moduli space is a Shimura variety. The second part of this thesis proves the Attractor Conjecture in many cases of Calabi-Yau variations of Hodge structures (CYVHS) on Shimura varieties. More precisely, we study the canonical CYVHS on Shimura varieties constructed by Gross, and prove that attractor points are CM points.
590 $a School code: 0084.
650 4 $a Mathematics. $3 515831
650 4 $a Physics. $3 516296
650 4 $a String theory. $3 3684064
650 4 $a Algebra. $3 516203
650 4 $a Investigations. $3 3561159
650 4 $a Friendship. $3 611043
650 4 $a Geometry. $3 517251
653 $a Attractor Conjecture
653 $a Shimura variety
653 $a CYVHS
690 $a 0405
690 $a 0605
710 2 $a Harvard University. $b Mathematics. $3 2049814
773 0 $t Dissertations Abstracts International $g 83-02B.
790 $a 0084
791 $a Ph.D.
792 $a 2021
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28499096