Search results for "Cycles de ramification double"

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Integrable systems, Frobenius manifolds and cohomological field theories

2022

In this dissertation, we study the underlying geometry of integrable systems, in particular tausymmetric bi-Hamiltonian hierarchies of evolutionary PDEs and differential-difference equations.First, we explore the close connection between the realms of integrable systems and algebraic geometry by giving a new proof of the Witten conjecture, which constructs the string taufunction of the Korteweg-de Vries hierarchy via intersection theory of the moduli spaces of stable curves with marked points. This novel proof is based on the geometry of double ramification cycles, tautological classes whose behavior under pullbacks of the forgetful and gluing maps facilitate the computation of intersection…

Cohomological field theorySystème intégrableHiérarchie de Dubrovin et Zhang[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Espace de modules de courbes stablesDouble ramification cyclesThéorie cohomologique des champsNonlinear Sciences::Exactly Solvable and Integrable SystemsIntegrable systemsModuli space of stable curvesDubrovin-Zhang hierarchyFrobenius manifoldsCycles de ramification doubleMathematics::Symplectic GeometryVariété de Frobenius
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