Graduate Number Theory Seminar (GNTS)/ Learning Seminar (LS)

These two seminars run periodically throughout the semester. The Graduate Number Theory Seminar is for talks by the graduate students (and sometimes post docs) for the graduate students. The Learning Seminar this semester (and possibly next) will focus on Ratner's Theorems and we will be using the book by Dave Witte Morris, "Ratner's Theorems on Unipotent Flows." A link to the book may be found on the archive.

### Meeting Time/Loctation:

Wednesdays 10:30-11:30 am in Hill 425

### Organizer:

Brooke Ogrodnik

bl481@math.rutgers.edu
### Next Talk:

Wednesday October 16th (GNTS):

Speaker: Louis Gaudet

Title: A zero-density theorem for the Riemann zeta function

Abstract: A zero-density theorem is an upper bound on the number of zeros of the zeta function in a rectangle in the critical strip. We will prove one such estimate that implies, in particular, that zero percent of the zeta function's zeros have real part greater than A, for any A > 1/2. We will see how the proof uses a mollifier, that is, a function that pretends to behave like 1/zeta.
### Upcoming Talks:

Octber 23rd (GNTS): Edna Jones, Title- TBA

October 30th (LS): Alex Walker, Title- TBA
### Past Talks:

Wednesday October 9th (GNTS): Alex Karlovitz gave a talk entitled, "An Introduction to Maass Forms and their Fourier Expansions."

Wednesday October 2nd (GNTS): George Hauser gave a talk entitled, "The Dedekind Eta Function and Its Multiplier System."

Wednesday September 25th (LS): Matthew Welsh gave a talk entitled, "The Oppenhiem conjecture and Ratner's theorems." The talk covered 1.1 of the text.

Wednesday September 18th (LS): Alex Kontorovich gave an introductory talk where it was established that the topic for the learning seminar will be Ratner's Theorems.

Wednesday September 11th (GNTS): Brooke Ogrodnik gave a talk entitiled "Reciprocal Geodesics"