10 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…