Class meets at: Goldsmith 101,
MWTh 12 NOON - 1 PM
Lecturer: Dmitry Kleinbock
Office: Goldsmith 207, phone 6-3059
Office Hours: Th 2-3 or by appt.
E-mail address: kleinboc@brandeis.edu
Useful online sources are: lecture notes by Bryna Kra, and a book by Mark Pollicott and Michiko Yuri.
Links to some of the topics mentioned in class: Collatz Problem, cat map animation, solenoid animation, well-rounded lattices,
arithmetic progressions in primes,
a book by Dave Morris
on Ratner Theorem, with a chapter about entropy
Further reading: a long survey paper by Bergelson,
and two short unpublished drafts related to shrinking targets: by myself and Margulis and Fayad.
(easy): make sure you can do it and talk to me if you cannot; do not hand in
standard: work it out and hand in your solution
challenging: don't panic if you cannot do it, but if you can, hand in your solution for extra credit
| 1 | Problems (1.1.1-2), (1.2.1), 1.2.2-3, 1.2.4, (1.3.1), 1.3.2-3, (1.3.4), 1.3.5 | September 15 |
| 2 | Problems 1.4.1-2, (1.4.3-4), (1.6.1), 1.6.2, (1.6.3), (1.7.1-2), 1.7.3, 1.11.1, 1.11.3 | September 22 |
| 3 | Problems (2.1.1-5), 2.1.6, (2.1.7-8), 2.1.9-11 | September 29 |
| 4 | Problems (2.8.1-3), 2.8.4, and five more problems (pdf) | October 13 |
| 5 | Problems (2.2.1-3), 2.2.6, (2.3.1-4), and eight more problems (pdf) | October 27 |
| 6 | Problems (2.5.1-5), 2.5.6, (2.5.7), (2.6.1-2), (7.1.1-2), 7.1.3-4 and five more problems (pdf) | November 10 |
| 7 | Problems 4.1.1, (4.2.2), 4.2.3 and seven more problems (pdf) | November 17 |
| 8 | Problems (4.3.1), 4.3.2, 4.3.5, (4.3.6-7), (4.4.3-4), 4.5.1, 4.5.6, 4.6.3, (4.6.4), 4.6.5 | December 2 |
| 9 | Problems (9.1.1-3), 9.2.2, 9.3.1, (9.3.2), 9.3.4-7 | December 9 |