Related papers: Elliptic pfaffians and solvable lattice models

In this paper Tricomi-Gellerstedt-Keldysh-type fractional elliptic equations are studied. The results on the well-posedness of fractional elliptic boundary value problems are obtained for general positive operators with discrete spectrum…

A nontrivial trigonometric limit of the three-coloring statistical model with the domain wall boundary conditions is considered. In this limit the functional equations, constructed in the previous paper, are solved and a new determinant…

In this paper, we study the diagonal restrictions of certain Hilbert theta series for a totally real field $F$, and prove that they span the corresponding space of elliptic modular forms when the $F$ is quadratic or cubic. Furthermore, we…

We show factorization formulas for a class of partition functions of rational six vertex model. First we show factorization formulas for partition functions under triangular boundary. Further, by combining the factorization formulas with…

I consider the partition function of the inhomogeneous 6-vertex model defined on the $n$ by $n$ square lattice. This function depends on 2n spectral parameters $x_i$ and $y_i$ attached to the horizontal and vertical lines respectively. In…

We derive sets of functional equations for the eight vertex model by exploiting an analogy with the functional equations of the chiral Potts model. From these equations we show that the fusion matrices have special reductions at certain…

We study a nonlinear elliptic problem defined in a bounded domain involving fractional powers of the Laplacian operator together with a concave-convex term. We characterize completely the range of parameters for which solutions of the…

We study the signature $\sigma_g(\frac q p)$ of $\mathrm{SU}_2$-TQFT vector spaces associated to surfaces of genus $g$, as a function of the defining root of unity $\zeta=e^{i\pi q/p}$. We prove that $\frac{1}{p^2}\sigma_2(\frac{q}{p})$…

We consider an integrable system in five unknowns having three quartics invariants. We show that the complex affine variety defined by putting these invariants equal to generic constants, completes into an abelian surface; the jacobian of a…

Partial zeta functions of algebraic varieties over finite fields generalize the classical zeta function by allowing each variable to be defined over a possibly different extension field of a fixed finite field. Due to this extra variation…

In this paper we give a birational model for the theta divisor of the intermediate Jacobian of a generic cubic threefold $X$. We use the standard realization of $X$ as a conic bundle and a $4-$dimensional family of plane quartics which are…

We obtain asymptotic formulas for the partition function of the six-vertex model with domain wall boundary conditions and half-turn symmetry in each of the phase regions. The proof is based on the Izergin--Korepin--Kuperberg determinantal…

We consider a toy model of a 3-dimensional topological quantum gravity. In this model, a contribution of a given 3-manifold is given by the partition function of an abelian Topological Quantum Field Theory (TQFT), with a topological…

For a commutative Frobenius algebra $A$, we construct a $(2,3,3+\varepsilon)$-dimensional TQFT $\mathsf{AFK}_A$ that assigns to a 3-manifold a skein module of embedded $A$-decorated surfaces. These surface skein modules have been first…

We consider the trigonometric Felderhof model, of free fermions in an external field, on a finite lattice with domain wall boundary conditions. The vertex weights are functions of rapidities and external fields. We obtain a determinant…

We give an algorithm to compute the zeta function of the Fano surface of lines of a smooth cubic threefold $F$ into $\mathbb{P}^4$ defined over a finite field. We obtain some examples of Fano surfaces with supersingular reduction.

We introduce a Pfaffian formula that extends Schur's $Q$-functions $Q_\lambda$ to be indexed by compositions $\lambda$ with negative parts. This formula makes the Pfaffian construction more consistent with other constructions, such as the…

We express the branch points cross ratio of Hyper-elliptic Mumford curves as quotients of p adic theta functions evaluated at the p adic period matrix

A Fuchsian system of rank 8 in 3 variables with 4 parameters is presented. The singular locus consists of six planes and a cubic surface. The restriction of the system onto the intersection of two singular planes is an ordinary differential…

We study motivic zeta functions for $\mathds{Q}$-divisors in a $\mathds{Q}$-Gorenstein variety. By using a toric partial resolution of singularities we reduce this study to the local case of two normal crossing divisors where the ambient…