Related papers: Hyperbolic algebraic and analytic curves
We study the form of possible algebraic relations between functions satisfying linear differential equations. In particular , if f and g satisfy linear differential equations and are algebraically dependent, we give conditions on the…
This textbook is an introductory course on hyperbolic geometry, intended for students at the advanced undergraduate (Bachelor) or early graduate (Master) level.
We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms…
In $\mathbb{R}^3$, a hyperbolic paraboloid is a classical saddle-shaped quadric surface. Recently, Elser has modeled problems arising in Deep Learning using rectangular hyperbolic paraboloids in $\mathbb{R}^n$. Motivated by his work, we…
We study the algebraic hyperbolicity of certain subvarieties of homogeneous varieties, building on the techniques introduced by Coskun-Riedl, Yeong and Mioranci. This generalizes earlier known results for hypersurfaces to higher…
In this paper we consider a large family of graphs of hierarchically hyperbolic groups (HHG) and show that their fundamental groups admit HHG structures. To do that, we will investigate the notion of hierarchical quasi convexity and show…
A study of triangulations of cycles in the Cayley diagrams of finitely generated groups leads to a new geometric characterization of hyperbolic groups.
In this paper, we will obtain new algebraic transformations of the $_2F_1$-hypergeometric functions. The main novelty in our approach is the interpretation of identities among $_2F_1$-hypergeometric functions as identities among automorphic…
We prove that a real-valued function (that is not assumed to be continuous) on a real analytic manifold is analytic whenever all its restrictions to analytic submanifolds homeomorphic to the 2-sphere are analytic. This is a real analog for…
We study the set of algebraic numbers of bounded height and bounded degree where an analytic transcendental function takes algebraic values.
We show the existence of group-theoretic sections of certain geometrically pro-nilpotent by abelian arithmetic fundamental groups of hyperbolic curves over p-adic local fields which are non-geometric, i.e., which do not arise from rational…
We study the interplay between the classical theory of linear series on curves, and the recent theory of linear series on graphs. We prove that every d-gonal (weighted) graph of Hurwitz type is the dual graph of a d-gonal curve. Conversely…
In this paper we continue our investigation concerning the hyperbolic geometry on the noncommutative ball $[B(H)^n]_1^-$, where $B(H)$ is the algebra of all bounded linear operators on a Hilbert space $H$, and its implications to…
The mathematical model representing the equation of motion of a pendulum is nonlinear. Solutions that satisfy the equation cannot be represented by elementary functions, such as trigonometric functions. To solve such problems, it is common…
We study entire holomorphic curves in the algebraic torus, and show that they can be characterized by the ``growth rate'' of their derivatives.
The computation of the partition function of supersymmetric gauge theories on compact manifolds can be reduced to matrix integrals by using the supersymmetric localization technique. Such matrix integrals in the case of three-dimensional…
An algebraic theory of dualities is developed based on the notion of bond algebras. It deals with classical and quantum dualities in a unified fashion explaining the precise connection between quantum dualities and the low temperature…
In this paper, we study the notion of chordality and cycles in hypergraphs from a commutative algebraic point of view. The corresponding concept of chordality in commutative algebra is having a linear resolution. However, there is no…
We explore some intersection properties of divisors associated to polarized dynamical systems on algebraic surfaces. As a consequence, we obtain necessary geometric conditions for the existence of polarizations of hyperbolic type and…
The multicorns are the connectedness loci of unicritical antiholomorphic polynomials $\bar{z}^d + c$. We investigate the structure of boundaries of hyperbolic components: we prove that the structure of bifurcations from hyperbolic…