Group Actions Seminar: Li, Thomas

The next Group Actions Seminar will be on Monday 31 October at the University of
Sydney.  The schedule, titles and abstracts are below.  

-------------------------------------------------------------------------- 
12 noon-1pm, Carslaw 373

Speaker: Huanhuan Li, Western Sydney University 

Title: The projective Leavitt complex 

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

1-3pm Lunch 

3-4pm, Carslaw 373 

Speaker: Anne Thomas, University of Sydney 

Title: Commensurability classification of certain Coxeter groups and amalgams of free
groups 

Abstract: Two groups G and H are (abstractly) commensurable if they have finite index
subgroups G’ and H’ so that G’ and H’ are abstractly isomorphic.  Commensurability in
this sense is an equivalence relation on abstract groups.  We give explicit necessary
and sufficient conditions for commensurability within certain families of Coxeter groups
and amalgams of free groups.  Our methods are topological, and involve a new geometric
realisation of the Coxeter groups involved.  This is joint work with Pallavi Dani and
Emily Stark.  

-------------------------------------------------------------------------