Speaker: Lars Winther Christensen (Texas Tech University)
Title: Quotients of the polynomial algebra in three variables.
Abstract: Let K be a field, for example that of complex numbers, and let R be a
quotient of the polynomial algebra Q = K[x,y,z]. The minimal free
resolution of R as a module over Q is a sequence of linear maps
between free modules. One may think of such free resolutions as the result of a
linearization process that unwinds the structure of R in a series of
maps. This point of view, which goes back to Hilbert, already yields a
wealth of information about R, but there is more to the picture: The
resolution $F$ carries a multiplicative structure; it is itself a
ring! For algebraists this is Gefundenes Fressen, and in the
talk I will discuss what kind of questions this structure has helped
answer and what new questions it raises.