Related papers: Elliptic Selberg integrals and conformal blocks
We discuss some aspects of the theory of subelliptic estimates.
We review certain classes of iterated integrals that appear in the computation of Feynman integrals that involve elliptic functions. These functions generalise the well-known class of multiple polylogarithms to elliptic curves and are…
We prove the existence of one or more solutions to a singularly perturbed elliptic problema with two potential functions.
We present some elliptic beta integrals with a base parameter on the unit circle, together with their basic degenerations.
We prove existence of strong solutions to a family of some semilinear parabolic free boundary problems by means of elliptic regularization. Existence of solutions is obtained in two steps: we first show some uniform energy estimates and…
We derive new integral representations for objects arising in the classical theory of elliptic functions: the Eisenstein series $E_s$, and Weierstrass' $\wp$ and $\zeta$ functions. The derivations proceed from the Laplace-Mellin…
We prove an $\mathbb F_p$-Selberg integral formula of type $A_n$, in which the $\mathbb F_p$-Selberg integral is an element of the finite field $\mathbb F_p$ with odd prime number $p$ of elements. The formula is motivated by analogy between…
We derive expressions for conformal blocks involving operators with arbitrary spins in 3-dimensional CFTs. We use previous results on the action of the OPE in the embedding space to derive the conformal blocks. The blocks are given as…
The two parameter generalization of the complete elliptic integral of the second kind discussed recently by Barsan is expressed in terms of ordinary complete elliptic integrals.
In this note, we observe a relation between dialgebras (in particular, Leibniz algebras) and conformal algebras. The purpose is to show how the methods of conformal algebras help solving problems on dialgebras, and, conversely, how the…
We construct an integral form for the universal enveloping algebra of the Onsager algebra and an explicit integral basis for this integral form. We also formulate straightening identities among some products of basis elements.
In this paper we study the existence of solutions of thedegererate elliptic system.
We establish the equivalence of Gromov ellipticity and subellipticity in the algebraic category.
To answer a question about the distribution of products of elliptic curves in isogeny classes of abelian surfaces defined over finite fields, we compute specific orbital integrals in the group $\mathrm{GSp}_4$. More precisely, we compute…
We summarize recent computations with a class of elliptic generalizations of polylogarithms, arising from the massive sunrise integral. For the case of arbitrary masses we obtain results in two and four space-time dimensions. The iterated…
The theory of Selberg zeta functions is generalized to higher rank spaces. Applications towards analytic torsion numbers are given.
Recently we proposed a generic construction of the additional integrals of motion for the St\"ackel systems applying addition theorems to the angle variables. In this note we show some trivial examples associated with angle variables for…
In this talk we discuss a class of Feynman integrals, which can be expressed to all orders in the dimensional regularisation parameter as iterated integrals of modular forms. We review the mathematical prerequisites related to elliptic…
We find an explicit formula for the elliptic stable envelope in the case of the Hilbert scheme of points on a complex plane. The formula has a structure of a sum over trees in Young diagrams. In the limit we obtain the formulas for the…
A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized…