The  Weizmann  Institute  of  Science
                  Faculty of Mathematics and Computer Science
 
              Algebraic Geometry and Representation Theory Seminar
 
                                Anton Khoroshkin
                                     E.T.H.
 
                                 will speak on
 
                           Free monomial resolutions
 
                    Seminar Room, Room 261, Ziskind Building
                          on Thursday, March 25, 2010
                                 13:00 - 14:15
 
                             Note unusual day/time
 
Abstract:
The main goal of the talk consists of the combinatorial construction of the
free resolutions for the algebraic objects that are defined in terms of
generators and relations.
 For the case of associative algebras this resolution is due to Anick and looks
as follows:  you start from the algebra $A$, first one should find the algebra
$\hat{A}$ of the same size but with monomial relations (this can be done using
the theory of  Grobner bases), second one constructs the free resolution of
$\hat{A}$ using the combinatorics of words. Now to get the resolution of $A$ it
is enough to deform the differential in the latter monomial resolution of
$\hat{A}$.  I will show what can and what can not be done in more general case
like operads.  As a conclusion I will show how one can compute the homology of
the operad of Batalin-Vilkoviski algebras.
 
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Technion Math Net-2 (TECHMATH2)
Editor: Gershon Wolansky <techm@math.technion.ac.il>
Announcement from: Diana Mandelik <diana.mandelik@weizmann.ac.il>