Seminar

Frank Sottile: "Welschinger Signs and the Wronski Map (New conjectured reality)" 

A general real rational plane curve C of degree d has 3(d-2) flexes and (d-1)(d-2)/2 complex double points. Those double points lying in RP² are either nodes or solitary points. The Welschinger sign of C is (-1)^s, where s is the number of solitary points. When all flexes of C are real, its parameterization comes from a point on the Grassmannian under the Wronskii map, and every parameterized curve with those flexes is real (this is the Mukhin-Tarasov-Varchenko Theorem). Thus to C we may associate the local degree of the Wronskii map, which is also 1 or -1. My talk will discuss work with Brazelton and McKean towards a possible conjecture that that these two signs associated to C agree, and the challenges to gathering evidence for this

Liana Sega: "Relations between Poincare series for quasi-complete intersection homomorphisms"

Quasi-complete intersection (q.c.i.) homomorphisms are surjective homomorphisms of local rings for which the Koszul homology on a minimal generating set of the kernel is an exterior algebra. We study base change results for Poincare series along a q.c.i. homomorphism in situations that extend results known for complete intersection (c.i.) homomorphisms. The main new result is joint work with Josh Pollitz, and generalizes a well-known result of Shamash for c.i. homomorphisms which makes use of systems of higher homotopies. Our proof develops base change results involving Poincare series over the Koszul complex.