Event time:
Monday, March 2, 2009 - 11:30am to 12:30pm
Location:
431 DL
Speaker:
Uri Shapira
Speaker affiliation:
Hebrew University Jerusalem
Event description:
We prove existence of real numbers x,y, possessing
the following property:
For any real $a,b,$ $ \liminf |n| ||nx - a|| ||ny - b|| = 0$,
where $||c|| $ denotes the distance of c to the nearest integer.
This answers a 50 years old question of Cassels.
The most interesting part of the result is that there are algebraic
numbers with the above property!