Related papers: Analyticity of Nekrasov Partition Functions

Convergence analysis of Nesterov's accelerated gradient method has attracted significant attention over the past decades. While extensive work has explored its theoretical properties and elucidated the intuition behind its acceleration, a…

We consider partial sum rules for the homogeneous limit of the solution of the q-deformed Knizhnik--Zamolodchikov equation with reflecting boundaries in the Dyck path representation. We show that these partial sums arise in a solution of…

In this work, we compute the $0$th cohomology group of a complex of groups of cobordism-framed correspondences, and prove the isomorphism to Milnor $K$-groups. An analogous result for common framed correspondences has been proved by A.…

We analyze the convergence rate of a family of inertial algorithms, which can be obtained by discretization of an inertial system with Hessian-driven damping. We recover a convergence rate, up to a factor of 2 speedup upon Nesterov's…

We consider the partition function of beta-gamma systems in curved space of the type discussed by Nekrasov and Witten. We show how the Koszul resolution theorem can be applied to the computation of the partition functions and to characters…

An analytico-geometric reflection principle is established by means of normal deformations of analytic discs.

M-theoretic construction of N=2 gauge theories implies that the instanton partition function is expressed as the scalar product of coherent states (Whittaker states) in the Verma module of an appropriate two dimensional conformal field…

Isoradial dimer models were introduced in \cite{Kenyon3} - they consist of dimer models whose underlying graph satisfies a simple geometric condition, and whose weight function is chosen accordingly. In this paper, we prove a conjecture of…

The main goal of this work is to perform a nonolonomic deformation (Fedosov type) quantization of fractional Lagrange geometries. The constructions are provided for a (fractional) almost Kahler model encoding equivalently all data for…

A conjectural formula for the $k$-point generating function of Gromov--Witten invariants of the Riemann sphere for all genera and all degrees was proposed in \cite{DY2}. In this paper, we give a proof of this formula together with an…

The Dirac-Coulomb equation with positive-energy projection is solved using explicitly correlated Gaussian functions. The algorithm and computational procedure aims for a parts-per-billion convergence of the energy to provide a starting…

We use the exact instanton expansion to illustrate various string characteristics of noncommutative gauge theory in two dimensions. We analyse the spectrum of the model and present some evidence in favour of Hagedorn and fractal behaviours.…

Analytical solutions of the Klein-Gordon equation are obtained by reducing the radial part of the wave equation to a standard form of a second order differential equation. Differential equations of this standard form are solvable in terms…

This paper is intended to serve as a review of a series of papers with Nikita Nekrasov, where we achieved several important results concerning the relation between the moduli space of instantons and classical integrable systems. We derive…

We consider the AGT relation, expressing conformal blocks for the Virasoro and W-algebras in terms of Nekrasov's special functions, in the simplest case of the 4-point functions for the first non-trivial W_3 algebra. The standard set of…

Given an anisotropic integrand $F:\text{Gr}_k(\mathbb R^n)\to(0,\infty)$, we can generalize the classical isotropic area by looking at the functional $$\mathcal{F}(\Sigma^k):=\int_\Sigma F(T_x\Sigma)\,d\mathcal{H}^k.$$ While a monotonicity…

We study the kinetic mean-field limits of the discrete systems of interacting particles used for halftoning of images in the sense of continuous-domain quantization. Under mild assumptions on the regularity of the interacting kernels we…

For a partition $\underline{\lambda} = (\lambda_{1}^{\rho _1}>\lambda_{2}^{\rho _2}>\lambda_{3}^{\rho _3}>\ldots>\lambda_{k}^{\rho _k})$ and its associated finite $\mathcal{R}$-module…

We compute the instanton partition function for ${\cal N}=4$ U(N) gauge theories living on toric varieties, mainly of type $\R^4/\Gamma_{p,q}$ including $A_{p-1}$ or $O_{\PP_1}(-p)$ surfaces. The results provide microscopic formulas for the…

We propose a Riemannian version of Nesterov's Accelerated Gradient algorithm (RAGD), and show that for geodesically smooth and strongly convex problems, within a neighborhood of the minimizer whose radius depends on the condition number as…