iuteich verification report 2013-12

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1、ONTHEVERIFICATIONOFINTER-UNIVERSALTEICHMULLERTHEORY:APROGRESS¨REPORT(ASOFDECEMBER2013)ShinichiMochizuki(RIMS,KyotoUniversity,Professor)ɹNearlyayearandfourmonthshaveelapsedsinceIreleasedmyseriesofpapersoninter-universalTeichm¨ullertheory(IUTeich)inAugust2012.Inthefollowing,Iwould

2、liketoreportonvariousdevelopmentsthathavecometopassduringthistimewithregardtotheverificationofIUTeich.(1)AttheendofAugust2012,IreleasedmyseriesoffourpapersconcerningIUTeichandsubmittedthemtoamathematicaljournal.Ihavenointentionofdisclosingthenameofthejournalorotherinformationrela

3、tedtothisjournalsubmission.ThepaperswerereleasedinordertomakeitpossibleforspecialiststostudyandassessthevalidityofIUTeich;theywereneverintendedasanan-nouncementtothegeneralpublic.Moreover,Ineverenvisagedthatthesepapersmightelicitreactionsconsistingofnon-mathematicalcontentfromno

4、n-specialists.Ihavenointentionofrespondingtosuchnon-mathematicalreactions.(2)Asofthetimeofwriting,IhavegiventwotalksonIUTeichatKyotoUniversity—inOctober2010(i.e.,aone-hour“preview”talk)andDecember2012(onehour)—andonetalkonIUTeichattheUniversityofTokyo—inJune2013(oneandahalfhours

5、).Theslidesforthesetalksareavailableonmywebsite(onthepageentitled“TravelandLectures”).ItislikelythatIwillagaingiveatleastonetalkatsomeacademicinstitutioninJapanin2014.ThevarioustalksthatIhavegivensofarcoveressentiallythesamecontent;thiscontentisexposedinmoredetailinthesurvey[Pan

6、o].Thissurveyisavailableonthepageofmywebsiteentitled“Papers”andisscheduledtoappearintheproceedingsfortheworkshopatwhichmyDecember2012talkwasdelivered.2ONTHEVERIFICATIONOFINTER-UNIVERSALTEICHMULLERTHEORY¨(3)IhavebeenconductingaseminardevotedtothedetailedexaminationofIUTe-ichwithG

7、oYamashita(ResearchFellowatToyotaCentralResearchandDevel-opmentLaboratories;ProjectLecturerattheCenterforResearchInteractioninMathematicalSciencesofRIMS,KyotoUniversity)onceamonth(for2days≈12hours),sinceOctober2012.Moreprecisely,duringtheperiodOctober∼Decemberof2012,Yamashitastu

8、diedthe“preparatorypapers”(i.e.,[HASurI],[HASur