Events for 02/19/2024 from all calendars

Geometry Seminar

Time: 3:00PM - 3:50PM

Location: BLOC 302

Speaker: Frank Sottile, Texas A&M University

Title: Welschinger signs and the Wronski map

Abstract: 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 RP^2 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.