Search results for "Systèmes intégrables"
showing 3 items of 3 documents
Integrable systems and moduli spaces of curves
2016
This document has the purpose of presenting in an organic way my research on integrable systems originating from the geometry of moduli spaces of curves, with applications to Gromov-Witten theory and mirror symmetry. The text contains a short introduction to the main ideas and prerequisites of the subject from geometry and mathematical physics, followed by a synthetic review of some of my papers (listed below) starting from my PhD thesis (October 2008), and with some open questions and future developements. My results include: • the triple mirror symmetry among P 1-orbifolds with positive Euler characteristic , the Landau-Ginzburg model with superpotential −xyz + x p + y q + z r with 1 p + …
Instanton Counting, Quantum Geometry and Algebra
2020
The aim of this memoir for "Habilitation \`a Diriger des Recherches" is to present quantum geometric and algebraic aspects of supersymmetric gauge theory, which emerge from non-perturbative nature of the vacuum structure induced by instantons. We start with a brief summary of the equivariant localization of the instanton moduli space, and show how to obtain the instanton partition function and its generalization to quiver gauge theory and supergroup gauge theory in three ways: the equivariant index formula, the contour integral formula, and the combinatorial formula. We then explore the geometric description of $\mathcal{N} = 2$ gauge theory based on Seiberg-Witten geometry together with it…
Asymptotic analysis of the form-factors of the quantum spin chains
2020
Since a long-time, the quantum integrable systems have remained an area where modern mathematical methods have given an access to interesting results in the study of physical systems. The exact computations, both numerical and asymptotic, of the correlation function is one of the most important subject of the theory of the quantum integrable models. In this context an approach based on the calculation of form factors has been proved to be a more effective one. In this thesis, we develop a new method based on the algebraic Bethe ansatz is proposed for the computation of the form-factors in thermodynamic limit. It is applied to and described in the context of isotropic XXX Heisenberg chain, w…