Fall 2005 schedule of speakers.

• Speaker John Bryk
• Title Introduction to the p-Adics
• Time/place Tuesday, 12/13/2005 2:00pm in Hill 425
• Abstract This is a basic introduction to the p-adic numbers. We will introduce the p-adics as the completion of the rationals with respect to the p-adic absolute value. The algebraic and topological properties of these fields will be discussed. We will cover topics and applications such as Hensel's lemma, field extensions of the p-adics, and p-adic interpolation.

• Speaker Satadal Ganguly
• Title Central values of L-functions of Hecke characters
• Time/place Tuesday, 12/6/2005 2:00pm in Hill 425
• Abstract For weight one, the L-functions don't vanish at the central point unless forced to by the functional equation. I shall give a sketch of a proof of this fact due to Rohrlich and Montgomery. For higher weights, the situation is different and I shall describe the work of Rodriguez-Villegas in this context, and some of my own.

• Speaker Ritabrata Munshi, Princeton University
• Title Rational points on elliptic surfaces,II
• Time/place Tuesday, 11/29/2005 2:00pm in Hill 425
• Abstract The generalized riemann hypothesis predicts existence of rational points on some elliptic surfaces of generic rank 0. attempts to remove the assumption of the GRH give rise to interesting problems in analytic number theory. i will briefly describe how far i have been able to overcome these obstacles.

• Speaker Ritabrata Munshi, Princeton University
• Title Rational points on elliptic surfaces
• Time/place Tuesday, 11/15/2005 2:00pm in Hill 425
• Abstract The generalized riemann hypothesis predicts existence of rational points on some elliptic surfaces of generic rank 0. attempts to remove the assumption of the GRH give rise to interesting problems in analytic number theory. i will briefly describe how far i have been able to overcome these obstacles.

• Speaker Satadal Ganguly
• Title The Arithmetic of The Central Value of L-Functions
• Time/place Tuesday, 11/08/2005 2:00pm in Hill 425
• Abstract I shall try to give some background on why central values are important as well as explain some of the basic techniques like Galois averaging that goes into investigating central values.

• Speaker Roman Holowinsky
• Title Attempts at Unique Ergodicity
• Time/place Tuesday, 11/01/2005 2:00pm in Hill 425
• Abstract I will restate the Quantum Unique Ergodicity conjecture for SL(2,Z) in terms of shifted convolution sums and summarize some analytic methods that have been applied in the hopes of showing Quantum Unique Ergodicity.

• Speaker Goran Djankovic
• Title Generalized Ramanujan-Selberg Conjecture (Part II)
• Time/place Tuesday, 10/25/2005 2:00pm in Hill 425
• Abstract We will state the Ramanujan Conjectures and reformulate them in terms of Representation Theory. This will lead us into the relevant Langlands functoriality, Generalized Ramanujan-Selberg Conjecture and functorial lifts. May combine with some analytic techniques.

• Speaker Goran Djankovic
• Title Generalized Ramanujan-Selberg Conjecture
• Time/place Tuesday, 10/18/2005 2:00pm in Hill 425
• Abstract We will state the Ramanujan Conjectures and reformulate them in terms of Representation Theory. This will lead us into the relevant Langlands functoriality, Generalized Ramanujan-Selberg Conjecture and functorial lifts. May combine with some analytic techniques.

• Speaker Prof. M. Ram Murty (Queen's University)
• Title Multiple Hurwitz Zeta Functions
• Time/place Tuesday, 10/11/2005 2:00pm in Hill 425
• Abstract We will discuss the analytic continuation of multiple Hurwitz zeta functions after giving a brief overview of the theory of multiple zeta values.

• Speaker Goran Djankovic
• Title Selberg's Eigenvalue Conjecture
• Time/place Tuesday, 10/04/2005 2:00pm in Hill 425
• Abstract Background and description of Selberg's Conjecture(1965). Exceptional eigenvalues, Selberg Kloosterman-zeta function, and Density Theorems.

• Speaker Roman Holowinsky
• Title Quantum Mechanics and Chaos
• Time/place Tuesday, 09/27/2005 2:00pm in Hill 425
• Abstract Mechanics Interpretation of Quantum Unique Ergodicity Conjecture. Description of classically regular and chaotic systems and where chaos can be seen in quantum mechanics. Hamiltonian flow as we'll describe on X=SL(2,Z)\H is known to be classically chaotic, yet numerical evidence from its quantization suggests that it is a regular system.

• Speaker Roman Holowinsky
• Title Introduction to Spectral Theory of Automorphic forms
• Time/place Tuesday, 09/20/2005 2:00pm in Hill 425
• Abstract The necessary fundamentals for describing the Quantum Unique Ergodicity Conjecture. Automorphic forms, Spectral decomposition, etc.

• Speaker Prof. Henryk Iwaniec
• Title Introduction to Elliptic Curves
• Time/place Tuesday, 09/13/2005 2:00pm in Hill 425
• Abstract Basic facts about Elliptic Curves including conjectures and what is known about the rank of an Elliptic Curve.