Browsing by Author "Guest, Martin A."

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    Isomonodromy Aspects of the tt* Equations of Cecotti and Vafa I. Stokes Data
    (Oxford, 2015-02) Guest, Martin A.; Its, Alexander R.; Lin, Chang-Shou; Department of Mathematical Sciences, School of Science
    We describe all smooth solutions of the two-function tt*-Toda equations (a version of the tt* equations or equations for harmonic maps into SLnR/SOn SLnR/SOn ) in terms of (1) asymptotic data, (2) holomorphic data, and (3) monodromy data, and we compute all of this data explicitly. This allows us, in particular, to find all solutions with integral Stokes data. These include solutions associated to non-linear sigma models (quantum cohomology) or Landau–Ginzburg models (unfoldings of singularities), as conjectured by Cecotti and Vafa in the 1990s.
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    Isomonodromy Aspects of the tt* Equations of Cecotti and Vafa III: Iwasawa Factorization and Asymptotics
    (Springer, 2020-03) Guest, Martin A.; Its, Alexander R.; Lin, Chang-Shou; Mathematical Sciences, School of Science
    This paper, the third in a series, completes our description of all (radial) solutions on C∗ of the tt*-Toda equations 2(wi)tt¯=−e2(wi+1−wi)+e2(wi−wi−1), using a combination of methods from p.d.e., isomonodromic deformations (Riemann–Hilbert method), and loop groups. We place these global solutions into the broader context of solutions which are smooth near 0. For such solutions, we compute explicitly the Stokes data and connection matrix of the associated meromorphic system, in the resonant cases as well as the non-resonant case. This allows us to give a complete picture of the monodromy data, holomorphic data, and asymptotic data of the global solutions.