## Number Theory Seminar: Alexander Mondar

- Date: 03/03/2011
- Time: 15:00

Simon Fraser University

Affine minimal rational functions

AbstractMany arithmetic geometric results have an arithmetic dynamic analogue. For instance, Siegel's theorem that an elliptic curve has only finitely many integer points is analogous to the fact that any orbit under a rational function whose second iterate has non-constant denominator has only finitely many distinct integer values. A conjecture of Lang states that the number of integer points on a minimal Weierstrass model of an elliptic curve is uniformly bounded. In order to translate this conjecture, one needs a dynamic concept of minimality. We present one such notion, affine minimality, an algorithm to compute affine minimal forms of rational functions and some recent results pertaining to the dynamical analogue of Lang's conjecture.

Location: ASB 10900 (IRMACS - SFU Campus)

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