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CRM > English > Activities > Curs 2018-2019 > INTENSIVE RESEARCH PROGRAMME LIGAT
 May 15th to July 15th, 2019​ 
General information
This intensive research programme aims to bring together top-level researchers in geometry, algebra, and topology with a part​icular focus on how these areas interact. The idea grew from the recently founded “Laboratory of Interactions between Geometry, Algebra, and Topology (LIGAT)” based at the Universitat Autònoma de Barcelona (UAB). The programme will consist of eight weeks of different activities conducted by senior research visitors and local researchers from the LIGAT. There will be an advanced course consisting of different lecture series on a variety of topics. These courses are ideal for PhD students and young researchers and participants will also have the opportunity to present their own work. The central part of the programme is a series of workshops on selected topics in geometry, algebra, and topology. The programme is completed by weekly seminars, promoting interactions and collaborations among participants and facilitating communication between the different research directions. All together, we aim to promote high level and quality research in diverse but interrelated areas of research, and to facilitate the inclusion of younger researchers in these areas.
Florent Balacheff
Universitat Autònoma de Barcelona
Carles Broto
​Universitat Autònoma de Barcelona
​John Greenlees ​University of Warwick
​Francesc Perera ​​Universitat Autònoma de Barcelona
​Invited visiting researchers


AlbertoAbbondandoloRuhr-Universität Bochum
AlejandroAdemThe University of British Columbia
IvanBabenkoUniversité de Montpellier
FlorentBalacheffUniversitat Autònoma de Barcelona
GabrieleBenedettiHeidelberg University
JeffBrockYale University
CarlesBrotoUniversitat Autònoma de Barcelona
DavidChataurUniversité de Lille
DmitriFaifmanUniversité de Montréal
FedericaFanoniInstitut de Recherche Mathématique Avancée (IRMA)
MaximeFortier BourqueUniversity of Glasgow
JoeFuUniversity of Georgia
JohnGreenleesUniversity of Warwick
JeanGuttUniversität zu Köln
RoozbehHazratWestern Sydney University
Umberto LeoneHryniewiczRWTH Aachen University
RomanKarasevMoscow Institute of Physics and Technology
RanLeviUniversity of Aberdeen
HuanhuanLiWestern Sydney University
MarcoMazzucchelliÉcole Normale Supérieure de Lyon
Jesper M.MollerUniversity of Copenhagen
AlexanderNabutovskyUniversity of Toronto
BobOliverUniversité Paris 13
EduardOrtegaNorwegian University of Science and Technology
PanagiotisPapazoglouUniversity of Oxford
HugoParlierUniversité du Luxembourg
FrancescPereraUniversitat Autònoma de Barcelona
BramPetriUniversität Bonn
ReginaRotmanUniversity of Toronto
FranzSchusterTechnische Universität Wien
AnnaSiffertMax Planck Institute for Mathematics (Bonn)
GilSolanesUniversitat Autònoma de Barcelona
JuanSoutoUniversité de Rennes
AlinaStancuConcordia University
JianchaoWuThe Pennsylvania State University


 ​Main activities of the programme

Related activities


Date: July 4th, 2019
Location: Room C1/028 (CRM)

Title: The injective Leavitt complex 
Huanhuan Li  

Abstract: For a finite graph E without sinks, we consider the corresponding finite dimensional algebra A with radical square zero. We construct an explicit compact generator for the homotopy category of acyclic complexes of injective A-modules. We call such a generator the injective Leavitt complex of E. This terminology is justified by the following result: the differential graded endomorphism algebra of the injective Leavitt complex of E is quasi-isomorphic to the Leavitt path algebra of E. Here, the Leavitt path algebra is naturally Z-graded and viewed as a differential graded algebra with trivial differential.

TitleThe talented monoid of a Leavitt path algebra
Roozbeh Hazrat

Abstract.  There is a tight relation between the geometry of a directed graph and the algebraic structure of a Leavitt path algebra associated to it. We show a similar connection between the geometry of the graph and the structure of a certain monoid associated to it. This monoid is isomorphic to the positive cone of the graded K0-group of the Leavitt path algebra which is naturally equipped with a Z-action. As an example, we show that a graph has a cycle without an exit if and only if the monoid has a periodic element. Consequently a graph has Condition (L) if and only if the group Z acts freely on the monoid. We go on to show that the algebraic structure of Leavitt path algebras (such as simplicity, purely infinite simplicity, or the lattice of ideals) can be described completely via this monoid. Therefore an isomorphism between the monoids (or graded K0’s) of two Leavitt path algebras implies that the algebras have similar algebraic structures. These all confirm that the graded Grothendieck group could be a sought-after complete invariant for the classification of Leavitt path algebras.

This is joint work with Huanhuan Li. 

  1200px-University_of_Luxembourg_logo_(fr).svg.png                 logo_cempi.png           
​ Further information
For inquiries about the programme please contact the research programme's coordinator Ms. Núria Hernandez at​