We will start by briefly recalling some of the tools from analytic number theory which go into the study of L-functions. This will include the summation formula, the trace formula (Petersson/Kuznetsov) and the circle method. The main focus will be the subconvexity problem (and its applications). We will briefly recall the ideas of Weyl and Burgess, and then in some detail cover the amplification technique as developed by Duke, Friedlander and Iwaniec. We will also discuss the works of Michel and his collaborators. After discussing the scopes and shortfalls of the amplification technique, we will move towards more current techniques. The ultimate goal will be to discuss the status of GL(3) subconvexity.

We will start by briefly recalling some of the tools from analytic number theory which go into the study of L-functions. This will include the summation formula, the trace formula (Petersson/Kuznetsov) and the circle method. The main focus will be the subconvexity problem (and its applications). We will briefly recall the ideas of Weyl and Burgess, and then in some detail cover the amplification technique as developed by Duke, Friedlander and Iwaniec. We will also discuss the works of Michel and his collaborators. After discussing the scopes and shortfalls of the amplification technique, we will move towards more current techniques. The ultimate goal will be to discuss the status of GL(3) subconvexity.

We will start by briefly recalling some of the tools from analytic number theory which go into the study of L-functions. This will include the summation formula, the trace formula (Petersson/Kuznetsov) and the circle method. The main focus will be the subconvexity problem (and its applications). We will briefly recall the ideas of Weyl and Burgess, and then in some detail cover the amplification technique as developed by Duke, Friedlander and Iwaniec. We will also discuss the works of Michel and his collaborators. After discussing the scopes and shortfalls of the amplification technique, we will move towards more current techniques. The ultimate goal will be to discuss the status of GL(3) subconvexity.

We will start by briefly recalling some of the tools from analytic number theory which go into the study of L-functions. This will include the summation formula, the trace formula (Petersson/Kuznetsov) and the circle method. The main focus will be the subconvexity problem (and its applications). We will briefly recall the ideas of Weyl and Burgess, and then in some detail cover the amplification technique as developed by Duke, Friedlander and Iwaniec. We will also discuss the works of Michel and his collaborators. After discussing the scopes and shortfalls of the amplification technique, we will move towards more current techniques. The ultimate goal will be to discuss the status of GL(3) subconvexity.

Let $(Q, q)$ be a inner product space over a commutative ring $R$, and consider the Dickson-Siegel-Eichler-Roy's subgroup of the orthogonal group $O_R(Q \perp H(R)^n)$, $n \geq 1$. We show that it is a normal subgroup of $O_R(Q \perp H(R)^n)$, for all $n$, except when $n = 2$. This is a joint work with A.A. Ambily.

We will start by briefly recalling some of the tools from analytic number theory which go into the study of L-functions. This will include the summation formula, the trace formula (Petersson/Kuznetsov) and the circle method. The main focus will be the subconvexity problem (and its applications). We will briefly recall the ideas of Weyl and Burgess, and then in some detail cover the amplification technique as developed by Duke, Friedlander and Iwaniec. We will also discuss the works of Michel and his collaborators. After discussing the scopes and shortfalls of the amplification technique, we will move towards more current techniques. The ultimate goal will be to discuss the status of GL(3) subconvexity.

Let E be an elliptic curve, over a number field K, without complex multiplication. A theorem of Serre says that the image of the Galois representation of the absolute Galois group of K on the l-adic Tate module T_l(E) has open image in GL_2(Z_l). We shall give an outline of Serre's original proof of this theorem, emphasizing the ideas involved.

We will start by briefly recalling some of the tools from analytic number theory which go into the study of L-functions. This will include the summation formula, the trace formula (Petersson/Kuznetsov) and the circle method. The main focus will be the subconvexity problem (and its applications). We will briefly recall the ideas of Weyl and Burgess, and then in some detail cover the amplification technique as developed by Duke, Friedlander and Iwaniec. We will also discuss the works of Michel and his collaborators. After discussing the scopes and shortfalls of the amplification technique, we will move towards more current techniques. The ultimate goal will be to discuss the status of GL(3) subconvexity.

We will start by briefly recalling some of the tools from analytic number theory which go into the study of L-functions. This will include the summation formula, the trace formula (Petersson/Kuznetsov) and the circle method. The main focus will be the subconvexity problem (and its applications). We will briefly recall the ideas of Weyl and Burgess, and then in some detail cover the amplification technique as developed by Duke, Friedlander and Iwaniec. We will also discuss the works of Michel and his collaborators. After discussing the scopes and shortfalls of the amplification technique, we will move towards more current techniques. The ultimate goal will be to discuss the status of GL(3) subconvexity.

We will give a construction to state a conjecture of Gan, Gross and Prasad about generic representations in L-Packets. We will use this construction to give a new proof of the classification of the Knapp-Stein R group associated to a unitary unramified character of a torus. Finally we prove the conjecture in a special case.