Michael Magee

Durham University Durham University


Convergence of unitary representations


Colloquia Seminar


27th January 2025, 4:00 pm – 5:00 pm
Fry Building, 2.04


Understanding the unitary representations of discrete groups is one of the pervading problems of mathematics. Already in two of its simplest forms it leads to the Fourier transform and to matrix models of quantum mechanics (the integers, and the Heisenberg group, respectively).

For general discrete groups (e.g. free groups or hyperbolic three manifold groups) the general problem is intractable but one way to proceed is via studying ways that finite dimensional representations can converge as their dimension tends to infinity. In some cases, we can sensibly also ask probabilistic questions about random finite dimensional unitary representations of groups. In my talk I'll discuss weak and strong forms of convergence of unitary representations and cover some results at the frontier of our knowledge.





Organiser: Ayalvadi Ganesh

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