Symplectic aspects of the tt*-Toda equations

  title={Symplectic aspects of the tt*-Toda equations},
  author={Ryosuke Odoi},
  journal={Journal of Physics A: Mathematical and Theoretical},
  • Ryosuke Odoi
  • Published 30 November 2021
  • Mathematics
  • Journal of Physics A: Mathematical and Theoretical
We evaluate explicitly, in terms of the asymptotic data, the ratio of the constant pre-factors in the large and small x asymptotics of the tau functions for global solutions of the tt*-Toda equations. This constant problem for the sinh–Gordon equation, which is the case n = 1 of the tt*-Toda equations, was solved by Tracy (1991 Commun. Math. Phys. 142 297–311). We also introduce natural symplectic structures on the space of asymptotic data and on the space of monodromy data for a wider class of… 


Connection Problem for the Tau-Function of the Sine-Gordon Reduction of Painlevé-III Equation via the Riemann-Hilbert Approach
We evaluate explicitly, in terms of the Cauchy data, the constant pre-factor in the large $x$ asymptotics of the Painleve III tau-function. Our result proves the conjectural formula for this
Asymptotics of a Class of Solutions to the Cylindrical Toda Equations
t asymptotics of a class of solutions to the 2D cylindrical Toda equations is computed. The solutions, , have the representation where Kk$ are integral operators. This class includes the n-periodic
Isomonodromy Aspects of the tt* Equations of Cecotti and Vafa II: Riemann–Hilbert Problem
In Guest et al. (arXiv:1209.2045) (part I) we computed the Stokes data for the smooth solutions of the tt*-Toda equations whose existence we had previously established by p.d.e. methods. Here we
Topological-antitopological fusion and the quantum cohomology of Grassmannians
  • M. Guest
  • Physics, Mathematics
    Japanese Journal of Mathematics
  • 2021
We suggest an explanation for the part of the Satake Correspondence which relates the quantum cohomology of complex Grassmannians and the quantum cohomology of complex projective space, as well as
Quasi-Hamiltonian geometry of meromorphic connections
For each connected complex reductive group G, we find a family of new examples of complex quasi-Hamiltonian G-spaces with G-valued moment maps. These spaces arise naturally as moduli spaces of
Connection Problem for the Sine-Gordon/Painlevé III Tau Function and Irregular Conformal Blocks
The short-distance expansion of the tau function of the radial sine-Gordon/Painlev\'e III equation is given by a convergent series which involves irregular $c=1$ conformal blocks and possesses
Harmonic Bundles and Toda Lattices With Opposite Sign II
We study the integrable variation of twistor structure associated to any solution of the Toda lattice with opposite sign. In particular, we give a criterion when it has an integral structure. It
Topological-anti-topological fusion
Gauge theory and symplectic geometry
Preface. Participants. Contributors. Lectures on Gauge Theory and Integrable Systems M. Audin. Symplectic Geometry of Plurisubharmonic Functions Y. Eliashberg. Frobenius Manifolds N. Hitchin. Moduli