Colloquium
Speaker: Frank Sottile (Texas A&M University)
"Webs and Welschinger signs"
Time: 15:30 - 15:30
Room: MC 107
A 3-dimensional subspace f of real polynomials defines a map f : P^1 -> P^2
whose image is a rational plane curve. It is maximally inflected when all
of its flexes are real, equivalently, when its Wronski determinant has only
real roots. We associate two a priori distinct signs (\pm 1) to f: the
Welschinger invariant of the rational curve and the degree of the Wronski
map at f. Extensive computation suggests that these signs coincide. While
studying this conjecture we were led to a deeper conjecture: From f, we
define a a function W : CP^1 -> CP^1 which encodes some real geometry of f
and conjecturally gives an object called a web. We conjecture that known
bijections between webs and standard Young tableaux and between tableaux and
maximally inflected curves recovers the curve.
This talk will explain this picture with compelling evidence and beautiful
pictures. It is joint work with Brazelton, Karp, Le, Levinson, McKean,
Peltola, and Speyer.