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Identification of the Givental Formula with the Spectral Curve Topological Recursion Procedure
We identify the Givental formula for the ancestor formal Gromov–Witten potential with a version of the topological recursion procedure for a collection of isolated local germs of the spectral curve.Expand
Tautological relations and the r-spin Witten conjecture
A geometric interpretation of Y.P. Lee’s algorithm leads to a much simpler proof of the fact that every tautological relation gives rise to a universal relation, and implies that in any semi-simple Gromov–Witten theory where arbitrary correlators can be expressed in genus 0 correlators using only tautology relations, the formal and the geometric Gronov– Witten potentials coincide. Expand
Pre-Lie deformation theory
In this paper, we develop the deformation theory controlled by pre-Lie algebras; the main tool is a new integration theory for pre-Lie algebras. The main field of application lies in homotopy algebraExpand
Quantum spectral curve for the Gromov-Witten theory of the complex projective line
We construct the quantum curve for the Gromov-Witten theory of the complex projective line.
Chiodo formulas for the r-th roots and topological recursion
We analyze Chiodo’s formulas for the Chern classes related to the r-th roots of the suitably twisted integer powers of the canonical class on the moduli space of curves. The intersection numbers ofExpand
Wheeled PROPs, graph complexes and the master equation
Abstract We introduce and study wheeled PROPs, an extension of the theory of PROPs which can treat traces and, in particular, solutions to the master equations which involve divergence operators. WeExpand
Chamber behavior of double Hurwitz numbers in genus 0
We study double Hurwitz numbers in genus zero counting the number of covers CP 1 → CP 1 with two branching points with a given branching behavior. By the recent result due to Goulden, Jackson andExpand
Combinatorics of loop equations for branched covers of sphere
We prove, in a purely combinatorial way, the spectral curve topological recursion for the problem of enumeration of bi-colored maps, which in a certain way generalize the notion of dessins d'enfant.Expand
On deformations of quasi-Miura transformations and the Dubrovin–Zhang bracket
Abstract In our recent paper, we proved the polynomiality of a Poisson bracket for a class of infinite-dimensional Hamiltonian systems of partial differential equations (PDEs) associated toExpand
Blobbed topological recursion: properties and applications
  • G. Borot, S. Shadrin
  • Mathematics, Physics
  • Mathematical Proceedings of the Cambridge…
  • 3 February 2015
Abstract We study the set of solutions (ωg,n ) g⩾0,n⩾1 of abstract loop equations. We prove that ω g,n is determined by its purely holomorphic part: this results in a decomposition that we callExpand