Damien Simon - 14h00 - Classifying reductive algebraic groups

Salle Grisvard, IHP, Paris

Reductive algebraic groups are ubiquitous in areas such as geometric representation theory, geometric invariant theory, number theory... It is absolutely

outstanding that such objects have a perfectly understood classification.

I will give the main ideas of how this classification works by building intuition from the notion of a root system from the theory of semi-simple Lie algebras,

and then introduce the root datum attached to a reductive algebraic group. I will illustrate all the notions and subtleties appearing in the theory with the

groups GL_1, GL_2, SL_2 and PGL_2. If time allows I will discuss the representation theoretic aspect and introduce the so-called Langlands dual of a reductive

group and hopefully explain some properties of this (mysterious) duality.

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