1,021 reputation
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bio website math.tamu.edu/~branimir
location College Station, TX
age 29
visits member for 5 years, 2 months
seen 6 hours ago

I'm a noncommutative geometer doing a postdoc at Texas A&M, having just completed my PhD at Caltech.


Aug
26
comment An extension of $K$-theory to topological $^*$-algebras
You can forget about involutions entirely, since the $K$-theory of a $C^\ast$-algebra as a $C^\ast$-algebra (i.e., in terms of projections and unitaries) is identical to its $K$-theory as a Banach algebra (i.e., in terms of idempotents and invertible matrices).
Aug
15
comment Formula for the distance in noncommutative geometry
This certainly takes care of the problem at the base point $x$, but you're still left, in general, with non-differentiability of the distance function on the cut locus of $x$, no?
Aug
15
comment Formula for the distance in noncommutative geometry
@NikWeaver Thank you for the correction. I had a silly idée fixe about approximating in the Lipschitz seminorm, so I just didn't see that it was enough to bound it from above.
Aug
15
revised Formula for the distance in noncommutative geometry
Corrected major error in answer to Question 1, thanks to Nik Weaver's comment.
Aug
15
awarded  Yearling
Aug
14
awarded  Revival
Aug
14
revised Formula for the distance in noncommutative geometry
deleted 472 characters in body
Aug
14
comment Realisation of the noncommutative torus as a universal $ C^{*} $-algebra
+1 I'm very late to the party, but this is an excellent answer.
Aug
14
answered Formula for the distance in noncommutative geometry
May
16
answered Name for construction on two vector bundles
Apr
26
comment A survey for various $K$-homology theories and their relationship
A possible first step towards this might be found in Hilsum's notion of bordism of unbounded KK-cycles---nothing to do with cobordism of bounded cycles---which has recently been developed further by Deeley--Goffeng--Mesland: arxiv.org/abs/1503.07398
Mar
22
awarded  Announcer
Feb
27
awarded  Announcer
Jan
4
comment Correspondences as generalized morphism between $C^*$-algebras
See, for instance, mathoverflow.net/questions/82871/… and similar discussions on MathOverflow and Math.SE. I suppose the point is that naive $\ast$-homomorphisms $A \to B$ aren't necessarily all that natural in the nonunital case, when seen through the guiding lens of Gelfand–Naimark.
Jan
4
comment Correspondences as generalized morphism between $C^*$-algebras
I think that the heart of the matter here is that Gelfand–Naimark duality for locally compact Hausdorff spaces is a subtle business. One way to cut the Gordian knot is Woronowicz's approach, which identifies a continuous map $f: X \to Y$ as inducing a nondegenerate $\ast$-homomorphism $f^t : C_0(Y) \to M(C_0(X))$, where $M(C_0(X))$ denotes the multiplier algebra of $C_0(X)$; indeed, if $\phi : A \to M(B)$ is a nondegenerate $\ast$-homomorphism, so that $\phi(A)B$ is dense in $B$, then the induced bimodule ${}_A B_B$ satisfies both nondegeneracy and fullness.
Jan
4
comment Correspondences as generalized morphism between $C^*$-algebras
I completely forgot; thanks for reminding me. There is a corresponding condition on the right, which says that $(E,E)$ should be dense in $A$; again, it holds for ${}_A A_A$ precisely because $A$ admits an approximate unit.
Jan
3
comment Correspondences as generalized morphism between $C^*$-algebras
In particular, observe that the “trivial line bundle” ${}_A A_A$ satisfies this condition precisely because $A$ admits an approximate unit.
Jan
3
comment Correspondences as generalized morphism between $C^*$-algebras
In the nonunital case, one often imposes the additional condition on ${}_A E_B$ that $A E$ be dense in $E$; this should take care of the issue in your edit.
Jan
3
awarded  Announcer
Jan
1
comment Commutative spectral triples
...firmly from the perspective of mathematical physics.