Number Theory Seminar: Alexander Mondar
Topic
Affine minimal rational functions
Speakers
Details
Abstract
Many 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.
Many 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.
Additional Information
Location: ASB 10900 (IRMACS - SFU Campus)
For more information please visit UBC Mathematics Department
Alexander Molnar