Τρίτη 23 Μαρτίου, 11:15 – 12:00. Η ομιλία θα γίνει ONLINE.
Ομιλητής: Tom Kempton (University of Manchester)
Τίτλος: How to count things using ergodic theory
Περίληψη: Given a space X and a transformation T : X → X, ergodic theory involves using measures to study orbits (x, T(x), T2(x),…) of the dynamical system (X,T). Loosely, you can think of the ergodic theorem as being a bit like the strong law of large numbers, except instead of studying a sequence of independent events you study orbits of the dynamical system.
None of this seems to have anything to do with counting things. We will show the link with some examples, including counting how many Pythagorean triples (a,b,c) there are with c < n for large n. Towards the end of the talk I will introduce some of my own work which uses these counting ideas to study the dimension of a family of fractal measures.
No knowledge of ergodic theory, number theory or fractal geometry will be assumed.