40 citations · 307 across the 25 of their papers we have counts for
25 papers
Around Zilber's quasiminimality conjecture
Jonathan Kirby
This is an extended abstract for a survey talk given in Oberwolfach on 1st December 2022, slightly updated in June 2023. I survey some work around the notion of quasiminimality and…
Quasiminimality of complex powers
Francesco Gallinaro, Jonathan Kirby
The complex field, equipped with the multivalued functions of raising to each complex power, is quasiminimal, proving a conjecture of Zilber and providing evidence towards his stro…
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 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…