3:45PM: STABILITY OF BETTI NUMBERS UNDER SOME REDUCTION PROCESSES WITH APPLICATION TO CHORDALITY OF CLUTTERSMina BigdeliOne of the most challenging problems in combinatorial commutative algebra is to give a characterization of the square free monomial ideals with linear resolution independent of the characteristic of the base field. Thanks to Fröberg, the problem is solved for quadratic ideals. In trying to generalize the result of Fröberg, in this talk, we first introduce a reduction process on a duniform clutter C under which the nonlinear Betti numbers of the ideal associated to the complement of C do not change. Motivated by this result, we define a class of duniform clutters, called chordal, with the property that the ideal I(C) has a dlinear resolution over any field, if C is the complement of an element in this class. We also introduce a class of duniform clutters whose associated ideals have linear quotients. Finally, we state some open problems regarding these two classes.

5:00PM: Tor as a module over an exterior algebraDavid EisenbudLet S is a regular local ring with residue field k, let f = f1..fc in S be a regular sequence, set R = S/(f), and suppose that M is a finitely generated Rmodule. In this setting Tor^S(M,k) is naturally a module over an exterior algebra on c generators, and Ext_R(M,k) is naturally a module over the “dual” polynomial ring on c generators. I will explain these structures and something about their relationship. This is joint work with Irena Peeva and FrankOlaf Schreyer.
