Growth of symmetry groups by Arne Smeets

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Title Growth of symmetry groups
Lecturer Arne Smeets
Type Lecture
Time and location 10:00 - 11:00 @ van Ruthzaal

About Growth of symmetry groups

I will discuss the notion of growth rate for finitely generated groups, which yields some kind of 'symmetry measure'. Some groups have polynomial growth; a famous theorem of Gromov characterises these groups. Many groups have maximal - i.e. exponential - growth rate. Milnor asked in 1968 whether there exist groups exhibiting 'intermediate growth' (i.e. between polynomial and exponential), and Grigorchuk managed to construct an example of such a group in 1984. We will explore some of these important ideas, take a look at Grigorchuk's famous example, and find out that open problems still abound!

About Arne Smeets

Arne Smeets was born in 1986 in Leuven, Belgium, on Saint Nicholas day - i.e. on December 6, even though some people seem to (erroneously) believe that this should be celebrated on December 5. He studied mathematics in Leuven and Paris, graduating in 2010, and obtained his PhD in 2014 with a dissertation entitled 'Cohomological contributions to the study of rational points on algebraic varieties'.

After postdoctoral research in London and Bonn, he became an assistant professor at Radboud University in 2016. He does research in arithmetic geometry, enjoys teaching various courses and supervising students, and represents pure mathematics in 'De Jonge Akademie' (KNAW). He is the proud father of a 2 year old daughter called Ada; she knows how to count to 10 already, but invariably skips 4.