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Seminario del 2020
2020
09 gennaio
Alessio Savini (Università di Bologna)
Seminario interdisciplinare
Lie groups are one of the most fundamental tool in mathematics. They are ubiquitous, starting from mathematical physics, passing through number theory and
landing into the world of dynamical systems.
In this talk I will give a general overview about the definition of Lie group and I will list some of its property. My attention will be mainly focused
on two aspects. I am going to talk about the Iwasawa decomposition of non-compact Lie groups, which can be interpretated as a suitable generalization of
QR-factorization. This decomposition result will allow to study some topological properties of Lie groups. Then I will move to some analytical aspects
related to measure theory. Studying unimodular lattices on the plane we will "compute" the volume of the quotient SL(2,R)/SL(2,Z) in terms of Haar measure.
This will be a very introductory seminar which will be the starting point of a minicourse about Lie groups and representations of lattices.