Special Lecture Series by Prof. Mulase

Lecturer: Motohico Mulase (University of California, Davis)*

Title:    The Laplace transform, mirror symmetry, and the Eynard-Orantin recursion

Date:     February 20-22, 2012, 13:30--15:30 **

Place:    Room B314-316, Building B, Graduate School of Science, Kobe University


    The series of lectures aims at serving as an introduction to
    the Eynard-Orantin 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, Gromov-Witten invariants,
    Seiberg-Witten invariants, and knot invariants (2007-2012).
    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 Eynard-Orantin recursion, which is actually a process
    of quantization.

*)  invited to Kobe University under the support of JSPS (S) No. 19104002.
**) A one-day workshop related to this lecture series,
      "Workshop on integrable systems and mirror symmetry",
    will be held on February 23, 2012.