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location University of Maryland
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visits member for 2 years, 8 months
seen Dec 19 at 23:03

I am a PhD student at the University of Maryland working on tilings and their relationship to harmonic analysis and noncommutative geometry.


Dec
7
comment Can any Delone set be approximated by a model set?
I make no comment on what the spelling ought to be, nor do I have any power over how it is generally used, as this type of choice is made over time, often somewhat arbitrarily, by the community at large...
Dec
7
comment Can any Delone set be approximated by a model set?
The vast majority of recent papers in the theory of tilings use the spelling Delone, although the spelling Delaunay can be found in some older papers. Examples: arxiv.org/abs/1411.0578, arxiv.org/abs/1401.3725, arxiv.org/abs/1407.1787.
Dec
7
comment Can any Delone set be approximated by a model set?
I think that's right? I've seen both spellings in papers before.
Dec
6
revised Can any Delone set be approximated by a model set?
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Dec
6
comment Can any Delone set be approximated by a model set?
Edited to include complete definition of $\Lambda_W.$ A cut and project set (or model set) is any set of the same form as $\Lambda_W$ above, where we can vary the lattice $L,$ the subspace $H,$ and the window $W,$ so long as $H$ remains in irrational position w.r.t. $L.$ A Meyer set is any subset of a model set.
Dec
6
revised Can any Delone set be approximated by a model set?
added 135 characters in body
Dec
6
asked Can any Delone set be approximated by a model set?
Sep
29
answered Projective modules over noncommutative tori?
Sep
26
comment Morita Equivalence of Full Corners in $C^*$-algebras
Thanks Alain - suppose I'm given a projection in $\mathcal{A}$ or in $M_n(\mathcal{A}).$ Based on this method, is it easy to construct a projection in $M_k(\mathcal{B})$ that it gets mapped to under this isomorphism?
Sep
26
asked Morita Equivalence of Full Corners in $C^*$-algebras
Sep
24
awarded  Autobiographer
Sep
2
awarded  Enlightened
Sep
2
awarded  Nice Answer
Aug
6
revised Generators of the $ K_{0} $-group of the non-commutative torus $ A_{\theta} $ with $ \theta \in \mathbb{Q} $ (i.e. rational rotation algebra)
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Aug
4
revised K-theory for the $C^*-$algebra of the continuous functions on the $2-$torus and the Bott projection
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Aug
4
answered K-theory for the $C^*-$algebra of the continuous functions on the $2-$torus and the Bott projection
Aug
4
revised Generators of the $ K_{0} $-group of the non-commutative torus $ A_{\theta} $ with $ \theta \in \mathbb{Q} $ (i.e. rational rotation algebra)
added 6 characters in body
Aug
4
comment Generators of the $ K_{0} $-group of the non-commutative torus $ A_{\theta} $ with $ \theta \in \mathbb{Q} $ (i.e. rational rotation algebra)
Look at Theorem 3.6 in Luef's paper. This gives an explicit construction of such projections, which is explicit in the sense that it gives a power series type expansion in terms of products of the generators of the rotation algebra. This is somewhat different than the presentation of Rieffel's original projection, which used functional calculus.
Aug
4
comment Generators of the $ K_{0} $-group of the non-commutative torus $ A_{\theta} $ with $ \theta \in \mathbb{Q} $ (i.e. rational rotation algebra)
In general, given a finitely generated projective module with a standard module frame, there is a procedure for constructing the associated projection. Luef's paper above essentially gives what you're asking for, although it is phrased partially in frame theoretic language since this is the easiest way to describe standard module frames for these modules.
Aug
4
answered Generators of the $ K_{0} $-group of the non-commutative torus $ A_{\theta} $ with $ \theta \in \mathbb{Q} $ (i.e. rational rotation algebra)