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13397
bio website sbseminar.wordpress.com
location Bloomington, Indiana
age 33
visits member for 4 years, 6 months
seen 2 hours ago
Assistant Professor at Indiana University, working on tensor categories and their relationships to operator algebras and topology.

14h
comment What is Chern-Simons theory expected to assign to a point?
@AndréHenriques: I'm confused, don't you have to modify the notion of center? In your talk you make the point that you need to restrict to continuous half-braidings. Or did I misunderstand?
14h
answered What is Chern-Simons theory expected to assign to a point?
1d
awarded  Popular Question
2d
accepted Are the higher homotopy groups of the Hawaiian earring trivial?
Apr
20
awarded  Nice Question
Apr
20
comment Are the higher homotopy groups of the Hawaiian earring trivial?
Also available publicly via an author's website
Apr
20
asked Are the higher homotopy groups of the Hawaiian earring trivial?
Mar
17
comment Is the category of spherical fusion categories regular? (i.e. is image factorisation possible?)
There's a 2-category of tensor categories, tensor functors, and tensor natural transformations. You're talking about a 1-category, so do you mean tensor functors up to natural isomorphism?
Mar
17
comment Is the category of spherical fusion categories regular? (i.e. is image factorisation possible?)
Do you mean functors up to equivalence? Otherwise it's a 2-category, not a category.
Mar
3
awarded  Nice Answer
Mar
1
awarded  Nice Question
Mar
1
revised Operator Theoretical Models for $(K(\mathbb{Z}, 3)$
Fixed tex
Feb
28
revised Groups which are only defined up to conjugation
Rewrote to make a better question.
Feb
28
awarded  Disciplined
Feb
28
comment Groups which are only defined up to conjugation
Fair enough, this may be NARQ. I remember though when I learned about Galois representations that a big deal was made about how you have to look at Galois representations because that's something invariant under conjugation, unlike other properties. Perhaps the point is that for these examples you need choice to build it in the first place so you can't just agree before hand on what you mean. Unlike with the cube where we can just agree.
Feb
28
asked Groups which are only defined up to conjugation
Feb
19
comment Is “being a modular category” a universal or categorical/algebraic property?
@Turion: Ok. That direction is essentially a coherence theorem for braided monoidal categories. Making that rigorous is going to be tricky, since making anything about 3-categories rigorous is tricky, but morally it just comes down to Artin's presentation for the braid group. That is, you need to check that braided tensor categories have an action of braids on them.
Feb
17
comment Is “being a modular category” a universal or categorical/algebraic property?
As a warmup you might want to think through why a 2-category with one object and one 1-morphism is automatically a commutative monoid by EH.
Feb
16
comment What are the intermediate subfactors of the tensor product of two maximal subfactors?
I would be shocked if you could get an iff statement along those lines. Generically there's no more intermediates, but there might be many very different special ways to get intermediates. Can you even prove that when the two subfactors are not isomorphic there can't be other intermediates? It's not even clear to me that the indices need to be the same!
Feb
16
comment Is “being a modular category” a universal or categorical/algebraic property?
You just do EH... $x \otimes y \rightarrow (x \star 1) \otimes (1 \star y) \rightarrow (x \otimes 1) \star (1 \otimes y) \rightarrow x \star y$ and then do the same thing once more to end up at $y \otimes x$. See also cheng.staff.shef.ac.uk/degeneracy/eggclock.pdf