Room: Van Vleck B119
Time: Fridays, 2.25pm-3.25pm
Reference: We will follow the book "Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis" by Hugh L . Montgomery which is available online through the UW-Madison library.
Instructors: Rajula Srivastava, Niclas Technau
Talks should be 45 min long, with 5-10 mins for questions/discussion.
For students enrolled for three credits, the talk must be supplemented by a 2-3 page handout summarizing the talk. This should preferably be typed, but cleanly handwritten notes are also fine. Please make copies (or send them in advance to the instructors) so they can be passed around before your talk.
You are welcome to discuss your topic with either of the instructors 1-2 weeks before you present.
When presenting, you do not need to give all details but focus on explaining the main ideas.
Schedule (All chapters are from the above textbook unless stated otherwise.)
Sep 5: Organizational Meeting
Sep 12: No meeting!
Sep 19: Chapter 1 - Seong Jung
Sep 26: Chapter 3: Weyl Diff (3.2) + van der Corput A process (3.3 beginning) - Kaiwen Jin
Oct 3: No meeting - Attend the Harmonic Analysis Workshop instead!
Oct 10: Method of Stationary Phase (Reference: Chapter 6 from Wolff's notes Ch 6) - Gisel Flores
Oct 17: Chapter 3 (contd.): van der Corput B process (Section 3.3) - Jiankun Li
Oct 24: Arkhipov-Chubarikov-Karatsuba Estimates (Chapter 1.1, Theorems 1.1 and 1.1' from this reference), or Section 3.1 from this recent paper. If there is time, discuss applications to counting rational points near curves in three dimensions.- Sam Craig
Oct 31: Chapter 4 (Vinogradov method): 4.1, 4.4 (Proof of Thm 4) - Dijia (Mark) Chen
Nov 7: Chapter 6 - Inbo Gottlieb
Nov 14: Chapter 7: moment estimates and majorisation principles (7.1, 7.2, 7.3) - Chiara Paulsen
Nov 21: Chapter 7: duality principles, large value bounds (7.4, 7.5, 7.6) - Mingfeng Chen
Nov 28: No meeting - Thanksgiving break
Dec 5: Chapter 8 (8.1-8.3, 8.4 if time) - Still free!