Status | Confirmed |
Seminar Series | SEM-DARBOUX |
Subjects | math.AG |
Date | Thursday 26 September 2019 |
Time | 11:00 |
Institute | LPTHE |
Seminar Room | bibliothèque du LPTHE, tour 13-14, 4eme étage |
Speaker's Last Name | Eynard |
Speaker's First Name | Bertrand |
Speaker's Email Address | eynard [at] ihes [dot] fr |
Speaker's Institution | IPHT Saclay, IHES Bures sur Yvette, CRM Montreal |
Title | Topological recursion: from spectral curve to conformal blocks |
Abstract | Topological recursion, takes as inpout data a "spectral curve" S (ex: an algebraic equation P(x,y)=0 with P a polynomial, but can be more general), and associates to it an infinite sequence of differential n-forms W_{g,n}(S), called the invariants of the spectral curve. The scalar invariants n=0 are often denoted F_g(S)=W_{g,0}(S). Many invariants of enumerative geometry are special cases of these, like Gromov-Witten invariants, Hurwitz numbers,... The formal series of scalar invariants is formally like a Tau-function $\Tau(S)=exp{\sum_g F_g(S)}$, and has OPE and Ward indentities that enables to interpret them as heavy limit asymptotic expansion of conformal blocks in a 2dCFT on a surface. We shall make a short presentation of the topological recursion, and its application to Mirzakhani's recursion, and to Liouville 2dCFT. |
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