**2 oct 2018 - 18 dec 2018**

Università degli Studi dell'Insubria

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Università degli Studi dell'Insubria

Dipartimento di Scienza e Alta Tecnologia

Via Valleggio 11, Como

TYPOLOGY OF GROUPS

Prof. Laurent Lafforgue (IHES)

Schedule

October 2, 2018 - December 18, 2018

Each Tuesday, 11:00 - 13:00 and 14:00 - 16:00

room Aula Magna Via Valleggio

Program

1. The notion of real or complex Lie group

2. The splitting of Lie groups in the discrete part and the continuous (connected) part and then the splitting of connected Lie groups into simple groups

3. The algebraic nature of simple groups

4. The splitting of algebraic groups into linear groups and abelian varieties

5. The splitting of linear algebraic groups into unipotent radical and reductive quotient

6. Structure of reductive groups and parametrization by discrete parameters

7. Groups of points of an algebraic group with values in

a. a finite field (which defines the Lie-type finite groups)

b. the fields of real or complex numbers (which defines the main Lie groups)

c. the p-adic fields (which defines p-adic groups)

d. the ring of integers (which defines arithmetic groups)

8. Other families of discrete subgroups of continuous groups

a. Weyl groups and more generally Coxeter groups

Laurent Lafforgue is Permanent Professor at the Institut des Hautes
Études Scientifiques.

In 2002, he received the Fields Medal for his fundamental
contributions to the Langlands program.

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