
Date Time 
Location  Speaker 
Title – click for abstract 

09/08 1:00pm 
BLOC 220 
Lenny Fukshansky Claremont McKenna College 
On some algebraic constructions of extremal lattices
A lattice in a Euclidean space is called extremal if it is a local maximum of the packing density function in its dimension. An old theorem of Voronoi gives a beautiful characterization of extremal lattices in terms of their geometric properties. We will review Voronoi's criterion, and then apply it to exhibit families of extremal lattices coming from some algebraic and arithmetic constructions. Abstract 

09/27 1:45pm 
BLOC 220 
Oguz Gezmis Texas A&M University 
De Rham isomorphism for Drinfeld modules over Tate algebras
Two main concepts of the arithmetic on function fields are elliptic (Drinfeld) modules and LSeries. On 1970's, Drinfeld introduced elliptic modules which can be seen as an analogue of elliptic curves in function field setting and D. Goss introduced a new type of LSeries as an anologue of Rieamann Zeta Function. In 2012, Pellarin defined an Lseries in Tate algebras which is a deformation of Goss's Lseries. In order to give new identities for Pellarin LSeries, Angles, Pellarin and Tavares Ribeiro introduced Drinfeld modules over Tate algebras. In this talk, we talk about Drinfeld modules over Tate algebras of arbitrary rank. We also prove De Rham isomorphism for these modules under some conditions. Finally, we prove Legendre's Relation under this new setting. This is joint work with Matthew A. Papanikolas. Abstract 

10/13 1:00pm 
BLOC 605AX 
Dinesh Thakur University of Rochester 
Multizeta values and related structures in the function field setting
We will introduce multizeta and compare the number field situation with the function field situation. Abstract 

10/18 1:45pm 
BLOC 220 
Junehyuk Jung Texas A&M University 
Counting immersed totally geodesic surfaces via arithmetic means
The prime geodesic theorem allows one to count the number of closed geodesics having length less than X in a given hyperbolic manifold. As a naive generalization of the prime geodesic theorem, we are interested in the the number of immersed totally geodesic surfaces in a given hyperbolic manifold. I am going to talk about this question when the underlying hyperbolic manifold is an arithmetic hyperbolic $3$manifold corresponding to a Bianchi group SL(2,O_{d}), where O_{d} is the ring of integers of Q[sqrt{d}] for some positive integer d. Abstract 

11/01 1:45pm 
BLOC 220 
John Doyle Louisiana Tech University 
Dynamical modular curves and strong uniform boundedness
In an unpublished 1996 preprint, Nguyen and Saito proved the strong uniform boundedness conjecture for torsion points on elliptic curves over function fields by reducing the problem to that of showing that the gonalities of the modular curves Y_1(n) tend to infinity. By studying the geometry of dynamical modular curves, we have recently proven uniform boundedness of preperiodic points for certain interesting families of polynomial maps over function fields. I will discuss this result as well as a consequence for the dynamical uniform boundedness conjecture over number fields, originally posed by Morton and Silverman. This is joint work with Bjorn Poonen. Abstract 

11/15 1:45pm 
BLOC 220 
Riad Masri Texas A&M University 
Inequalities satisfied by the Andrews smallest parts function
I will discuss a proof of recent conjectures of Chen concerning inequalities satisfied by the Andrews smallest parts function. The proof relies on a new method for bounding coefficients of weak Maass forms which are given as finite sums of singular moduli. This is joint work with Maddie Locus. Abstract 

11/29 1:45pm 
BLOC 220 
Brad Rodgers University of Michigan 
On the distribution of RudinShapiro polynomials
RudinShapiro polynomials are a special sequence of trigonometric polynomials with all coefficients equal to 1 or 1 which do not become too large. In this talk I will discuss conjectures of B. Saffari and H. Montgomery regarding the distribution of these polynomials, and outline how these conjectures were resolved by making use of an analogy to random walks on compact groups. Prerequisites will be kept to a minimum. Abstract 

12/06 1:45pm 
BLOC 220 
Shin Hattori Kyushu University 
Duality of Drinfeld modules and Padic properties of Drinfeld modular forms
Let p be a rational prime, q>1 a ppower and P a nonconstant irreducible polynomial in F_q[t]. The notion of Drinfeld modular form is an analogue over F_q(t) of that of elliptic modular form. On the other hand, following the analogy with padic elliptic modular forms, Vincent defined Padic Drinfeld modular forms as the Padic limits of Fourier expansions of Drinfeld modular forms. Numerical computations suggest that Drinfeld modular forms should enjoy deep Padic structures comparable to the elliptic analogue, while at present their Padic properties are far less well understood than the padic elliptic case.
In this talk, I will explain how basic properties of Padic Drinfeld modular forms are obtained from the duality theories of Taguchi for Drinfeld modules and finite vmodules. Abstract 