3:45PM: Grobner bases for twisted commutative algebrasSteven SamRecent work of DraismaKuttler, Snowden, and ChurchEllenbergFarb in commutative algebra, algebraic geometry, and homological algebra, seeks to understand stability results (say, of some invariant of a sequence of algebraic objects) as the finite generation of some other algebraic object. Examples include the Deltamodules in the study of free resolutions of Segre embeddings and FImodules in the study of cohomology of configuration spaces. This finite generation often reduces to establishing the Noetherian property: subobjects of finitely generated objects are again finitely generated. I will discuss the situation of modules over twisted commutative algebras, which realize some of these topics as special cases. I will introduce a Grobner basis theory and show how it proves these Noetherian results. The talk will be mostly combinatorial and I will suggest some open problems. This is based on joint work with Andrew Snowden.

5:00PM: Smoothing of limit linear series on metrized complexes of algebraic curvesMadhusudan ManjunathThe theory of limit linear series on curves of compact type (reducible curves whose dual graph is a tree) was introduced by Eisenbud and Harris in 1986 and this theory has several applications to algebraic curves. This theory has recently been generalized to objects called ``metrized complexes of curves" by Amini and Baker. A metrized complex of curves is essentially a metric graph with algebraic curves plugged into the vertices of this metric graph. Eisenbud and Harris showed that any limit $g^1_d$ on a curve of compact type can be smoothed. We study the question of smoothing a limit $g^1_d$ on a metrized complex. We provide an effective characterization of a smoothable limit $g^1_d$ on a metrized complex and the talk will include examples demonstrating this characterization. This is ongoing work with Matthew Baker and Luo Ye.
