10 citations · 59 across the 20 of their papers we have counts for
22 papers
Modular Zilber-Pink for geometrically generic varieties
Vahagn Aslanyan, Sebastian Eterović, Guy Fowler
We prove that the modular Zilber--Pink conjecture (in Pink's formulation in terms of unlikely intersections) holds for all subvarieties of for which no proje…
Exponential sums equations and the Exponential Closedness conjecture
Vahagn Aslanyan, Francesco Gallinaro
This is an expository paper aiming to introduce Zilber's Exponential Closedness conjecture to a general audience. Exponential Closedness predicts when (systems of) equations involv…
Complex solutions of polynomial equations on the unit circle
Vahagn Aslanyan
We explore systems of polynomial equations where we seek complex solutions with absolute value 1. Geometrically, this amounts to understanding intersections of algebraic varieties…
Algebraic types in Zilber's exponential field
Vahagn Aslanyan, Jonathan Kirby
We characterise the model-theoretic algebraic closure in Zilber's exponential field. A key step involves showing that certain algebraic varieties have finite intersections with cer…
The mathematical work of Anania Shirakatsi
Vahagn Aslanyan
This paper aims to give a brief account of the mathematical work of the 7th-century Armenian polymath and natural philosopher Anania Shirakatsi. The three sections of Anania's ``Bo…
The Existential Closedness and Zilber-Pink Conjectures
Vahagn Aslanyan
In this paper we survey the history of, and recent developments on, two major conjectures originating in Zilber's model-theoretic work on complex exponentiation -- Existential Clos…
Equations involving the modular -function and its derivatives
Vahagn Aslanyan, Sebastian Eterović, Vincenzo Mantova
We show that for any polynomial , the equation has a Zariski dense set of solutions in the hypersurfac…
Multiplicative relations among differences of singular moduli
Vahagn Aslanyan, Sebastian Eterović, Guy Fowler
Let . We prove that there exist a finite set and finitely many algebraic curves with the following property: if $(x_1, \ldots, x_n, y)…
Independence relations for exponential fields
Vahagn Aslanyan, Robert Henderson, Mark Kamsma +1
We give four different independence relations on any exponential field. Each is a canonical independence relation on a suitable Abstract Elementary Class of exponential fields, sho…
A note on unlikely intersections in Shimura varieties
Vahagn Aslanyan, Christopher Daw
We discuss the relationships between the André-Oort, André-Pink-Zannier, and Mordell-Lang conjectures for Shimura varieties. We then combine the latter with the geometric Zilber-Pi…
A geometric approach to some systems of exponential equations
Vahagn Aslanyan, Jonathan Kirby, Vincenzo Mantova
Zilber's Exponential Algebraic Closedness conjecture (also known as Zilber's Nullstellensatz) gives conditions under which a complex algebraic variety should intersect the graph of…
A closure operator respecting the modular -function
Vahagn Aslanyan, Sebastian Eterović, Jonathan Kirby
We prove some unconditional cases of the Existential Closedness problem for the modular -function. For this, we show that for any finitely generated field we can find a "conveni…
Blurrings of the -function
Vahagn Aslanyan, Jonathan Kirby
Inspired by the idea of blurring the exponential function, we define blurred variants of the -function and its derivatives, where blurring is given by the action of a subgroup o…
Differential Existential Closedness for the -function
Vahagn Aslanyan, Sebastian Eterović, Jonathan Kirby
We prove the Existential Closedness conjecture for the differential equation of the -function and its derivatives. It states that in a differentially closed field certain equati…
Some Remarks on Atypical Intersections
Vahagn Aslanyan
In this paper we show how some known weak forms of the Zilber--Pink conjecture can be strengthened by combining them with the Mordell--Lang conjecture or its variants. We illustrat…
Existentially closed De Morgan algebras
Vahagn Aslanyan
We show that the theory of De Morgan algebras has a model completion and axiomatise it. Then we prove that it is -categorical and describe definable and algebraic closure…
Ax-Schanuel and strong minimality for the -function
Vahagn Aslanyan
Let be a differentially closed field of characteristic with field of constants . In the first part of the paper we explore the connection…
Weak Modular Zilber-Pink with Derivatives
Vahagn Aslanyan
In unpublished notes Pila proposed a Modular Zilber-Pink with Derivatives (MZPD) conjecture, which is a Zilber-Pink type statement for the modular -function and its derivatives.…
Adequate Predimension Inequalities in Differential Fields
Vahagn Aslanyan
In this paper we study predimension inequalities in differential fields and define what it means for such an inequality to be \emph{adequate}. Adequacy was informally introduced by…
Ax-Schanuel type theorems and geometry of strongly minimal sets in differentially closed fields
Vahagn Aslanyan
Let be a differentially closed field. In this paper we explore the connection between Ax-Schanuel type theorems (predimension inequalities) for a differentia…
Ax-Schanuel for Linear Differential Equations
Vahagn Aslanyan
We generalise the exponential Ax-Schanuel theorem to arbitrary linear differential equations with constant coefficients. Using the analysis of the exponential differential equation…
Definability of derivations in the reducts of differentially closed fields
Vahagn Aslanyan
Let be a differentially closed field. We consider the question of definability of the derivation in reducts of of the form $\mathc…