Special Lecture Series by Prof. Mulase
Lecturer: Motohico Mulase (University of California, Davis)*
Title: The Laplace transform, mirror symmetry, and the EynardOrantin recursion
Date: February 2022, 2012, 13:3015:30 **
Place: Room B314316, Building B, Graduate School of Science, Kobe University
Abstract:
The series of lectures aims at serving as an introduction to
the EynardOrantin theory. This theory, originally discovered
in random matrix theory in 2007, has been effectively applied to
many geometric enumeration problems by physicists, including
certain Hurwitz numbers, GromovWitten invariants,
SeibergWitten invariants, and knot invariants (20072012).
Yet to date only a few cases have been rigorously proved.
I will present these mathematical theories in these lectures,
based on my recent work on Hurwitz numbers and Grothendieck's
dessins d'enfants.
We will start with asking the following questions.
1) What is the mirror dual of the number of trees?
2) What is the mirror dual of the Catalan numbers?
The homological mirror symmetry is a categorial equivalence,
so it can be formulated without mentioning the underlying
spaces. Then the above questions make perfect sense. Indeed,
answers to these questions lead us to a mathematical formulation
of the EynardOrantin recursion, which is actually a process
of quantization.
*) invited to Kobe University under the support of JSPS (S) No. 19104002.
**) A oneday workshop related to this lecture series,
"Workshop on integrable systems and mirror symmetry",
will be held on February 23, 2012.
