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Identification of the Givental Formula with the Spectral Curve Topological Recursion Procedure

- P. Dunin-Barkowski, N. Orantin, S. Shadrin, L. Spitz
- Mathematics, Physics
- 16 November 2012

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

- C. Faber, S. Shadrin, D. Zvonkine
- Mathematics, Medicine
- 18 December 2006

TLDR

Pre-Lie deformation theory

- V. Dotsenko, S. Shadrin, B. Vallette
- Mathematics
- 11 February 2015

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 algebra… Expand

Quantum spectral curve for the Gromov-Witten theory of the complex projective line

- P. Dunin-Barkowski, M. Mulase, P. Norbury, A. Popolitov, S. Shadrin
- Physics, Mathematics
- 18 December 2013

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

- D. Lewa'nski, A. Popolitov, S. Shadrin, D. Zvonkine
- Physics, Mathematics
- 28 April 2015

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 of… Expand

Wheeled PROPs, graph complexes and the master equation

- M. Markl, S. Merkulov, S. Shadrin
- Mathematics
- 23 October 2006

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. We… Expand

Chamber behavior of double Hurwitz numbers in genus 0

- S. Shadrin, M. Shapiro, A. Vainshtein
- Mathematics
- 15 January 2008

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 and… Expand

Combinatorics of loop equations for branched covers of sphere

- P. Dunin-Barkowski, N. Orantin, A. Popolitov, S. Shadrin
- Physics, Mathematics
- 4 December 2014

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

- A. Buryak, H. Posthuma, S. Shadrin
- Mathematics, Physics
- 14 April 2011

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 to… Expand

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 call… Expand

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