5,618 reputation
22163
bio website math.berkeley.edu/~cgerig
location UC Berkeley
age 26
visits member for 4 years, 4 months
seen 2 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


2d
revised actual dimension of concrete moduli space of holomorphic curves vs its virtual dimension
added 307 characters in body
May
19
revised actual dimension of concrete moduli space of holomorphic curves vs its virtual dimension
clarifications
May
19
comment actual dimension of concrete moduli space of holomorphic curves vs its virtual dimension
The branch points are in the image; it's the critical values that you're really counting.
May
19
comment How to learn QFT from mathematical perspective?
Based on the OP's first sentence, his honest interest must be in TQFT, for which @Vectornaut's answer hits. As such, it is really not learning QFT.
May
19
revised actual dimension of concrete moduli space of holomorphic curves vs its virtual dimension
added 343 characters in body
May
18
comment How to learn QFT from mathematical perspective?
This should be upvoted way more than it currently is. We should also add the 1994 IAS lecture notes "Geometry and QFT".
May
18
answered actual dimension of concrete moduli space of holomorphic curves vs its virtual dimension
May
17
comment Hochschild-Serre spectral sequence
This is found in the standard book on group cohomology, by Ken Brown. In particular, yes, it's the usual structure (given in Chapter III.8.2 of that book).
Apr
28
comment Frame-bundle reduction from spinor-bundle reduction
Why does it fail to be transitive for $d\ge 10$?
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!