Activities This Week
Geometry and Group Theory
Sharply 2-transitive linear groups
Feb 23, 14:00—14:50, 2017, -101
Speaker
Dennis Gulko (BGU)
Abstract
Sharply 2-transitive groups are groups that admit a transitive and free action on pairs of distinct points. Finite sharply 2-transitive groups have been thoroughly studied, and completely classified by H. Zassenhaus in the 1930’s, but up to some few years back, relatively little was known about the infinite case. In this lecture we will survey the latest developments regarding infinite sharply 2-transitive groups, and present our results in this field.
Probability and ergodic theory (PET)
Diophantine approximation in function fields
Feb 28, 10:50—12:00, 2017, Math -101
Speaker
Erez Nesharim (University of York)
Abstract
Irrational rotations of the circle $T:\mathbb{R}/\mathbb{Z}\to \mathbb{R}/\mathbb{Z}$ are amongst the most studied dynamical systems. Rotations by badly approximable angels are exactly those for which the orbit of zero do not visit certain shrinking neighborhoods of zero, namely, there exists c>0 such that $T^n(0)\notin B\left(0,\frac{c}{n}\right)$ for all n. Khinchine proved that every orbit of any rotation of the circle misses a shrinking neighborhood of some point of the circle. In fact, he proved that the constant of these shrinking neighborhoods may be taken uniformly. The largest constant, however, remains unknown.
We will introduce the notion of approximation by rational functions in the field $\mathbb{F}_q((t-1)) ,$ formulate the analogue of Khinchine’s theorem over function fields and calculate the largest constant in this context.