Point-counting results for sets in real Euclidean space have found remarkable applications
to diophantine geometry, enabling significant progress on the André–Oort and Zilber–Pink …

We introduce the notion of a complex cell, a complexification of the cells/cylinders used in
real tame geometry. For δ∈(0,1) and a complex cell C, we define its holomorphic extension …

Hyperbolic Ax-Lindemann theorem in the cocompact case Page 1 HYPERBOLIC AX–LINDEMANN
THEOREM IN THE COCOMPACT CASE EMMANUEL ULLMO and ANDREI YAFAEV Abstract …

We prove an analog of the Yomdin–Gromov lemma for, in analogy to results by Pila and
Wilkie, and by Bombieri and Pila, respectively. Along the way we prove, for definable …

We consider the structure R^RE obtained from (R,\lt,+,⋅) by adjoining the restricted
exponential and sine functions. We prove Wilkie's conjecture for sets definable in this …

Let Z be a subvariety of the moduli space of principally polarised abelian varieties of
dimension g over the complex numbers. Suppose that Z contains a Zariski dense set of …

The o-minimal structure generated by the restricted Pfaffian functions, known as restricted
sub-Pfaffian sets, admits a natural measure of complexity in terms of a format, recording …

Abstract Let X⊂ Y⁢(1) n be a subvariety defined over a number field 𝔽 and let (P 1,…, P
n)∈ X be a special point not contained in a positive-dimensional special subvariety of X. We …

Employing a proof technique suggested by Zannier and first successfully implemented by
Pila and Zannier to give a reproof of the Manin-Mumford conjecture on algebraic relations …

Smooth parametrization consists in a subdivision of the mathematical objects under
consideration into simple pieces, and then parametric representation of each piece, while …