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SUMMARY:Approximate lattices and Ulam stability - Simon Machado (ETH Züri
 ch)
DTSTART:20251128T101500Z
DTEND:20251128T111500Z
UID:TALK240439@talks.cam.ac.uk
DESCRIPTION:While classical lattices are central to geometry\, approximate
  lattices offer a generalization that relaxes the subgroup requirement whi
 le preserving discreteness and "finite covolume" properties.&nbsp\; Introd
 uced by Yves Meyer in the 1970s for the abelian case (linked to Pisot numb
 ers and quasi-crystals)\, the theory has recently been successfully extend
 ed to all locally compact groups.\nThis talk will provide an overview of t
 his non-abelian structure theory\, which relies on a synthesis of additive
  combinatorics\, model theory\, dynamics and bounded cohomology. After est
 ablishing the fundamentals\, I will discuss open problems and highlight a 
 striking connection to uniform Ulam stability. We will explore how the geo
 metry and dynamics&nbsp\;of these sets may offer a new perspective on stab
 ility questions.
LOCATION:Seminar Room 1\, Newton Institute
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