Approximate lattices and Ulam stability

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• Simon Machado (ETH Zürich)
• Friday 28 November 2025, 10:15-11:15
• Seminar Room 1, Newton Institute.

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OGGW04 - Stability and probabilistic methods

While classical lattices are central to geometry, approximate lattices offer a generalization that relaxes the subgroup requirement while preserving discreteness and “finite covolume” properties.  Introduced by Yves Meyer in the 1970s for the abelian case (linked to Pisot numbers and quasi-crystals), the theory has recently been successfully extended to all locally compact groups. This talk will provide an overview of this non-abelian structure theory, which relies on a synthesis of additive combinatorics, model theory, dynamics and bounded cohomology. After establishing the fundamentals, I will discuss open problems and highlight a striking connection to uniform Ulam stability. We will explore how the geometry and dynamics of these sets may offer a new perspective on stability questions.

This talk is part of the Isaac Newton Institute Seminar Series series.

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