Related papers: $H^2(SL_3(\mathbb{Z}[t]); \mathbb{Q})$ is infinite…
Following the prequel work \cite{VO3}, we prove a generalization of "Mazur's conjecture" for $L$-functions of elliptic curves in abelian extensions of imaginary quadratic fields, including the assertion that the Mordell-Weil rank of an…
Colding and Gabai have given an effective version of Li's theorem that non-Haken hyperbolic 3-manifolds have finitely many irreducible Heegaard splittings. As a corollary of their work, we show that Haken hyperbolic 3-manifolds have a…
It is well-known that global hyperbolicity implies that the Lorentzian distance is finite and continuous. By carefully analysing the causes of discontinuity of the Lorentzian distance, we show that in most other respects the finiteness and…
Objects with large symmetry groups have been an interest for many mathematicians. A classical question in geometry is whether a surface with certain geometric features, such as completeness, curvature, etc..., can embed in $\mathbb{R}^3.$…
In this note we introduce the transcendental part $t(X)$ of the motive of a cubic fourfold $X$ and prove that it is isomorphic to the (twisted) transcendental part $h_2^{tr}(F(X))$ in a suitable Chow-K\"unneth decomposition for the motive…
We prove that rational homology of the Torelli group of genus g is infinite dimensional, provided g>6. This means that rational homology of the Torelli space of genus g>6 is infinite dimensional. The Torelli groups with marked points are…
Infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial domain with full boundary control and without internal damping are studied. This class of systems includes models of beams and waves as well as the transport…
In this article we collect results obtained by the authors jointly with other authors and we discuss old and new ideas. In particular we discuss singularities of the exponential map, completeness and homogeneity for Riemannian Hilbert…
We prove that the hierarchical hull of any finite set of interior points, hierarchy rays, and boundary points in a hierarchically hyperbolic space (HHS) is quasi-median quasi-isometric to a CAT(0) cube complex of bounded dimension. Our…
Let $R(x)=g(x)/h(x)$ be a rational expression of degree three over the finite field $\mathbb{F}_q$. We count the irreducible polynomials in $\mathbb{F}_q[x]$, of a given degree, which have the form $h(x)^{\mathrm{deg}\, f}\cdot…
The linear $\delta$ expansion (LDE) is applied to the Hamiltonian $H=(p^2 +m^2 x^2)/2 + igx^3$, which arises in the study of Lee-Yang zeros in statistical mechanics. Despite being non-Hermitian, this Hamiltonian appears to possess a real,…
In this article we study polynomial logarithmic $q$-forms on a projective space and characterize those that define singular foliations of codimension $q$. Our main result is the algebraic proof of their infinitesimal stability when $q=2$…
This paper studies the infinitesimal variation of the Lefschetz decomposition associated with a compatible sl_2-representation on a graded algebra. This allows to prove that the Jordan-Lefschetz property holds infinitesimally for the…
Finite and Infinite-dimensional representations of symmetry algebras play a significant role in determining the spectral properties of physical Hamiltonians. In this paper, we introduce and apply a practical method to construct infinite…
We calculate the third homology of $\mathrm{SL}_2(\mathbb{Q})$ with half-integral coefficients. Corresponding to each prime $p$ there is an operator on this group with square the identity. The kernel of the (split surjective) homomorphism…
We prove that the complete $L$-function associated to any cuspidal automorphic representation of $GL_2(\mathbb{A}_{\mathbb Q})$ has infinitely many simple zeros.
By employing Husimi quasiprobability distributions, we show that a bounded portion of an unbounded phase space induces a finite effective dimension in an infinite dimensional Hilbert space. We compare our general expressions with numerical…
A new (in)finite dimensional algebra which is a fundamental dynamical symmetry of a large class of (continuum or lattice) quantum integrable models is introduced and studied in details. Finite dimensional representations are constructed and…
It is shown that the compositum $ \mathbb Q^{(2)}$ of all degree 2 extensions of $\mathbb Q$ has undecidable theory.
Infinitesimal bendings for classes of two-dimensional surfaces in $\mathbb{R}^3$ are investigated. The techniques used to construct the bending fields include reduction to solvability of Bers-Vekua type equations and systems of differential…