This web page provides the links to the videos and descriptions of these videos associated to the listed activities of mine.
Kernels for Langlands' Transfer and Nonlinear Poisson Formulas 


Lecture 1: Spectral Decomposition and Fourier Transform Prof. L.Lafforgue (IHES) QuickTime, 55m24s 
Classical spectral decomposition, both local and global, are introduced. In particular, when applied to the general linear group $GL_r$, this leads to the local and global $L$ and $\varepsilon$factors, once we enlarge the base space from $GL_r$ to $M_r$, the space of $r\times r$matrices. Recorded from 10:10am of April 26, 2013, this is the first talk given at the symposium on 'Automorphic Functions and Arithmetic Geometry', held at the Graduate School of Mathematics, Kyushu University, Fukuoka, Japan. 

Lecture 2: $L$factors and $\epsilon$Factors Prof. L.Lafforgue (IHES) QuickTime, 54m05s 
Local and global $L$ and $\varepsilon$factors are introduced and their standard properties are summarized. The results are classical, but the way they are presented here is original. Recorded from 11:10am of April 26, 2013, this is the 2th talk given at the symposium on 'Automorphic Functions and Arithmetic Geometry', held at the Graduate School of Mathematics, Kyushu University, Fukuoka, Japan. 

Lecture 3: Langlands Automorphic Transfor Conjecture Prof. L.Lafforgue (IHES) QuickTime, 1h00m57s 
Langlands' automorphic transfer conjecture and its consequences are presented. The transfer rules by a transfer representation $\rho$ proposed by Langlands lead to the definition of non linear $L$functions, whose global propoerties are deduced from the automorphic transfer conjecture. Recorded from 10:10am of April 27, 2013, this is the 3th talk given at the symposium on 'Automorphic Functions and Arithmetic Geometry', held at the Graduate School of Mathematics, Kyushu University, Fukuoka, Japan. 

Lecture 4: $(L,\rho)$Fourier Transforms Prof. L.Lafforgue (IHES) QuickTime, 59m42s 
New types of function spaces and of $(\rho,L)$Fourier transforms on these spaces are associated to transfer representations $\rho$, through local spectral decomposition. Nonlinear Poisson formulas without boundary terms are presented and are deduced from Langlands' automorphic transfer conjecture. Recorded from 11:10am of April 27, 2013, this is the 4th talk given at the symposium on 'Automorphic Functions and Arithmetic Geometry', held at the Graduate School of Mathematics, Kyushu University, Fukuoka, Japan. 

Lecture 5: NonLinear Poisson Formulas Prof. L.Lafforgue (IHES) QuickTime, 43m56s 
The nonlinear Poisson formulas without boundary terms introduced in the previous lecture are conjecturally generalised to nonlinear Poisson formulas with boundary terms. Recorded from 10:10am of April 28, 2013, this is the 5th talk given at the symposium on 'Automorphic Functions and Arithmetic Geometry', held at the Graduate School of Mathematics, Kyushu University, Fukuoka, Japan. 

Lecture 6: Kerner of Langlands' Transfer Prof. L.Lafforgue (IHES) QuickTime, 1h16m45s 
The notion of 'kernels' of Langlands' automorphic tranfer is introduced. As an application, Langlands' automorphic tranfer conjecture is deduced from the nonlinear Poisson formulas. Recorded from 11:00am of April 28, 2013, this is the last talk given at the symposium on 'Automorphic Functions and Arithmetic Geometry', held at the Graduate School of Mathematics, Kyushu University, Fukuoka, Japan. 
Kyushu Joint Seminar 


Introduction to Langlands Programme Prof. L.Lafforgue (IHES) QuickTime, 1h26m11s 
This talk presents the Langlands programme as a set of conjectures linking together two (or even three) mathematical theories which are a priori completely different: (1) the theory of the finite separable extensions of a base field which happens to be a global field, (2) the conjectural theory of pure motives over such a global field, related to the previous theory through the ladic cohomology functors, (3) the theory of automorphic representations of linear groups (or more generally reductive groups) over such a field. Recorded from 16:00, May 1, 2013, this is the talk of Prof. Lafforgue given at the First Kyushu Joint Seminar, held at the Graduate School of Mathematics, Kyushu University, Fukuoka, Japan. 