Termine

Arithmetic groups, i.e. groups such as GL_n(Z), and their cohomology are of central interest in various areas of mathematics, including topology, geometric group theory and representation theory. In this mini course we aim to give an example based introduction to the relation of these cohomology groups with the cohomology of locally symmetric spaces, to Lie-algebra cohomology, and to automorphic representations, hence establishing a link with arithmetic aspects. We finally will outline what phenomena about the cohomology of arithmetic groups are predicted as a consequence of this together with the deep conjectures about the relation of automorphic forms and Galois representations, known as the Langlands program.

Talk 1: Cohomology of arithmetic groups and locally symmetric spaces
Talk 2: Top-cohomology, modular symbols and operators
Talk 3: Hecke algebras, Hecke eigensystems and automorphic forms
Talk 4: Representation theory of real Lie groups and (g,K)-cohomology
Talk 5: The conjectural relation with motives and Galois representations

Arithmetic groups, i.e. groups such as GL_n(Z), and their cohomology are of central interest in various areas of mathematics, including topology, geometric group theory and representation theory. In this mini course we aim to give an example based introduction to the relation of these cohomology groups with the cohomology of locally symmetric spaces, to Lie-algebra cohomology, and to automorphic representations, hence establishing a link with arithmetic aspects. We finally will outline what phenomena about the cohomology of arithmetic groups are predicted as a consequence of this together with the deep conjectures about the relation of automorphic forms and Galois representations, known as the Langlands program.

Talk 1: Cohomology of arithmetic groups and locally symmetric spaces
Talk 2: Top-cohomology, modular symbols and operators
Talk 3: Hecke algebras, Hecke eigensystems and automorphic forms
Talk 4: Representation theory of real Lie groups and (g,K)-cohomology
Talk 5: The conjectural relation with motives and Galois representations

Arithmetic groups, i.e. groups such as GL_n(Z), and their cohomology are of central interest in various areas of mathematics, including topology, geometric group theory and representation theory. In this mini course we aim to give an example based introduction to the relation of these cohomology groups with the cohomology of locally symmetric spaces, to Lie-algebra cohomology, and to automorphic representations, hence establishing a link with arithmetic aspects. We finally will outline what phenomena about the cohomology of arithmetic groups are predicted as a consequence of this together with the deep conjectures about the relation of automorphic forms and Galois representations, known as the Langlands program.

Talk 1: Cohomology of arithmetic groups and locally symmetric spaces
Talk 2: Top-cohomology, modular symbols and operators
Talk 3: Hecke algebras, Hecke eigensystems and automorphic forms
Talk 4: Representation theory of real Lie groups and (g,K)-cohomology
Talk 5: The conjectural relation with motives and Galois representations

Further information

Arithmetic groups, i.e. groups such as GL_n(Z), and their cohomology are of central interest in various areas of mathematics, including topology, geometric group theory and representation theory. In this mini course we aim to give an example based introduction to the relation of these cohomology groups with the cohomology of locally symmetric spaces, to Lie-algebra cohomology, and to automorphic representations, hence establishing a link with arithmetic aspects. We finally will outline what phenomena about the cohomology of arithmetic groups are predicted as a consequence of this together with the deep conjectures about the relation of automorphic forms and Galois representations, known as the Langlands program.

Talk 1: Cohomology of arithmetic groups and locally symmetric spaces
Talk 2: Top-cohomology, modular symbols and operators
Talk 3: Hecke algebras, Hecke eigensystems and automorphic forms
Talk 4: Representation theory of real Lie groups and (g,K)-cohomology
Talk 5: The conjectural relation with motives and Galois representations

Further information

Arithmetic groups, i.e. groups such as GL_n(Z), and their cohomology are of central interest in various areas of mathematics, including topology, geometric group theory and representation theory. In this mini course we aim to give an example based introduction to the relation of these cohomology groups with the cohomology of locally symmetric spaces, to Lie-algebra cohomology, and to automorphic representations, hence establishing a link with arithmetic aspects. We finally will outline what phenomena about the cohomology of arithmetic groups are predicted as a consequence of this together with the deep conjectures about the relation of automorphic forms and Galois representations, known as the Langlands program.

Talk 1: Cohomology of arithmetic groups and locally symmetric spaces
Talk 2: Top-cohomology, modular symbols and operators
Talk 3: Hecke algebras, Hecke eigensystems and automorphic forms
Talk 4: Representation theory of real Lie groups and (g,K)-cohomology
Talk 5: The conjectural relation with motives and Galois representations