Equidistribution in Bun2(P1)

Equidistribution in Sharing Games

Games often provide a good introduction to interesting phenomena in mathematics. In this note, we examine three variations of an iterative sharing game played around a circular (or not so circular) table. More precisely, for each variation we study the tendency toward equal distribution among the players. In the first variation, the players have discrete amounts at each step. The second variati...

Equidistribution and Primes

We begin by reviewing various classical problems concerning the existence of primes or numbers with few prime factors as well as some of the key developments towards resolving these long standing questions. Then we put the theory in a natural and general geometric context of actions on affine n-space and indicate what can be established there. The methods used to develop a combinational sieve i...

Notes on Equidistribution

Variational Mesh Adaptation: Isotropyand Equidistribution

We present a new approach for developing more robust and error-oriented mesh adaptation methods. Specifically, assuming that a regular (in cell shape) and uniform (in cell size) computational mesh is used (as is commonly done in computation), we develop a criterion for mesh adaptation based on an error function whose definition is motivated by the analysis of function variation and local error ...

Equidistribution over function fields

We prove equidistribution of a generic net of small points in a projective variety X over a function field K. For an algebraic dynamical system over K, we generalize this equidistribution theorem to a small generic net of subvarieties. For number fields, these results were proved by Yuan and we transfer here his methods to function fields. If X is a closed subvariety of an abelian variety, then...