May 15^{th} to July 15^{th}, 2019
General information
Description
This intensive research programme aims to bring together toplevel researchers in geometry, algebra, and topology with a particular 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
Alberto   Abbondandolo   RuhrUniversität Bochum      Alejandro   Adem   The University of British Columbia      Ivan   Babenko   Université de Montpellier      Florent   Balacheff   Universitat Autònoma de Barcelona      Gabriele   Benedetti   Heidelberg University      Jeff   Brock   Yale University      Carles   Broto   Universitat Autònoma de Barcelona      David   Chataur   Université de Picardie Jules Verne      Dmitri   Faifman   Université de Montréal      Federica   Fanoni   Institut de Recherche Mathématique Avancée (IRMA)      Maxime   Fortier Bourque   University of Glasgow      Joe   Fu   University of Georgia      John   Greenlees   University of Warwick      Jean   Gutt   Universität zu Köln      Roozbeh   Hazrat   Western Sydney University      Umberto Leone   Hryniewicz   RWTH Aachen University      Roman   Karasev   Moscow Institute of Physics and Technology      Ran   Levi   University of Aberdeen      Huanhuan   Li   Western Sydney University      Marco   Mazzucchelli   École Normale Supérieure de Lyon      Jesper M.   Moller   University of Copenhagen      Alexander   Nabutovsky   University of Toronto      Bob   Oliver   Université Paris 13      Eduard   Ortega   Norwegian University of Science and Technology      Panagiotis   Papazoglou   University of Oxford      Hugo   Parlier   Université du Luxembourg      Francesc   Perera   Universitat Autònoma de Barcelona      Bram   Petri   Universität Bonn      Regina   Rotman   University of Toronto      Franz   Schuster   Technische Universität Wien      Anna   Siffert   Max Planck Institute for Mathematics (Bonn)      Gil   Solanes   Universitat Autònoma de Barcelona      Juan   Souto   Université de Rennes      Alina   Stancu   Concordia University      Jianchao   Wu   The Pennsylvania State University     


Main activities of the programme
Seminar
Date: July 4th, 2019
Location: Room C1/028 (CRM)
11:0012:50
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 Amodules. 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
quasiisomorphic to the Leavitt path algebra of E. Here, the
Leavitt path algebra is naturally Zgraded and viewed as a
differential graded algebra with trivial differential.
12:0512:55
Title: The 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 K0group of the Leavitt path algebra which is
naturally equipped with a Zaction. 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 soughtafter complete invariant for the classification
of Leavitt path algebras.
This is joint work with Huanhuan Li.
Acknowledgements
For inquiries about the programme please contact the research programme's coordinator Ms. Núria Hernandez at
nhernandez@crm.cat