Related papers: Elliptic Integrable Models and Their Spectra from …

The superconformal index of a 4d gauge theory is computed by a matrix integral arising from localization of the supersymmetric path integral on S^3 x S^1 to the saddle point. As the radius of the circle goes to zero, it is natural to expect…

The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Discrete 1-matrix, 2-matrix, ``conformal'' (multicomponent) and Kontsevich models are considered in some detail, together with the…

Remarkable parallelism between the theory of integrable systems of first-order quasilinear PDE and some old results in projective and affine differential geometry of conjugate nets, Laplace equations, their Bianchi-Baecklund transformations…

We consider DPG methods with optimal test functions and broken test spaces based on ultra-weak formulations of general second order elliptic problems. Under some assumptions on the regularity of solutions of the model problem and its…

We consider a known sequence of dualities involving $4d$ ${\cal N}=1$ theories with $Spin(n)$ gauge groups and use it to construct a new sequence of models exhibiting IR symmetry enhancement. Then, motivated by the observed pattern of IR…

We describe our recent work on deformations of hyperelliptic curves by means of integrable hierarchy of hydrodynamic type (nlin.SI/0205012). We also discuss a further extension to the case of non-hyperelliptic curves.

We display a new integrable perturbation for both N=1 and N=2 superconformal minimal models. These perturbations break supersymmetry explicitly. Their existence was expected on the basis of the classification of integrable perturbations of…

One of the most fascinating and technically demanding parts of the theory of two-dimensional integrable systems constitute the models with the spectral parameter on an elliptic curve, including Landau-Lifshitz and Krichever-Novikov…

We reconsider non-degenerate second order superintegrable systems in dimension two as geometric structures on conformal surfaces. This extends a formalism developed by the authors, initially introduced for (pseudo-)Riemannian manifolds of…

A relation between the 4d superconformal index and the S^3 partition function is studied with focus on the 4d and 3d actions used in localization. In the case of vanishing Chern-Simons levels and round S^3 we explicitly show that the 3d…

The Dirichlet problem for a class of quasilinear elliptic systems of equations with small-BMO coefficients in Reifenberg-flat domain is considered. The lower order terms supposed to satisfy controlled growth conditions. It is obtained…

We classify two dimensional integrable mappings by investigating the actions on the fiber space of rational elliptic surfaces. While the QRT mappings can be restricted on each fiber, there exist several classes of integrable mappings which…

We lay out the foundations of the theory of second-order conformal superintegrable systems. Such systems are essentially Laplace equations on a manifold with an added potential: $(\Delta_n+V({\bf x}))\Psi=0$. Distinct families of…

Nonlinear elliptic Neumann problems, possibly in irregular domains and with data affected by low integrability properties, are taken into account. Existence, uniqueness and continuous dependence on the data of generalized solutions are…

The additional data necessary to univocally fix the gauge group for a given algebra are represented by the same charge lattices of mutually local Wilson and 't Hooft lines for both 4d $\mathcal{N}=4$ SYM and $\mathcal{N}=2$ elliptic models.…

We review aspects of superconformal indices in three dimension. Three dimensional superconformal indices can be exactly computed by using localization method including monopole contribution, and can be applied to provide evidences for…

In this article we review the Duistermaat-Heckman integration formula and the ensuing equivariant cohomology structure, in the finite dimensional case. In particular, we discuss the connection between equivariant cohomology and classical…

We review and give detailed description for ${\rm gl}_{NM}$ Gaudin models related to holomorphic vector bundles of rank $NM$ and degree $N$ over elliptic curve with $n$ punctures. Then we introduce their generalizations constructed by means…

We propose new 3d $\mathcal{N}=2$ Seiberg-like dualities by considering various monopole superpotential deformations on 3d $\mathcal{N}=2$ $U(N_c)$ SQCDs with fundamental and adjoint matter fields. We provide nontrivial evidence of these…

We consider D-term hybrid inflation in the framework of superconformal supergravity. In part of the parameter space, inflation continues for subcritical inflaton field value. Consequently, a new type of inflation emerges, which gives…