Dr. Nidal Ali:

Title:
Stability of the generic polynomial of an algebraic number field

Abstract:
Let K be an algebraic number field of degree , A is its ring of integers and { } is a basis of A. Let  be  algebraically independent elements over Q, , and  is the minimal polynomial of  over . The polynomial  is homogeneous of degree , irreducible over  . We will study the stability of  over  i.e the irreducibility of all the iterates of  over .

Dr. Jannis A. Antoniadis :

Title:
On Artin's Conjecture

Abstract:

The talk shall be of informal nature about the conjecture. We are going to discuss the results which are known and describe  the methods used for the proofs in these special cases.

Dr. Nikolaos Diamantis :

Title:
Unitary Hecke module structures on higher-order forms

Abstract:
We define a Hecke action and an inner product on the space of higher-order forms. This inner product induces a unitary Hecke module structure on the space of higher-order forms (joint work with A. Deitmar).

Dr. Badih Ghusayni :

Title:
The Value of the Zeta Function at an Odd Argument

Abstract:
For over 300 years the values of the Zeta function at odd arguments have remained a mystery.  The PSLQ algorithm which is implemented in the Computer Algebra System Maple is considered one of the top ten algorithms of the 20th Century.  We employ PSLQ to discover an Euler-type identity for an odd argument.  A mathematical proof  follows the discovery.

Dr. Kamal Khuri-Makdisi :

Title:

Moduli interpretation of Eisenstein series

Abstract:

I will discuss how to “evaluate” a holomorphic Eisenstein series of arbitrary integral weight k≥1 and level the principal congruence subgroup Gamma(N) at a point p of the modular curve X(N). Here p describes an elliptic curve E, given in Weierstrass form, and its N-torsion E[N]; “evaluating” the Eisenstein series at p is a finite, purely algebraic calculation in the function field of E. Neither infinite series nor other limiting processes are involved.
I will also discuss the algebra of modular forms generated by the Eisenstein series of weight 1. For N≥3, all modular forms of weights ≥2 on Gamma(N) are included in this algebra; I will sketch my recent proof of this theorem. This result allows one to compute equations for X(N) from the data contained in a single (!) elliptic curve E_0 and its N-torsion.
 

Dr. Lloyd Kilford :

Title:
A Gentle Introduction to Overconvergent Modular Forms

Abstract:
In this talk we will give a general and gentle introduction to the subject of overconvergent modular forms, using explicit examples to motivate the theory and showcase some recent results.
 

Dr. Winfried Kohnen : 

Title:
Sign changes of Fourier coefficients of modular forms of half-integral weight

Abstract:
Fourier coefficients of cusp forms, in particular their signs, are quite mysterious. In this talk I would like to report on some recent results regarding sign changes of Fourier coefficients in the half-integral weight case.

Dr. Ramez N Maalouf :

Title
Some Algebraic Aspects for Functional Equations  Associated with Homomorphisms H of Group Actions on .

Abstract:
We consider group homomorphisms, where  and  are two group actions on C and both subgroups of a larger group action G, and the set of all meromorphic functions f that satisfy  for every . Such situations are immediately manifested in Elliptic and (what we call as) Generalized Elliptic Functions that present the simplest examples for such cases and their corresponding functions, where  is either the trivial group (for elliptic functions) or is a multiplicative subgroup of C (for generalized elliptic functions). Other cases in this respect will also be mentioned.
 

Our main interest in this work is more with some algebraic aspects associated with this situation of functional equations, rather than with constructing or studying meromorphic functions that satisfy such equations. We construct an invariance group (a subgroup of G) for the collection F of all meromorphic functions satisfying , and then proceed to some categorical constructions, first of a category associated with objects of the form , and then of a covariant functor from this category into the category of groups. We then discuss aspects of certain cohomology groups associated with this functor.
(joint work with Wissam Raji).

Dr. Tobias Mühlenbruch :

Title:
Classical mechanics and Maass cusp forms

Abstract:
It is well known that Maass cusp forms belong to the quantum mechanical picture of a freely moving particle on the hyperbolic surface H/PSL(2,Z). The connection to the classical mechanics picture is given by the Selberg trace formula.

We present the transfer operator approach to the classical mechanics model:
We introduce a nuclear operator L_s such that any eigenfunction of L_s with eigenvalue $1$ is in 1-1 correspondence to a Maass cusp form with spectral parameter s. In particular, the the Selberg zeta-function can be expressed in terms of the Fredholm determinant of the operator 1-L_s. Moreover, the eigenfunction relates directly to period functions which Lewis and Zagier associated to Maass cusp forms
 

Dr. Yiannis Petridis :

Title:

On the distribution of modular symbols, a survey

Abstract:
In the last 10 years a lot of work by Goldfeld, Diamantis, O'Sullivan, Chinta has been devoted to study Eisenstein series twisted by modular symbols. I will survey my work with Risager on the problem in a simple fashion.

Dr. Wissam Raji :

Title:

Eichler Cohomology of Generalized Modular Forms of Real Weights

Abstract:
We prove Eichler isomorphism theorems for parabolic generalized modular forms of large real weights.  Eichler isomorphism theorems were derived in a joint work with Knopp and Lehner using Stokes' theorem for parabolic generalized modular forms of integer and real weights.  In this talk we show a new proof for the case of large real weights using generalized Poincare series.