- Series
- Analysis Seminar
- Time
- Wednesday, October 2, 2024 - 2:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Niclas Technau – University of Bonn – ntechnau@uni-bonn.de
- Organizer
- Michael Lacey
Given x in $[0,1]^d$, this talk is about the fine-scale distribution of the Kronecker sequence $(n x mod 1)_{n\geq 1}$.
After a general introduction, I will report on forthcoming work with Sam Chow.
Using Fourier analysis, we establish a novel deterministic analogue of Beck’s local-to-global principle (Ann. of Math. 1994),
which relates the discrepancy of a Kronecker sequence to multiplicative diophantine approximation.
This opens up a new avenue of attack for Littlewood’s conjecture.