Date: 13 October 2017, 4:30pm
Location: Hempfield High School, Room 213
 Speaker: Samantha Pezzimenti, Bryn Mawr College
   Title: Fillings of Legendrian Knots: Obstructions and Constructions

Abstract. A classic question in knot theory is: Given a smooth
knot in the 3-sphere, what surfaces in the 4-ball can it bound?  A
version of this question can also be asked about Legendrian knots, which
are knots that satisfy an additional geometric condition imposed by a
contact structure.  Now the natural question is: Given a Legendrian
knot, what Lagrangian surfaces can it bound?  Whereas a smooth
knot always can be filled by an infinite number of topologically
distinct surfaces, a polynomial associated to the Legendrian knot
determines the genus of any embedded Lagrangian filling (or determines
that there is no Lagrangian filling!).  Although embedded fillings might
not exist, it is known that there will always be immersed
Lagrangian fillings. I will describe how this polynomial gives
information about the minimal number of double points in any immersed
Lagrangian filling. I will also cover some constructive arguments about
when these "minimal" immersed fillings can be realized.