5,570 reputation
22163
bio website math.berkeley.edu/~cgerig
location UC Berkeley
age 26
visits member for 4 years, 3 months
seen 4 hours ago

After doing my BS in engineering physics (with experimental research on gravity), I started my PhD in experimental atomic physics. But I quit to do math, and am now a 3rd year student of Michael Hutchings.

Current interest: the interplay between gauge theory and symplectic geometry


Apr
4
comment *The* open problem in General Relativity?
That means you're not looking for mathematical problems which relate GR to QFT. In which case, I haven't heard of there being the problem on everyone's minds. But, you'll be interested in the mathematical seminar paper of Penrose, Some Unsolved Problems in Classical General Relativity.
Apr
3
comment Nilpotence of the stable Hopf map via framed cobordism
@Qiaochu: It's more of a hunch. For some manifolds, vanishing signature implies framed-nullcobordance.
Apr
2
revised Universal coefficient theorem for group homology and cohomology
added 337 characters in body
Apr
2
revised Universal coefficient theorem for group homology and cohomology
added 284 characters in body
Apr
1
comment Universal coefficient theorem for group homology and cohomology
This isn't a UCT, though. You're only swapping $M$-coefficients for $M^\ast$-coefficients.
Apr
1
answered Universal coefficient theorem for group homology and cohomology
Mar
31
comment Nilpotence of the stable Hopf map via framed cobordism
I believe the answer is based on the existence of the signature, a cobordism-invariant. The 4-torus has a well-defined signature $\sigma(H^2(\mathbb{T}^4;\mathbb{R}),\smile)$, given geometrically in terms of the intersection pairing of cycles in 2-dimensional homology. But this doesn't exist for the 3-torus or 2-torus.
Mar
27
answered Why not develop a Hamiltonian-based Morse theory?
Mar
27
comment Mathematical statistical qm book-recommendation
Quantum Physics: A Functional Integral Point of View by Glimm and Jaffe (they're theoretical physicists). That's the closest I can think of, which should suffice since it is rigorous, but I find it hard to follow (they leave a lot up to the reader).
Mar
20
comment Pseudomanifolds and Poincaré duality
Oh I thought "Poincare duality space" just meant $H^k\approx H_{n-k}$ and not necessarily induced by maps, sorry.
Mar
20
comment Pseudomanifolds and Poincaré duality
Ah, the "kissing banana" is not a pseudomanifold (doesn't satisfy second bullet point), nevermind!
Mar
19
revised $\pi_0${plane fields}$\to\mathbb{Z}_2$
added 76 characters in body
Mar
18
reviewed Reject A metric for Grassmannians
Mar
16
answered What if the low-degree cohomology of a $G$-module and all its restrictions vanish?
Mar
4
comment Elliptic operators corresponds to non vanishing vector fields
Yes; I think the spherical harmonics won't be in the image, because they can't be integrated (when solving for the corresponding function in the domain). For example, in order for $D_X(f)=\cos\phi$ you need $f=\sin^2\theta\ln|\sin\phi|$ which blows up at $\phi=0,\pi$.
Feb
24
comment Elliptic operators corresponds to non vanishing vector fields
@AliTaghavi, I think the cokernel is infinite-dimensional.
Feb
24
comment liftings of principal bundles
OK, what then makes the coefficient system constant when $K$ is central? Some sort of reduction map must be arising somewhere?
Feb
23
comment liftings of principal bundles
Can you explain why local coefficients are required when $K$ is abelian but not central?
Feb
23
revised Coboundary of a cup-product
rolled back to a previous revision
Feb
23
revised Coboundary of a cup-product
added 232 characters in body