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On the Fukaya category of Grassmannians

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TitleInfo
Title
On the Fukaya category of Grassmannians
Name (type = personal)
NamePart (type = family)
Castronovo
NamePart (type = given)
Marco
DisplayForm
Marco Castronovo
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Woodward
NamePart (type = given)
Christopher
DisplayForm
Christopher Woodward
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Advisory Committee
Role
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chair
Name (type = personal)
NamePart (type = family)
Borisov
NamePart (type = given)
Lev
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Lev Borisov
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Buch
NamePart (type = given)
Anders
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Anders Buch
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Abouzaid
NamePart (type = given)
Mohammed
DisplayForm
Mohammed Abouzaid
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
outside member
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
School of Graduate Studies
Role
RoleTerm (authority = RULIB)
school
TypeOfResource
Text
Genre (authority = marcgt)
theses
Genre (authority = ExL-Esploro)
ETD doctoral
OriginInfo
DateCreated (qualifier = exact); (encoding = w3cdtf); (keyDate = yes)
2021
DateOther (type = degree); (qualifier = exact); (encoding = w3cdtf)
2021-05
Language
LanguageTerm (authority = ISO 639-3:2007); (type = text)
English
Abstract (type = abstract)
The Grassmannian of k-dimensional planes in a complex n-dimensional vector space has a natural symplectic structure, that one can use to construct a deformation of its cohomology ring. We begin the study of its Fukaya category, which is a refinement of the category of modules over this ring. When n is a prime number, we prove that a fiber of an integrable system introduced by Guillemin-Sternberg split-generates the Fukaya category. If n is not prime this generally fails, and we construct examples of Lagrangian tori that support nonzero objects in the missing part of the Fukaya category. The tori are parametrized by seeds of a cluster algebra in the sense of Fomin-Zelevinsky, and have associated Laurent polynomials with positive integer coefficients. We program a random walk that computes these Laurent polynomials explicitly, and observe that they encode the open genus zero Gromov-Witten invariants of the tori in some cases. We put forth a conjecture on the general meaning of the Laurent polynomials, which can be considered as a Symplectic Field Theory interpretation of the notion of scattering diagram proposed by Gross-Hacking-Keel-Kontsevich.
Subject (authority = RUETD)
Topic
Mathematics
Subject (authority = LCSH)
Topic
Cluster algebras
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_11577
PhysicalDescription
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application/pdf
InternetMediaType
text/xml
Extent
1 online resource (vii, 120 pages) : illustrations
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
RelatedItem (type = host)
TitleInfo
Title
School of Graduate Studies Electronic Theses and Dissertations
Identifier (type = local)
rucore10001600001
Location
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NjNbRU
Identifier (type = doi)
doi:10.7282/t3-veb9-f129
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Rights

RightsDeclaration (ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Castronovo
GivenName
Marco
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2021-03-22 13:09:49
AssociatedEntity
Name
Marco Castronovo
Role
Copyright holder
Affiliation
Rutgers University. School of Graduate Studies
AssociatedObject
Type
License
Name
Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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Technical

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ETD
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1.4
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pdfTeX
DateCreated (point = start); (encoding = w3cdtf); (qualifier = exact)
2021-03-23T18:34:01
DateCreated (point = start); (encoding = w3cdtf); (qualifier = exact)
2021-03-23T18:34:01
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