Uniform distribution Theory
Spring 2021, Tel Aviv
Schedule: Wed 13:10-16:00
At least until April the meetings will be on Zoom. Write to me for a link.
Syllabus:
The classical theory of uniform distribution modulo one began with the work of Herman Weyl in 1916 and deals with the distribution of fractional parts
of sequences of real numbers in the unit interval, with roots in Diophantine approximations but later extended to links with other parts of number theory,
ergodic theory and mathematical physics.
The course will cover some of the classical theory, both qualitative methods such as Weyl's criterion and quantitative methods (discrepancy theory).
We will explore links with number theory, and continue to modern versions of the theory of uniform distribution, which study microscopic statistics such as the level spacing distribution
and its connections with Random Matrix Theory.
Prerequisites: basic courses in number theory, measure theory, probability theory, complex analysis
Homework assignments
Bibliography
For the first part of the course:
- L. Kuipers and H. Niederreiter. Uniform Distribution of Sequences (Dover Books on Mathematics)
- Hugh L. Montgomery: Ten Lectures on the Interface between Analytic Number Theory and
Harmonic Analysis. CBMS Regional Conference Series in Mathematics
- Yann Bugeaud, Distribution Modulo One and Diophantine Approximation. Cambridge University Press
Contact me at: rudnick@tauex.tau.ac.il, Office : Schreiber 308