NTSGrad Spring 2018/Abstracts
This page contains the titles and abstracts for talks scheduled in the Spring 2018 semester. To go back to the main NTSGrad page, click here.
Jan 23
Solly Parenti 
RankinSelberg Lfunctions 
What do you get when you cross an Eisenstein series with a cuspform? An Lfunction! Since there's no modular forms course this semester, I will try to squeeze in an entire semester's course on modular forms during the first part of this talk, and then I'll explain the RankinSelberg method of establishing analytic continuation of certain Lfunctions. 
Jan 30
Wanlin Li 
Intersection Theory on Modular Curves 
My talk is based on the paper by François Charles with title "FROBENIUS DISTRIBUTION FOR PAIRS OF ELLIPTIC CURVES AND EXCEPTIONAL ISOGENIES". I will talk about the main theorem and give some intuition and heuristic behind it. I will also give a sketch of the proof.

Feb 6
Dongxi Ye 
Modular Forms, Borcherds Lifting and GrossZagier Type CM Value Formulas 
During the course of past decades, modular forms and Borcherds lifting have been playing an increasingly central role in number theory. In this talk, I will partially justify these by discussing some recent progress on some topics in number theory, such as representations by quadratic forms and GrossZagier type CM value formulas. 
Feb 20
Ewan Dalby 
The Cuspidal Rational Torsion Subgroup of J_0(p) 
I will define the cuspidal rational torsion subgroup for the Jacobian of the modular curve J_0(N) and try to convince you that in the case of J_0(p) it is cyclic of order (p1)/gcd(p1,12). 
Feb 27
Brandon Alberts 
A Brief Introduction to Iwasawa Theory 
A bare bones introduction to the subject of Iwasawa theory, its main results, and some of the tools used to prove them. This talk will serve as both a small taste of the subject and a prep talk for the upcoming Arizona Winter School. 