Related papers: Definite Determinantal Representations of Ternary …

We show that for a representation of the fundamental group of a triangulated closed 3-manifold (not necessarily hyperbolic) into $\PSL$ so that any edge loop has non-trivial image under the representation, there exist uncountably many…

We lift upper and lower estimates from linear functionals to $n$-homogeneous polynomials and using this result show that $l_\infty$ is finitely represented in the space of $n$-homogeneous polynomials, $n\ge2$, for any infinite dimensional…

In this paper we continue the study of non-diagonalisable hyperbolic systems with variable multiplicity started by the authors in \cite{Garetto2018}. In the case of space dependent coefficients, we prove a representation formula for…

In this paper, we consider the family of hyperbolic quadratic polynomials parametrised by a complex constant; namely $P_{c}(z) = z^{2} + c$ with $|c| < 1$ and the family of hyperbolic cubic polynomials parametrised by two complex constants;…

In hyperbolic dynamics, a well-known result is: every hyperbolic Lyapunov stable set, is attracting; it's natural to wonder if this result is maintained in the sectional-hyperbolic dynamics. This question is still open, although some…

We give a criterion which ensures that a group generated by Cartan involutions in the automorph group of a rational quadratic form of signature (n-1,1) is "thin", namely it is of infinite index in the latter. It is based on a graph defined…

Recently quantum-like representation algorithm (QLRA) was introduced by A. Khrennikov [20]--[28] to solve the so-called "inverse Born's rule problem": to construct a representation of probabilistic data by a complex or more general (in…

In this paper we generalize the formula of Frobenius-Stickelberger and the formula of Kiepert to genus-three case. The latter is well-known determinant expression for any division polynomial of any elliptic curve.

We discuss the application of the determinantal method to the proof of the Riemann hypothesis. We start from the fact that, if a certain doubly infinite set of determinants are all positive, then the hypothesis is true. This approach…

The first and second representation theorems for sign-indefinite, not necessarily semi-bounded quadratic forms are revisited. New straightforward proofs of these theorems are given. A number of necessary and sufficient conditions ensuring…

We study sets of univariate hyperbolic polynomials that share the same first few coefficients and show that they have a natural combinatorial description akin to that of polytopes. We define a stratification of such sets in terms of root…

Every volume-preserving centre-bunched fibred partially hyperbolic system with 2-dimensional centre either (1) has two distinct centre Lyapunov exponents, or (2) exhibits an invariant continuous line field (or pair of line fields) tangent…

We propose a definition of the Toledo invariant for representations of fundamental groups of smooth varieties of general type into semisimple Lie groups of Hermitian type. This definition allows to generalize the results known in the…

Let f be a dominant rational map of P^k such that there exists s <k, with lambda_s(f)>lambda_l(f) for all l. Under mild hypotheses, we show that, for A outside a pluripolar set of the group of automorphisms of P^k, the map f o A admits a…

A classification of partially hyperbolic diffeomorphisms on 3-dimensional manifolds with (virtually) solvable fundamental group is obtained. If such a diffeomorphism does not admit a periodic attracting or repelling two-dimensional torus,…

In this paper we introduce the notion of hybrid trigonometric parametrization as a tuple of real rational expressions involving circular and hyperbolic trigonometric functions as well as monomials, with the restriction that variables in…

In this paper, we study the representations of integral quadratic polynomials. Particularly, it is shown that there are only finitely many equivalence classes of positive ternary universal integral quadratic polynomials, and that there are…

This paper uses previous results of the authors on vector-valued modular forms to study certain non-congruence modular forms. We prove that these forms have unbounded denominators, and in certain cases we verify congruences of…

The Generalized Lax Conjecture asks whether every hyperbolicity cone is a section of a semidefinite cone of sufficiently high dimension. We prove that the space of hyperbolicity cones of hyperbolic polynomials of degree $d$ in $n$ variables…

We use the stabilization functors to study the combinatorial aspects of the $F$-polynomial of a representation of any finite-dimensional basic algebra. We characterize the vertices of their Newton polytopes. We give an explicit formula for…