Approximate lattices: structure and beyond

Abstract: Approximate lattices are aperiodic generalisations of lattices in locally compact groups. Yves Meyer first introduced them in abelian groups before studying them as mathematical models for quasi-crystals. Since then, their structure has been thoroughly investigated in both abelian and non-abelian settings. The primary motivation behind this research was to extend Meyer’s foundational theorem to non-abelian locally compact groups.

This generalisation has now been established, and I will discuss the resulting structure theory. I will highlight certain concepts, including a notion of cohomology that lies between group cohomology and bounded cohomology, which plays a significant role in their study. Additionally, I will formulate open problems and conjectures related to approximate lattices.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

( paper )

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Geometry and topology online

Series comments: You can also find up-to-date information on the seminar homepage - warwick.ac.uk/fac/sci/maths/research/events/seminars/areas/geomtop/

The talks start at 13:30. Talks are typically fifty minutes long, with ten minutes for questions.

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