Status  Confirmed 
Seminar Series  SEMDARBOUX 
Subjects  math.AG 
Date  Thursday 26 September 2019 
Time  11:00 
Institute  LPTHE 
Seminar Room  bibliothèque du LPTHE, tour 1314, 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 nforms 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 GromovWitten invariants, Hurwitz numbers,... The formal series of scalar invariants is formally like a Taufunction $\Tau(S)=exp{\sum_g F_g(S)}$, 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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