MATRIX Book Series 1 David R. Wood Editor-in-chief Jan de Gier · Cheryl E. Praeger Terence Tao Editors 2016 MATRIX Annals MATRIX Book Series 1 Editors DavidR.Wood(Editor-in-Chief) JandeGier CherylE.Praeger TerenceTao MATRIXisAustralia’sinternationalandresidentialmathematicalresearchinstitute. It facilitates new collaborations and mathematical advances through intensive residentialresearchprograms,eachlasting1–4weeks. Moreinformationaboutthisseriesathttp://www.springer.com/series/15890 David R. Wood Editor-in-Chief Jan de Gier(cid:129)Cheryl E. Praeger(cid:129)Terence Tao Editors 2016 MATRIX Annals 123 Editors DavidR.Wood(Editor-in-Chief) JandeGier MonashUniversity UniversityofMelbourne Clayton,Australia Melbourne,Australia CherylE.Praeger TerenceTao UniversityofWesternAustralia UCLA Crawley,Australia LosAngeles,USA ISSN2523-3041 ISSN2523-305X (electronic) MATRIXBookSeries ISBN978-3-319-72298-6 ISBN978-3-319-72299-3 (eBook) https://doi.org/10.1007/978-3-319-72299-3 LibraryofCongressControlNumber:2018930336 Mathematics Subject Classification (2010): 51-XX, 81-XX, 58-XX, 20-XX, 22-XX, 05-XX, 19-XX, 37-XX,41-XX,49-XX ©SpringerInternationalPublishingAG,partofSpringerNature2018 Chapter‘ThesmoothHom-stackofanorbifold’ispublishedwithkindpermissionof©DavidMichael RobertsandRaymondVozzo2018.AllRightsReserved. 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 Preface MATRIX is Australia’s first international and residential mathematical research institute. It was established in 2015 and launched in 2016 as a joint partnership between Monash University and the University of Melbourne, with seed funding from the ARC Centre of Excellence for Mathematical and Statistical Frontiers. The purpose of MATRIX is to facilitate new collaborations and mathematical advancesthroughintensiveresidentialresearchprograms,whicharecurrentlyheld inCreswick,a smalltownnestledinthe beautifulforestsoftheMacedonRanges, 130kmwestofMelbourne. Thisbook,2016MATRIXAnnals,isascientificrecordofthefiveprogramsheld atMATRIXin2016: (cid:129) HigherStructuresinGeometryandPhysics (cid:129) WinterofDisconnectedness (cid:129) ApproximationandOptimisation (cid:129) RefiningC*-AlgebraicInvariantsforDynamicsUsingKK-Theory (cid:129) Interactions Between Topological Recursion, Modularity, Quantum Invariants andLow-DimensionalTopology TheMATRIXScientificCommitteeselectedtheseprogramsbasedonscientific excellenceandtheparticipationrateofhigh-profileinternationalparticipants.This committee consists of Jan de Gier (Melbourne University, Chair), Ben Andrews (AustralianNationalUniversity),DarrenCrowdy(ImperialCollegeLondon),Hans De Sterck (Monash University), Alison Etheridge (University of Oxford), Gary Froyland(UniversityofNewSouthWales),LizaLevina(UniversityofMichigan), Kerrie Mengersen(QueenslandUniversityof Technology),Arun Ram (University of Melbourne), Joshua Ross (University of Adelaide), Terence Tao (University of California,LosAngeles),OleWarnaar(UniversityofQueensland),andDavidWood (MonashUniversity). The selected programs involved organisers from a variety of Australian uni- versities, including Federation, Melbourne, Monash, Newcastle, RMIT, Sydney, Swinburne, and Wollongong,along with internationalorganisersand participants. Eachprogramlasted1–4weeksandincludedampleunstructuredtimetoencourage v vi Preface collaborativeresearch.Someofthe longerprogramshadan embeddedconference orlectureseries.AllparticipantswereencouragedtosubmitarticlestotheMATRIX Annals. The articles were grouped into refereed contributions and other contributions. Refereed articles contain original results or reviews on a topic related to the MATRIX program. The other contributions are typically lecture notes based on talksoractivitiesatMATRIX.Aguesteditororganisedappropriaterefereeingand ensuredthescientificqualityofsubmittedarticlesarisingfromeachprogram.The editors(JandeGier,CherylE.Praeger,TerenceTao,andmyself)finallyevaluated andapprovedthepapers. Manythankstotheauthorsandtotheguesteditorsfortheirwonderfulwork. MATRIX has hosted eight programs in 2017, with more to come in 2018; see www.matrix-inst.org.au.Ourgoalistofacilitatecollaborationbetweenresearchers in universities and industry, and increase the international impact of Australian researchinthemathematicalsciences. DavidR.Wood MATRIXBookSeriesEditor-in-Chief Higher Structures in Geometry and Physics 6–17June2016 Organisers MarcyRobertson(Melbourne) PhilipHackney(Macquarie) The inaugural program at MATRIX took place on June 6–17, 2016, and was entitled“HigherStructuresinGeometryandPhysics”.Itwasbothapleasureanda privilegetotakepartinthisfirsteverprogramatMATRIX.Theexcellentworking conditions, cosy environment, friendly staff and energetic participants made this timebothmemorableandproductive. The scientific component of our program was comprised of a workshop with lecture series by several invited speakers, followed in the subsequent week by a conferencefeaturingtalksonarangeofrelatedtopicsfromspeakersfromaroundthe globe.Thetwoeventswereseparatedbyalongweekendwhichgavetheparticipants free time to discuss and collaborate. Within this volume is a collection of lecture notes and articles reflecting quite faithfully the ideas in the air during these two weeks. Our title HigherStructures(notunlikethe termdownunder)suggestsa certain fixed perspective. For the participants in our program, this perspective comes from the twentieth-century examples of algebraic and categorical constructions associated to topological spaces, possibly with geometric structures and possibly taking motivation from physicalexamples. From this common frame of reference stems a range of new and rapidly developing directions, activities such as this vii viii HigherStructuresinGeometryandPhysics program at MATRIX play a vital role in weaving these threads into a collective understanding.Theexcitementofworkinginthisrapidlydevelopingfieldwasfelt duringourtimeatMATRIX,andIhopeitcomesacrossinthisvolumeaswell. I would like to thank all of the authorswho took the time to contribute to this volume.I wouldalsoliketothanktheMATRIXstaffandofficialsforhostingand facilitating this event and giving us the opportunity to share our work with this volume. Most importantly, I would like to thank the organizers of our program Marcy and Philip for all of their hard work and for giving all of us participants thisuniqueopportunity. BenWard GuestEditor Participants Ramon Abud Alcala (Macquarie), Clark Barwick (Massachusetts Institute of Technology), Alexander Campbell (Macquarie), David Carchedi (George Mason), Gabriel C. Drummond-Cole (IBS Center for Geometry and Physics), Daniela Egas Santander (Freie Universitat Berlin), Nora Ganter (Melbourne), ChristianHaesemeyer(Melbourne),PhilipHackney(Osnabrueck),RalphKauffman (Purdue), Edoardo Lanari (Macquarie), Martin Markl (Czech Academy of Sciences), Branko Nikolic (Macquarie), Simona Paoli (Leicester), Sophia Raynor (Aberdeen), Emily Riehl (Johns Hopkins), David Roberts (Adelaide), Marcy Robertson (Melbourne), Chris Rogers (Louisiana), Martina Rovelli (EPFL), HigherStructuresinGeometryandPhysics ix Matthew Spong (Melbourne), Michelle Strumila (Melbourne), TriThang Tran (Melbourne),VictorTurchin(KansasState),DominicVerity(Macquarie),Raymond Vozzo (Adelaide), Ben Ward (Stony Brook), Mark Weber (Macquarie), Felix Wierstra (Stockholm), Sinan Yalin (Copenhagen), Jun Yoshida (Tokyo), Dimitri Zaganidis(EPFL)