The Dynamical Mordell-Lang Conjecture is an analogue of the classical Mordell-Lang
conjecture in the context of arithmetic dynamics. It predicts the behavior of the orbit of a point …

We study definably amenable NIP groups. We develop a theory of generics showing that
various definitions considered previously coincide, and we study invariant measures. As …

We study the postcritically finite maps within the moduli space of complex polynomial
dynamical systems. We characterize rational curves in the moduli space containing an …

We prove the equivalence of dynamical stability, preperiodicity, and canonical height 0, for
algebraic families of rational maps ft: ℙ 1 (ℂ)→ ℙ 1 (ℂ), parameterized by t in a …

In this paper, we study arithmetic dynamics in arbitrary characteristic, in particular in positive
characteristic. Applying the arithmetic degree and canonical height in positive characteristic …

arXiv:2311.16369v1 [math.AG] 27 Nov 2023 Page 1 arXiv:2311.16369v1 [math.AG] 27 Nov
2023 ADVANCES IN THE EQUIVARIANT MINIMAL MODEL PROGRAM AND THEIR …

A differential algebra with weight is an abstraction of both the derivation (weight zero) and
the forward and backward difference operators (weight±1). In 2010 Loday established the …

Let $ f $ be a dominant endomorphism of a smooth projective surface $ X $ over an
algebraically closed field $\mathbf {k} $ of characteristic $0 $. We prove that if there is no …

Let $ X $ be a quasi-projective variety and $ f\colon X\to X $ a finite surjective
endomorphism. We consider Zariski Dense Orbit Conjecture (ZDO), and Adelic Zariski …

We describe all special curves in the parameter space of complex cubic polynomials, that is
all algebraic irreducible curves containing infinitely many post-critically finite polynomials …