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Chairs:TorstenEkedahl&Jan-ErikRoos
12:30 Registration
13:00-13:05 Openingaddress Prof Staffan Normark, PermanentSecretaryoftheRoyalSwedishAcademyofSciences
13:05-13:50 Thegeneralbackgroundandhistoryoftheclassificationoffinitesimplegroups
Prof John Griggs Thompson, UniversityofCambridge,UK
13:55-14:40 Applyingtheclassificationinotherareasofmathematics
TheRolfSchockPrizeLaureateinMathe-maticsProf Michael Aschbacher,CaliforniaInstituteofTechnology,CA,USA
14:40-15:15 Refreshments
15:15-16:00 MichaelAschbacher’sworkandtheClassificationofFiniteSimpleGroups(CFSG)
Prof Stephen Smith, UniversityofIllinoisatChicago,IL,USA
16:05-16:50 Aglimpseintothefuture Prof Ronald Solomon, TheOhioStateUni-versity,OH,USA
16:50 Endofthesymposium
3Nov Mathematics
TheClassificationoffinitesimplegroupsSymposiuminthehonouroftheRolfSchockPrizeLaureateinMathematicsProfMichaelAschbacher.TheBeijerHall,theRoyalSwedishAcademyofSciences,LillaFrescativägen4A,Stockholm.Opentothepublic.Registration is required and must be made before 25 October 2011 at http://kva.se/events.
THEROLFSCHOCKPRIZEISAWARDEDBYTHEROYALSWEDISHACADEMIESOFFINEARTS,MUSICANDSCIENCES
COMPLETEPROGRAMMEFORTHEROLFSCHOCKPRIZE2011EVENTS,AVAILABLEATHTTP://ROLFSCHOCKPRIZES.SE/ANDHTTP://KVA.SE
ROLFSCHOCKPRIZE2011
Registeredparticipantsareinvitedtoparticipateinaninformalmingleafterthesymposium
3Nov MathematicsTheClassificationoffinitesimplegroups;symposiuminthehonouroftheRolfSchockPrizeLaureateinMathematicsProfMichaelAschbacher.Registration is required and must be made before 25 October 2011 at http://kva.se/events.
The general background and history of the classification of finite simple groups ProfJohnGriggsThompsonUniversityofCambridge,UK
Applying the classification in other areas of mathematicsTheRolfSchockPrizeLaureateinMathematicsProfMichaelAschbacherCaliforniaInstituteofTechnology,CA,USATherearemanyapplicationsoftheclassificationofthefinitesimplegroupsinmanyareasofmathematics.I’llbrieflymentionafewexamples,butmostofthetimewillbespentgivingsomeideaofhowaproblemonfinitegroupscanbereducedtothesimplecase,andwhatinformationaboutsimplegroupsisthenneededtocompletethesolution.
Michael Aschbacher’s work and the Classification of Finite Simple Groups (CFSG)ProfStephenSmithUniversityofIllinoisatChicago,IL,USAAnattemptismadetosurveyhowtheclassificationwasfinished.Amoredetailedabstractisgivenontheenclosedsheetofpaper.
A glimpse into the future ProfRonSolomonTheOhioStateUniversity,OH,USATheclassificationofthefinitesimplegroupsleavesopenmanyfascinatingquestionsconcerningfinitegroups,andpointstowardnumerousdirectionsforfutureinvestiga-tion.Iwillhighlightsomequestionsinthemodularrepresentationtheoryofgroups,notablytheWeightConjectureofAlperin,whichinturnfocusinterestonthecategoryofsaturatedfusionsystems,establishinganewinterfacebetweengrouptheoryandtopology,whichisactivelybeingexploredbyAschbacher,Chermak,Oliver,andothers.
THEROLFSCHOCKPRIZEISAWARDEDBYTHEROYALSWEDISHACADEMIESOFFINEARTS,MUSICANDSCIENCES
COMPLETEPROGRAMMEFORTHEROLFSCHOCKPRIZE2011EVENTS,AVAILABLEATHTTP://ROLFSCHOCKPRIZES.SE/ANDHTTP://KVA.SE
ROLFSCHOCKPRIZE2011
3Nov MathematicsAbstractProfStephenSmithUniversityofIllinoisatChicago,IL,USA
Michael Aschbacher’s work and the Classification of Finite Simple Groups (CFSG)Since“most”finitesimplegroupsGareinfactmatrixgroupsoverfinitefields,anearlyresultdeterminingtheoverallshapeoftheCFSGwastheDichotomyTheorem---whichshowsthatanabstractsimpleG(awayfromcaseswith2-subgroupsofrankatmost2)iseither:ofCOMPO-NENTTYPE(resemblingagroupoverafieldofoddorder),orofCHARACTERISTIC2-TYPE(resem-blingagroupincharacteristic2).
Thetreatmentofthe“oddcase”,namelycomponenttype,wasbasedonAschbacher’snotionofaquasisimplecomponentLofSTANDARDFORM,inthecentralizerinGofanelementtoforder2.ThevariouspossibleLweretreatedbyAschbacherandvariousotherresearchers.
Thetreatmentoftheremaining“evencase”,namelycharacteristic2-type,wasobtainedviasuit-ableanalogiesoftheabovecasedivisions---butreplacingtbyanelementofODDprimeorderp.
Heretheinitial“small”casecorrespondstoQUASITHINgroupsG;namelywheretherankofsuit-ablep-subgroupsisatmost2.
Thissituationinvolvesmanycomplications;itwaseventuallytreatedinalengthyworkofAsch-bacherandSmith.
Fortheremainingcasesinvolvingp-subgroupsofrankatleast3,theaboveDichotomyisre-placedbyaTrichotomy---establishedbyGorensteinandLyons(withcontributionsfromAsch-bacher).
Thethreebrancheswhichemergeare:
a(p-component)branchcalledStandardType;
a(roughlycharacteristicp-type)branchleadingto“GF(2)type”;andafurther“disconnected”branchcalledtheUniquenessCase.
ThegroupsofstandardtypeweredeterminedbyGilmanandGriess.
ThegroupsofGF(2)typeweredeterminedbyvariousauthors,includingAschbacher,Timmesfeld,andSmith.
AndthefinalcontradictionintheCFSG(althoughquasithingroupswerechronologicallythelasttobetreated)wasestablishedbyAschbacher,whoshowedthatnogroupcanactuallysatisfytheUniquenessCase.
(ThisoutlineoftheClassificationofFiniteSimpleGroupsisfurtherdevelopedinarecentbookofAschbacher,Lyons,Smith,andSolomon---SurveysoftheAMSvol.172.)
THEROLFSCHOCKPRIZEISAWARDEDBYTHEROYALSWEDISHACADEMIESOFFINEARTS,MUSICANDSCIENCES
ROLFSCHOCKPRIZE2011