Elliptic Gaudin models and elliptic KZ equations

Zn elliptic Gaudin model with open boundaries

The Zn elliptic Gaudin model with integrable boundaries specified by generic nondiagonal K-matrices with n+ 1 free boundary parameters is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz method. The eigenvalues and the corresponding Bethe ansatz equations are obtained. PACS: 03.65.Fd; 04.20.Jb; 05.30.-d; 75.10.Jm

Elliptic Fibrations and Elliptic Models

We study the Seiberg-Witten curves for N = 2 SUSY gauge theories arising from type IIA string configurations with two orientifold sixplanes. Such theories lift to elliptic models in M-theory. We express the M-theory background for these models as a nontrivial elliptic fibration over C. We discuss singularities of this surface, and write the Seiberg-Witten curve for several theories as a subvari...

Solving Elliptic Diophantine Equations Avoiding Thue Equations and Elliptic Logarithms

This research was supported by the Netherlands Mathematical Research Foundation SWON with nancial aid from the Netherlands Organization for Scienti c Research NWO. We determine the solutions in integers of the equation y = (x + p)(x + p) for p = 167, 223, 337, 1201. The method used was suggested to us by Yu. Bilu, and is shown to be in some cases more efficient than other general purpose method...

Elliptic Equations

Elliptic equations