Geometry & Topology: Johannes Schleischitz -- Sum and product sets of classes of sets relevant in Diophantine approximation

Monday 11 September 2023, 15:00-16:00, Carslaw 535

Speaker: Johannes Schleischitz (Middle East Technical University)

Title: Sum and product sets of classes of sets relevant in Diophantine approximation

Abstract: Liouville numbers are real numbers that admit very good approximation by 
rationals. Paul Erdos proved that every real number can be written as the sum (and 
product) of two Liouville numbers. We extend this result in several directions, in 
particular considering sum sets of classes of numbers with prescribed or bounded 
irrationality exponent (the case of infinite exponent recovers Erdos result). This 
will also admit conclusions on metrical properties of Cartesian products of these 
sets.