Webs and Maximally Inflected Curves ?

This  poster will  present a  surprising and  conjectural connection
between  maximally   inflected  plane  curves  of   degree  d+2  and
sl_3-webs.  Under a natural identification of each with 3xd standard
tableaux,  the web  appears to  encode  the topology  of the  curve,
including its  Welschinger invariant.   This behavior  persists when
the  flexes  (ramification points)  collide,  and  the webs  acquire
ramification data (a refinement of 'collapsed' webs).

While  this   relation  is  somewhat  conjectural,   it  would  have
remarkable  consequences in  real  algebraic  geometry and  enriched
enumerative geometry.   This represents  joint work  with Brazelton,
Karp, Levinson, and McKean.