38,825 reputation
10144364
bio website math.berkeley.edu/~qchu
location Berkeley, CA
age 23
visits member for 4 years, 6 months
seen 6 hours ago
I'm a second-year graduate student in pure mathematics at UC Berkeley. You can contact me at qchu[at]math[dot]berkeley[dot]edu.

6h
comment Chain homotopy of non-abelian category
Replace it with simplicial homotopy of maps between simplicial objects. (There's no reason, from the perspective of homotopical algebra, to work in the category of chain complexes of monoids, as the Dold-Kan theorem fails in this setting.)
2d
comment What is Chern-Simons theory expected to assign to a point?
For anyone else thinking of watching the video, Youtube has 1.5x and 2x speed options, and I promise that the video is still understandable at those speeds!
2d
accepted What is Chern-Simons theory expected to assign to a point?
2d
comment Generating function which has no singularity
You can use e.g. the saddle-point method. See in particular Example VIII.3 of Flajolet and Sedgewick.
Apr
15
comment What is Chern-Simons theory expected to assign to a point?
@André: thanks for the response! I worry that I asked you this question in person already and forgot your answer, so I'm glad it's now recorded electronically. I'll try to find some time to watch the video.
Apr
15
answered is the tensor product of projective modules again projective?
Apr
15
comment The Alexander-Conway polynomial: from knots to braids?
This is not the question you want to ask. Closing up a braid to a knot should be thought of as a trace, so what you really want is a map from braids to matrices with polynomial coefficients (probably a representation of the braid group) such that taking traces gives back the Alexander polynomial (this is exactly what happens for the Jones polynomial, where the corresponding representation is built using e.g. quantum groups). Maybe the Burau representation is such a representation?
Apr
14
comment What is Chern-Simons theory expected to assign to a point?
@Adrien: I'm willing to believe you can't go down to the point with the target $3$-category I described above, but that doesn't preclude the possibility of switching to a more sophisticated target $3$-category, right? I also admit that I don't understand this anomaly issue at all; going to have to read more about that.
Apr
14
awarded  Nice Question
Apr
14
comment G-spaces and manifolds
What a confusing term. A $G$-space should be a space equipped with an action of $G$...
Apr
14
revised What is Chern-Simons theory expected to assign to a point?
added 26 characters in body
Apr
14
asked What is Chern-Simons theory expected to assign to a point?
Apr
12
comment Eilenberg-MacLane Spaces of “large” groups
I think "infinite and discrete and not $\mathbb{Z}$" is too broad for the question you actually want to ask. There are lots of reasonable $K(G, 1)$ in this category, e.g. aspherical manifolds. Maybe uncountable $G$?
Apr
11
comment Square-free integers not divisible by any “small” primes
Some very rough heuristics suggest a constant times $\frac{kN}{\log N}$; see qchu.wordpress.com/2012/11/10/… for a rough description of those heuristics.
Apr
10
comment Algebraic topology vs. category theory
The morphisms are homotopy classes of functions. The resulting category is called the homotopy category of spaces. This is standard material.
Apr
8
comment Characters and conjugacy classes
For infinite groups there are examples of groups that have no finite-dimensional representations whatsoever (e.g. simple groups of cardinality strictly larger than the continuum).
Apr
7
comment What is an intuitive view of adjoints? (version 1: category theory)
Actually, it's the other way around: the left adjoint is the ceiling and the right adjoint is the floor. If $r \in \mathbb{R}$ and $n \in \mathbb{Z}$ then $\lceil r \rceil \le n$ if and only if $r \le n$, and dually $n \le \lfloor r \rfloor$ if and only if $n \le r$.
Apr
4
comment When a symplectic manifold is formal?
@user: perhaps the OP is using the symplectic form to identify forms and polyvector fields, then using the Schouten bracket?
Apr
4
awarded  Nice Question
Apr
2
awarded  Great Answer