- Series
- Algebra Seminar
- Time
- Monday, March 25, 2024 - 1:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Frank Sottile – Texas A&M University
- Organizer
- Changxin Ding
Please Note: There will be a pre-seminar (aimed toward grad students and postdocs) from 11:00 am to 11:30 am in Skiles 005.
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 these two signs associated to C agree, and the challenges to gathering evidence for this.