Brandeis-Harvard-MIT-Northeastern

JOINT MATHEMATICS COLLOQUIUM


 
Counting curves using the Fukaya category

 

Nick Sheridan

Princeton.
 

Northeastern University

Thursday, April 23, 2015


 

Talk at 4:30 p.m. in 509 Lake Hall

Tea at 4:00 p.m. in 553 Lake Hall


 
 

Abstract: In 1991, string theorists Candelas, de la Ossa, Green and Parkes made a startling prediction for the number of curves in each degree on a generic quintic threefold, in terms of periods of a holomorphic volume form on a `mirror manifold'. Givental and Lian, Liu and Yau gave a mathematical proof of this version of mirror symmetry for the quintic threefold (and many more examples) in 1996. In the meantime (1994), Kontsevich had introduced his `homological mirror symmetry' conjecture and stated that it would `unveil the mystery of mirror symmetry'. I will explain how to prove that the number of curves on the quintic threefold matches up with the periods of the mirror via homological mirror symmetry. I will also attempt to explain in what sense this is `less mysterious' than the previous proof. This is based on joint work with Sheel Ganatra and Tim Perutz.



Here are some directions to Northeastern University. Lake Hall can be best accessed from the entrance on the corner of Greenleaf Street and Leon Street.

There is free parking available for people coming to the Colloquium at Northeastern's visitor parking (Rennaisance Garage). The entrance is from Columbus Avenue. If coming by car, you should park there and take the parking talon. After the lecture, you may pick up the payment coupon from Ivan Losev.



Home Web page:  Alexandru I. Suciu   Comments to:  i.loseu@neu.edu  
Posted: February 28, 2015    URL: http://www.northeastern.edu/iloseu/bhmn/sheridan15.html