Existence of full Gabor frames with Schwartz windows on Delone sets equals lower Beurling density >1, with non-uniform Balian-Low theorem for arbitrary point sets and dimensions proven via groupoid and C*-methods.
Almost elementariness and fiberwise amenability for ´ etale groupoids.arXiv: 2011.01182
4 Pith papers cite this work. Polarity classification is still indexing.
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Introduces the equivariant coarse groupoid G(X,Γ) and proves that the equivariant coarse Baum–Connes conjecture for (X,Γ) is equivalent to a groupoid Baum–Connes conjecture, with applications to the equivariant coarse Novikov conjecture.
Minimal ample groupoids exist that are neither almost finite nor purely infinite, including amenable transformation groupoids and new essentially principal ones built from twisted topological groupoid constructions.
Proves that virtual properties including virtually RFRS, virtually (compact) special, virtually CAT(0) cube, and virtually normally poly-free are closed under graph products, with an elementary proof of the underlying strong commensurability theorem.
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Full Gabor frames, its existence problem, and a non-uniform Balian-Low type theorem
Existence of full Gabor frames with Schwartz windows on Delone sets equals lower Beurling density >1, with non-uniform Balian-Low theorem for arbitrary point sets and dimensions proven via groupoid and C*-methods.
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A groupoid approach to the equivariant coarse Baum--Connes conjecture
Introduces the equivariant coarse groupoid G(X,Γ) and proves that the equivariant coarse Baum–Connes conjecture for (X,Γ) is equivalent to a groupoid Baum–Connes conjecture, with applications to the equivariant coarse Novikov conjecture.
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Ample groupoids that are neither almost finite nor purely infinite
Minimal ample groupoids exist that are neither almost finite nor purely infinite, including amenable transformation groupoids and new essentially principal ones built from twisted topological groupoid constructions.
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Virtual inheritance properties of graph products
Proves that virtual properties including virtually RFRS, virtually (compact) special, virtually CAT(0) cube, and virtually normally poly-free are closed under graph products, with an elementary proof of the underlying strong commensurability theorem.