46,150 reputation
13172426
bio website math.berkeley.edu/~qchu
location Berkeley, CA
age 24
visits member for 5 years, 3 months
seen 30 mins ago

I am a third-year graduate student at UC Berkeley. I'm interested in the interplay between homotopy theory, quantum field theory, manifold topology, and higher category theory.


1h
asked Twisted equivariant modular forms?
2h
revised How many geometric structures on manifolds are there?
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2h
answered How many geometric structures on manifolds are there?
9h
comment Categorical proof subgroups of free groups are free?
@Todd: Oh, so a number theorist!
20h
comment Does this symmetrization operator have a name? Any theory?
It's averaging over an action of a particular finite group, namely $\mathbb{Z}_2^n$. I think in some contexts the more general operation of averaging over an action of a finite group is called the Reynolds operator.
1d
awarded  Nice Answer
1d
comment What is the original reference for disorientations on tangle diagrams?
Can you describe disoriented tangles by some universal property?
1d
revised Categorical proof subgroups of free groups are free?
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revised Categorical proof subgroups of free groups are free?
added 39 characters in body
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comment Categorical proof subgroups of free groups are free?
@HJRW: thanks for the warning. I picked that notation because I half-remembered that similar property, but it seems I remembered it wrong. I'll pick something else.
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revised Categorical proof subgroups of free groups are free?
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answered Categorical proof subgroups of free groups are free?
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comment Example of torsion in orientable manifolds?
I think this example would be more recognizable as $\mathbb{RP}^3$.
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comment Bar Construction Model of Ring Spectrum Quotient
Re: the last sentence, take $G$ discrete and work in an ordinary category. An action of $G$ on an object in a category $C$ is precisely a diagram $BG \to C$ and the categorical quotient of that object by that action is precisely the colimit of this diagram in $C$. The ABGHR definition is a natural generalization of this.
2d
comment Categorical proof subgroups of free groups are free?
Prospects for a categorical proof seem poor in that subgroups of free groups are not canonically free. I think freeness is in some sense a red herring and one should look for some other group-theoretic property equivalent to freeness but which makes no reference to a choice of free generators. Maybe cohomological dimension $1$?
Jan
24
awarded  Nice Answer
Jan
23
revised Examples of categorical adjunctions in analysis, Lie theory, and differential geometry?
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Jan
23
answered Examples of categorical adjunctions in analysis, Lie theory, and differential geometry?
Jan
22
awarded  Enlightened
Jan
22
awarded  Nice Answer