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Documents  11F70 | enregistrements trouvés : 12

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Let $p$ be a prime number and $F$ be a non-archimedean field with finite residue class field of characteristic $p$. Understanding the category of Iwahori-Hecke modules for $SL_2(F)$ is of great interest in the study of $p$-modular smooth representations of $SL_2(F)$, as these modules naturally show up as spaces of invariant vectors under the action of the standard pro-$p$-Iwahori subgroup. In this talk, we will discuss a work in progress in which we aim to classify all non-trivial extensions between these modules and to compare them with their analogues for $p$-modular smooth representations of $SL_2(F)$ and with their Galois counterpart in the setting of the local Langlands correspondences in natural characteristic. Let $p$ be a prime number and $F$ be a non-archimedean field with finite residue class field of characteristic $p$. Understanding the category of Iwahori-Hecke modules for $SL_2(F)$ is of great interest in the study of $p$-modular smooth representations of $SL_2(F)$, as these modules naturally show up as spaces of invariant vectors under the action of the standard pro-$p$-Iwahori subgroup. In this talk, we will discuss a work in progress in ...

11F70 ; 11F85 ; 20C08 ; 20G05 ; 22E50

Our first purpose is to show how aspects of the representation theory of (non-amenable) algebraic groups can be utilized to derive effective ergodic theorems for their actions. Our second purpose is to demonstrate some the many interesting applications that ergodic theorems with a rate of convergence have in a variety of problems. We will start by a discussion of property $T$ and show how to extend the spectral estimates it provides considerably beyond their usual formulations. We will also show how to derive best possible spectral estimates via representation theory in some cases. In turn, such spectral estimates will be used to derive effective ergodic theorems. Finally we will show how the rate of convergence in the ergodic theorem implies effective solutions in a host of natural problems, including the non-Euclidean lattice point counting problem, fast equidistribution of lattice orbits on homogenous spaces, and best possible exponents of Diophantine approximation on homogeneous algebraic varieties. Our first purpose is to show how aspects of the representation theory of (non-amenable) algebraic groups can be utilized to derive effective ergodic theorems for their actions. Our second purpose is to demonstrate some the many interesting applications that ergodic theorems with a rate of convergence have in a variety of problems. We will start by a discussion of property $T$ and show how to extend the spectral estimates it provides considerably ...

37A30 ; 37A15 ; 37P55 ; 11F70

Our first purpose is to show how aspects of the representation theory of (non-amenable) algebraic groups can be utilized to derive effective ergodic theorems for their actions. Our second purpose is to demonstrate some the many interesting applications that ergodic theorems with a rate of convergence have in a variety of problems. We will start by a discussion of property $T$ and show how to extend the spectral estimates it provides considerably beyond their usual formulations. We will also show how to derive best possible spectral estimates via representation theory in some cases. In turn, such spectral estimates will be used to derive effective ergodic theorems. Finally we will show how the rate of convergence in the ergodic theorem implies effective solutions in a host of natural problems, including the non-Euclidean lattice point counting problem, fast equidistribution of lattice orbits on homogenous spaces, and best possible exponents of Diophantine approximation on homogeneous algebraic varieties. Our first purpose is to show how aspects of the representation theory of (non-amenable) algebraic groups can be utilized to derive effective ergodic theorems for their actions. Our second purpose is to demonstrate some the many interesting applications that ergodic theorems with a rate of convergence have in a variety of problems. We will start by a discussion of property $T$ and show how to extend the spectral estimates it provides considerably ...

37A30 ; 37A15 ; 37P55 ; 11F70

Our first purpose is to show how aspects of the representation theory of (non-amenable) algebraic groups can be utilized to derive effective ergodic theorems for their actions. Our second purpose is to demonstrate some the many interesting applications that ergodic theorems with a rate of convergence have in a variety of problems. We will start by a discussion of property $T$ and show how to extend the spectral estimates it provides considerably beyond their usual formulations. We will also show how to derive best possible spectral estimates via representation theory in some cases. In turn, such spectral estimates will be used to derive effective ergodic theorems. Finally we will show how the rate of convergence in the ergodic theorem implies effective solutions in a host of natural problems, including the non-Euclidean lattice point counting problem, fast equidistribution of lattice orbits on homogenous spaces, and best possible exponents of Diophantine approximation on homogeneous algebraic varieties. Our first purpose is to show how aspects of the representation theory of (non-amenable) algebraic groups can be utilized to derive effective ergodic theorems for their actions. Our second purpose is to demonstrate some the many interesting applications that ergodic theorems with a rate of convergence have in a variety of problems. We will start by a discussion of property $T$ and show how to extend the spectral estimates it provides considerably ...

37A30 ; 37A15 ; 37P55 ; 11F70

Our first purpose is to show how aspects of the representation theory of (non-amenable) algebraic groups can be utilized to derive effective ergodic theorems for their actions. Our second purpose is to demonstrate some the many interesting applications that ergodic theorems with a rate of convergence have in a variety of problems. We will start by a discussion of property $T$ and show how to extend the spectral estimates it provides considerably beyond their usual formulations. We will also show how to derive best possible spectral estimates via representation theory in some cases. In turn, such spectral estimates will be used to derive effective ergodic theorems. Finally we will show how the rate of convergence in the ergodic theorem implies effective solutions in a host of natural problems, including the non-Euclidean lattice point counting problem, fast equidistribution of lattice orbits on homogenous spaces, and best possible exponents of Diophantine approximation on homogeneous algebraic varieties. Our first purpose is to show how aspects of the representation theory of (non-amenable) algebraic groups can be utilized to derive effective ergodic theorems for their actions. Our second purpose is to demonstrate some the many interesting applications that ergodic theorems with a rate of convergence have in a variety of problems. We will start by a discussion of property $T$ and show how to extend the spectral estimates it provides considerably ...

37A30 ; 37A15 ; 37P55 ; 11F70

Multi angle  Lecture 4: The relative trace formula
Offen, Omer (Auteur de la Conférence) | CIRM (Editeur )

In joint work with Hiraku Atobe, we determine the theta lifting of irreducible tempered representations for symplectic-metaplectic­orthogonal and unitary dual pairs in terms of the local Langlands correspondence. The main new tool for proving our result is the recently established local Gross-Prasad conjecture.

11F27 ; 11F70 ; 22E50

This is a joint work with J. Cogdell and T.-L. Tsai. I will report on the progress made in proving the equality of Artin epsilon factors for exterior and symmetric square L-functions with those on the representation theoretic side through the local Langlands correspondence. The equality for L-functions has already been established by Henniart. I will show how the equality can be proved if one has the stability of these factors under highly ramified twists for supercuspidal representations. I will then discuss the stability question for supercuspidals by discussing how it can be deduced from a generalization of germ expansions of Jacquet and Ye from Bessel functions to certain partial Bessel functions. I will elaborate by explaining the stability in the case of GL(2) through general lemmas proved so far. This is a joint work with J. Cogdell and T.-L. Tsai. I will report on the progress made in proving the equality of Artin epsilon factors for exterior and symmetric square L-functions with those on the representation theoretic side through the local Langlands correspondence. The equality for L-functions has already been established by Henniart. I will show how the equality can be proved if one has the stability of these factors under highly ...

11F66 ; 11F70 ; 11F80 ; 22E50

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