Blobbed topological recursion and matrix models

Series: 
Math Physics Seminar
Thursday, October 31, 2013 - 15:35
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
MPI Bonn and MIT
,  
The (blobbed) topological recursion is a recursive structure which defines, for any initial datagiven by symmetric holomorphic 1-form \phi_{0,1}(z) and 2-form \phi_{0,2}(z_1,z_2) (and symmetricn-forms \phi_{g,n} for n >=1 and g >=0), a sequence of symmetric meromorphic n-forms\omega_{g,n}(z_1,...,z_n) by a recursive formula on 2g - 2 + n.If we choose the initial data in various ways, \omega_{g,n} computes interesting quantities. A mainexample of application is that this topological recursion computes the asymptotic expansion ofhermitian matrix integrals. In this talk, matrix models with also serve as an illustration of thisgeneral structure.