Number Theory Seminar
Organizers:
Riad Masri —
Matt Papanikolas —
Shuhui Shi —
Matt Young

Date Time 
Location  Speaker 
Title – click for abstract 

02/27 09:45am 
BLOC 302 
Sumit Kumar Alfréd Rényi Institute of Mathematics 
Hybrid level aspect subconvexity for Lfunctions
Level aspect subconvextiy problem has always been elusive in number theory. In this talk we discuss history of the problem and prove the level aspect subconvexity for degree six GL(3) × Gl(2) RankinSelberg Lfunctions,
when level of both the associated forms vary in some range. Joint work with
Munshi and Singh. 

03/05 09:45am 
BLOC 302 
Huimin Zhang Shandong University 
Hybrid subconvexity bounds for twists of GL_2 × GL_2 Lfunctions
Subconvexity problem is one of the central topics in analytic number theory. In this talk, we report on hybrid subconvexity bounds for GL_2 × GL_2 RankinSelberg Lfunctions twisted by a primitive Dirichlet character χ modulo a prime power, in the t and depth aspects. This is a joint work with Chenchen Shao. 

03/26 09:45am 
BLOC 302 
Radu Toma University of Bonn 
The supnorm problem for newforms in higher rank
I will present some new results on the supnorm problem in the
level aspect for SL(n). The main novelties are in the geometry of numbers, where we develop a general reduction theory with level structure. Connected to it is an investigation of AtkinLehner operators in higher rank. The outcome is the first subbaseline bound in the level aspect for the size of HeckeMaass cuspidal newforms in unbounded rank. 

04/09 09:45am 
BLOC 302 
Zhining Wei Brown University 
Effective Open Image Theorem for pairs of elliptic curves
In 1972, Serre proved the celebrated Open Image Theorem, claiming that for a nonCM elliptic curve E over Q, the residue modulo $\ell$ Galois representation associated with E is surjective for sufficiently large prime $\ell$. An effective version of this theorem seeks to bound such least nonsurjective prime $\ell$. In the talk, I will review some results concerning the effective version of Serre's Open Image Theorem. Then, I will present a work in progress on the effective open image theorem for pairs of elliptic curves, especially the semistable elliptic curves. This is joint with Tian Wang. 

04/16 09:45am 
BLOC 302 
Eun Hye Lee Texas Christian University 
Subconvexity of Shintani Zeta Functions
Subconvexity problem has been a central interest in analytic number theory for over a century. The strongest possible form of the subconvexity problem is the Lindelof hypothesis, which is a consequence of the RH, in the Riemann zeta function case. There have been many attempts to break convexity for diverse zeta and L functions, usually using the moments method. In this talk, I will introduce the Shintani zeta functions, and present another way to prove a subconvex bound. 

04/23 09:45am 
BLOC 302 
Shifan Zhao The Ohio State University 
Lowlying zeros of Lfunctions attached to Siegel modular forms
The KatzSarnak heuristic predicts that the distribution of lowlying zeros of families of automorphic Lfunctions are governed by certain classical compact groups determined by the family. In this talk I will present some recent progress concerning lowlying zeros of spinor and standard Lfunctions of Siegel modular forms. I will first describe these results in the $k$ (weight) aspect, and then explain how to extend the support of Fourier transforms of test functions by averaging over $k$. I will also discuss applications towards the nonvanishing of central Lvalues. 

04/30 9:45pm 
BLOC 302 
Junxian Li University of California, Davis 
TBA 