Women in Numbers Europe II: Contributions to Number Theory and Arithmetic Geometry

218 Pages·2018·2.98 MB·English

by  Irene I. Bouw

Association for Women in Mathematics Series
Irene I. Bouw · Ekin Ozman
Jennifer Johnson-Leung
Rachel Newton Editors
Women in
Numbers
Europe II
Contributions to Number Theory and
Arithmetic Geometry
Association for Women in Mathematics Series
Volume 11
SeriesEditor
KristinLauter
MicrosoftResearch
Redmond,Washington,USA
Association for Women in Mathematics Series
Focusingonthegroundbreakingworkofwomeninmathematicspast,present,and
future,Springer’sAssociationforWomeninMathematicsSeriespresentsthelatest
research and proceedings of conferences worldwide organized by the Association
forWomeninMathematics(AWM).Allworksarepeer-reviewedtomeetthehighest
standardsofscientificliterature,whilepresentingtopicsatthecuttingedgeofpure
andappliedmathematics.Sinceitsinceptionin1971,TheAssociationforWomenin
Mathematicshasbeenanon-profitorganizationdesignedtohelpencouragewomen
and girls to study and pursue active careers in mathematics and the mathematical
sciencesandtopromoteequalopportunityandequaltreatmentofwomenandgirls
inthemathematicalsciences.Currently,theorganizationrepresentsmorethan3000
members and 200 institutions constituting a broad spectrum of the mathematical
community,intheUnitedStatesandaroundtheworld.
Moreinformationaboutthisseriesathttp://www.springer.com/series/13764
Irene I. Bouw (cid:129) Ekin Ozman
Jennifer Johnson-Leung (cid:129) Rachel Newton
Editors
Women in Numbers Europe II
Contributions to Number Theory
and Arithmetic Geometry
123
Editors
IreneI.Bouw EkinOzman
InstitutfürReineMathematik DepartmentofMathematics
UniversitätUlm BogaziciUniversity
Ulm,Baden-Württemberg,Germany Istanbul,Istanbul,Turkey
JenniferJohnson-Leung RachelNewton
DepartmentofMathematics DepartmentofMathematicsandStatistics
UniversityofIdaho UniversityofReading
Moscow,ID,USA Reading,UK
ISSN2364-5733 ISSN2364-5741 (electronic)
AssociationforWomeninMathematicsSeries
ISBN978-3-319-74997-6 ISBN978-3-319-74998-3 (eBook)
https://doi.org/10.1007/978-3-319-74998-3
LibraryofCongressControlNumber:2015946869
©TheAuthor(s)andtheAssociationforWomeninMathematics2018
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof
thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,
broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation
storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology
nowknownorhereafterdeveloped.
Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication
doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant
protectivelawsandregulationsandthereforefreeforgeneraluse.
Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook
arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor
theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany
errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional
claimsinpublishedmapsandinstitutionalaffiliations.
Printedonacid-freepaper
ThisSpringerimprintispublishedbytheregisteredcompanySpringerInternationalPublishingAGpart
ofSpringerNature.
Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland
WomeninNumbersEuropeII,LorentzCenter,September2016
Preface
ThisvolumegrewoutofthesecondWomeninNumbersEuropeconferenceheldat
theLorentzCenter,Leiden,from26thto30thSeptember2016.Thisconferencewas
one of an ongoing series of collaboration conferences for women in mathematics,
whichbeganwiththeWomeninNumbersconferenceheldattheBanffInternational
ResearchStationin2008.Thisvolumeincludesresearchreportsfromprojectsthat
werestartedattheconference,expositorypapersdescribingongoingresearchbegun
attheconference,andcontributedpapersfromotherwomennumbertheorists.All
ofthepapersincludedwerereviewedbyanonymousrefereeswhoverifiedthemas
worthyandvalidcontributionstotheseproceedings.Weareproudthatthisvolume
continues the tradition of supporting and highlighting the contributions of women
number theorists at a variety of career stages from graduate students to leading
expertsinthefield.
Thearticlescollectedherespanawiderangeoftopicsincontemporarynumber
theoryandarithmeticgeometrysuchasarithmeticdynamics,failureoflocal-global
principles, geometry in positive characteristic, and heights of algebraic integers.
The use of tools from algebra, analysis, and geometry, as well as computational
methods, exemplifies the wealth of techniques available to modern researchers in
numbertheory.
Several papers in this volume stem from collaborations between authors with
different mathematical backgrounds and expertise. These papers naturally explore
connections between different branches of mathematics and combine different
points of view. Another common theme is the provision of explicit examples to
complementnewtheoremsandtoprovideevidenceforconjectures.Theseconcrete
examplesprovideaneasilyaccessibleintroductiontothefieldandhavethepotential
toinspirefuturework.
Ulm,Germany IreneI.Bouw
Moscow,ID,USA JenniferJohnson-Leung
Reading,UK RachelNewton
Istanbul,Turkey EkinOzman
vii
Acknowledgement
We would like to thank the following organizations for their generous support of
the conference and this resulting volume: Clay Mathematics Institute, Foundation
CompositioMathematica,HeilbronnInstituteforMathematicalResearch,National
ScienceFoundationaspartoftheAdvancegrantfortheAssociationforWomenin
Mathematics,MicrosoftResearch,andtheNumberTheoryFoundation.
Weareparticularlythankfulfortheadditionalfinancialsupportwereceivedwhen
we were forced to relocate our workshop, originally planned to take place in the
Nesin Mathematics Village, due to instability in Turkey. The Lorentz Center was
very generous in accommodating our conference at short notice and provided us
with extremely valuable organizational support. We also would like to extend our
sinceregratitudetotheNesinMathematicsVillagefortheirunderstandingwhenwe
neededtorelocateattheverylastminute.
Wearedeeplygratefultotherefereesfortheircarefulandtimelyreviewofthe
papersincludedinthisvolume.
ix
Contents
LowerBoundsforHeightsinRelativeGaloisExtensions ................... 1
Shabnam Akhtari, Kevser Aktas¸, Kirsti D. Biggs, Alia Hamieh,
KathleenPetersen,andLolaThompson
ReductionsofAlgebraicIntegersII............................................ 19
AntonellaPerucca
ReductionsofOne-DimensionalToriII ....................................... 35
AntonellaPerucca
On the Carlitz Rank of Permutation Polynomials Over Finite
Fields:RecentDevelopments ................................................... 39
Nurdagül Anbar, Almasa Odžak, Vandita Patel, Luciane Quoos,
AnnaSomoza,andAlevTopuzog˘lu
DynamicalBelyiMaps........................................................... 57
Jacqueline Anderson, Irene I. Bouw, Ozlem Ejder, Neslihan Girgin,
ValentijnKaremaker,andMichelleManes
DiscriminantTwins .............................................................. 83
AlysonDeines
Thea-NumberofHyperellipticCurves........................................ 107
SarahFrei
Non-ordinaryCurveswithaPrymVarietyofLowp-Rank................. 117
Turku Ozlum Celik, Yara Elias, Burçin Günes¸, Rachel Newton,
EkinOzman,RachelPries,andLaraThomas
xi
xii Contents
EllipticFibrationsonCoversoftheEllipticModularSurfaceof
Level5............................................................................. 159
FrancescaBalestrieri,JulieDesjardins,AliceGarbagnati,CélineMaistret,
CecíliaSalgado,andIsabelVogt
OnBirchandSwinnerton-Dyer’sCubicSurfaces............................ 199
MckenzieWest