The geometry of algebraic dynamical systems
Connections for Women: Model Theory and Its Interactions with Number Theory and Arithmetic Geometry February 10, 2014 - February 11, 2014
Location: MSRI: Simons Auditorium
I consider the following question: what aspects of the geometry of a variety prohibit the existence of an "interesting" dynamical system on that variety? There are various geometric conditions on a variety which forbid the existence of algebraically or arithmetically interesting dynamical systems. I will discuss various conditions of this kind, and the consequences for conjectures regarding unlikely intersections in algebraic dynamics. Time permitting, I will discuss recent work with Paul Reschke on the non-existence of polarized endomorphisms for varieties with non-surjective Albanese map, and consider what kind of endomorphisms these varieties can carry.
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