CAPITAL REGION ALGEBRA/NUMBER THEORY SEMINAR 


Speaker:       Alexandre Tchernev, Univ. at Albany 

Time:          Wednesday, October 26, at 4:30pm       

Place:         Earth Sciences 152A, Univ. at Albany 

Title:         On the Betti numbers of multigraded modules


Abstract:

Let M be a multigraded module over a polynomial ring R.
In the case when M is cyclic (i.e. of the form  R/I for some
monomial ideal I) there are formulas due to Hochster that express
the Betti numbers of M in terms of the reduced homology of certain
simplicial complexes associated with the monomial generators of I.
No such formulas are known for general multigraded modules. In this
talk we will discuss what can be said on this question when the
module M is of what we call a "generic type". In that situation it
is possible to associate with  M  a collection of simplicial
complexes, and compute the Betti numbers of M from the reduced
homology of these complexes. This is joint work with H.
Charalambous. The talk will be accessible to graduate students.

Refreshments at 4:15pm in ES 152.