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