Manchester Existential Closedness Workshop
7-10 July 2026
The University of Manchester (UK)
Manchester Existential Closedness Workshop
7-10 July 2026
The University of Manchester (UK)
In the model theory of analytic functions, Existential Closedness problems aim to determine when systems of equations in several variables involving addition, multiplication, and some special transcendental functions (e.g. exponential or modular functions) have solutions in the complex numbers. This is a natural question at the boundary between complex geometry and model theory, and is an extension of the well-known problem of solvability of systems of polynomial equations in several variables, settled by Hilbert's Nullstellensatz.
The first conjecture on Existential Closedness was proposed by Boris Zilber in the early 2000s in the exponential setting. It is known as the Exponential Closedness conjecture. In recent years, analogues of this conjecture for other functions, most notably the modular j-function, were formulated, and significant progress has been made towards them.
The name Existential Closedness comes from the model-theoretic property of structures, known as existential closedness, describing when quantifier-free formulas with solutions in a larger model already have solutions in the original model. In the setting of complex functions, the Existential Closedness conjecture does not imply that the complex field equipped with the given function is existentially closed in a first-order sense; instead, it is existentially closed in certain self-sufficient extensions.
Upon entering the building, proceed past the lifts into the foyer. Turn left and keep to the left-hand side; you will find Room G.209 just beyond the café seating.
Note: You may also be interested in the Symposium on the Model Theory of Fields taking place in Manchester on Monday, 6th July (the day before the workshop starts).
Invited speakers
Martin Bays (Oxford)
Paola D'Aquino (Caserta)
Sebastian Eterović (Vienna)
Francesco Gallinaro (Pisa)
Jonathan Kirby (East Anglia)
Vincenzo Mantova (Leeds)
Adele Padgett (Vienna)
Thomas Scanlon (Berkeley)
Giuseppina Terzo (Naples)
Alex Wilkie (Oxford)
Roy Zhao (Tsinghua)
Boris Zilber (Oxford)
Contributed speakers
Spencer Dembner
Kai Ino
Angus Matthews
Davide Pantaleoni
Harry Schmidt
David Smith
William Stephenson
Upon entering the building, proceed past the lifts into the foyer. Turn left and keep to the left-hand side; you will find Room G.209 just beyond the café seating area.
During scheduled breaks, tea and coffee will be served on the first floor in the common area near the kitchen.
Please note that only water is permitted inside the lecture room. There is a water refill station situated on the opposite side of the foyer.
Pendulum Hotel Sackville Street
Ibis Manchester Centre Princess Street
Premier Inn Manchester City Centre Princess Street
Holiday Inn Express Manchester City Centre Oxford Road
Travelodge Manchester Upper Brook Street
Vahagn Aslanyan, Anna Dmitrieva
You can contact the organisers at FirstName(DOT)LastName(AT)manchester(DOT)ac(DOT)uk
This workshop is supported by the EPSRC Open Fellowship EP/X009823/1.