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bio website math.utoronto.ca/jmfisher
location Toronto
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visits member for 3 years, 1 month
seen Jul 4 at 1:39

I'm a PhD candidate interested in mathematics inspired by theoretical physics (QFT, strings, integrable systems, etc.).


Apr
12
comment Exactness Axiom of Homology Theory
$C_k(\cdot)$ are the chains, with boundary map $\partial: C_k(\cdot) \to C_{k-1}(\cdot)$, so that $H_k = \ker \partial_k / \mathrm{im} \partial_{k+1}$. They depend on what homology theory you are considering, but they are always there in the background somewhere. For the singular homology of a space $X$ they are formal linear combinations of maps $\Delta^k \to X$ where $\Delta^k$ is the standard $k$-simplex. For simplicial and cellular homology there are analogous definitions. Whenever you encounter any kind of homology you should think of it as the homology of some underlying chain complex.
Apr
9
answered subgroup problem in abstract algebra
Apr
8
comment Center of Clifford Algebra depending on the parity of $\dim V$?
The parity issue is discussed in detail in E. Meinrenken's Notes math.toronto.edu/mein/teaching/clif_main.pdf . See Proposition 2.6 in particular, which gives the result over $\mathbb{C}$. Another good reference is Chevalley's book.
Apr
8
revised Why is $W(V)\simeq D(k[X_1,\dots,X_n])$?
small commment added
Apr
8
answered Why is $W(V)\simeq D(k[X_1,\dots,X_n])$?
Apr
7
answered Exactness Axiom of Homology Theory
Mar
16
answered Structure Sheaf on Scheme
Feb
13
answered Fourier transform of gaussian times polynomial to a high power
Feb
9
comment Non-closed subgroups of Lie groups
Irrational flows on the torus are well-studied (and famous) examples in noncommutative geometry. So it might be worth looking at the noncommutative geometry literature to see if there is anything like what you're asking.
Feb
4
comment Expressing Differential Form in Different Coordinates
@Confused I edited it to include a few more details of the evaluation of the pushforward.
Feb
4
awarded  Editor
Feb
4
revised Expressing Differential Form in Different Coordinates
added some extra detail
Feb
2
answered Expressing Differential Form in Different Coordinates
Nov
25
awarded  Nice Answer
Nov
25
answered Solving $A(x) = 2A(x/2) + x^2$ Using Generating Functions
Nov
25
awarded  Enthusiast
Nov
25
answered Why the emphasis on Projective Space in Algebraic Geometry?
Nov
17
answered “Maximal symmetry” metric for a manifold?
Nov
16
comment Solving this Fourier transform?
I haven't thought about it too much, but a quick look at the wikipedia page suggests that these functions might be closely related to the Laguerre polynomials, and the Laguerre polynomials are indeed related to Bessel functions. In any case I'm sure these functions are listed in tables of Fourier transforms, so they probably have somebody's name attached to them.
Nov
16
answered Solving this Fourier transform?