Related papers: A Rationality Problem of Some Cremona Transformati…
Let G be the (special) affine group, semidirect product of SL_n and C^n. In this paper we study the representation theory of G and in particular the question of rationality for V/G where V is a generically free G-representation. We show…
We improve the arithmetic duality formalism of the rational etale site. This improvement allows us to avoid some exotic approximation arguments on local fields with ind-rational base, thus simplifying the proofs of the previously…
Explicit formulae describing the genus one characters and modular transformation properties of permutation orbifolds of arbitrary Rational Conformal Field Theories are presented, and their relation to the theory of covering surfaces is…
In this paper we introduce a family of rational approximations of the reciprocal of a $\phi$-function involved in the explicit solutions of certain linear differential equations, as well as in integration schemes evolving on manifolds. The…
A commentary is made on the recent work by Cardy, ArXiv:1603. 08267, on quantum revivals and higher dimensional CFT. The actual expressions used here are those derived some time ago. The calculation is extended to fermion fields for which…
We introduce a direct image formalism for constructible motivic functions. One deduces a very general version of motivic integration for which a change of variables theorem is proved. These constructions are generalized to the relative…
This paper deals with valuations of fields of formal meromorphic functions and their residue fields. We explicitly describe the residue fields of the monomial valuations. We also classify all the discrete rank one valuations of fields of…
This is a survey on the ancient question : Let G be a reductive group over an algebraically closed field k and let V be a vector space over k with an almost free linear action of G on V. Let k(V) denote the field of rational functions on V.…
It is known that a two-dimensional $F$-rational ring has a rational singularity. However a two-dimensional ring with a rational singularity is not $F$-rational in general. In this paper, we investigate $F$-rationality of a two-dimensional…
We study the class $\mathcal{M}_{\mathrm{ratio}}$ of those probability distributions for which the free $R$-transforms are rational functions. This class is closed under the additive free convolution, additive free powers and under the…
Mappings between models may be obtained by unitary transformations with preservation of the spectra but in general a change in the states. Non- canonical transformations in general also change the statistics of the operators involved. In…
A rational function is the ratio of two complex polynomials in one variable without common roots. Its degree is the maximum of the degrees of the numerator and the denominator. Rational functions belong to the same class if one turns into…
We formulate some problems and conjectures about semigroups of rational functions under composition. The considered problems arise in different contexts, but most of them are united by a certain relationship to the concept of amenability.
In 2021, Marco Besier and the first author introduced the concept of rationalizability of square roots to simplify arguments of Feynman integrals. In this work, we generalize the definition of rationalizability to field extensions. We then…
In this article we try to give a condensed panoramic view of the development of two-dimensional rational conformal field theory in the last twenty-five years.
The iteration of rational maps is well-understood in dimension 1 but less so in higher dimensions. We study some maps on spaces of matrices which present a weak complexity with respect to the ring structure. First we give some properties of…
We reconsider the conjecture by Gepner that the fusion ring of a rational conformal field theory is isomorphic to a ring of polynomials in $n$ variables quotiented by an ideal of constraints that derive from a potential. We show that in a…
I briefly describe two motivations, two mechanisms and two possible tests of the hypothesis that the physical parameters of the ground state of a theory can vary in different regions of the universe.
We study the rationality of some geometrically rational three-dimensional conic and quadric surface bundles, defined over the reals and more general real closed fields, for which the real locus is connected and the intermediate Jacobian…
If the denominator of a rational function of several variables is sum of even powers and the numerator is a monomial, then we give a numerical criterion, using the exponents involved in the expression of the rational function, to decide if…