90 reputation
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location University of California, San Diego
age 24
visits member for 1 year, 1 month
seen 21 hours ago
I am a graduate student at University of California, San Diego under the advice of Jim Agler.

Jan
11
awarded  Teacher
Jul
26
accepted Structure theorem for finite dimensional $C^*$-algebras and their representations
Jul
26
comment Structure theorem for finite dimensional $C^*$-algebras and their representations
This proof is interesting. Luckily, I know enough about the theory vN algebra for the context of this proof to make sense. I understand the feeling that this is somehow the decomposition into factors combined with some manipulatorics. However, I'm certain there are a lot of different ways to approach the problem. I was certainly more interested in the location of known solutions so that I could use this for some simplification of some proof.
Jul
26
awarded  Commentator
Jul
26
comment Structure theorem for finite dimensional $C^*$-algebras and their representations
This is a nice succinct explanation of the fact. I needed to use this to simplify some argument I was doing, and if someone asks why, this kind of logic/perspective will be useful.
Jul
24
comment Structure theorem for finite dimensional $C^*$-algebras and their representations
Thanks, Mike! That's exactly what I was looking for!
Jul
24
asked Structure theorem for finite dimensional $C^*$-algebras and their representations
Jun
25
awarded  Citizen Patrol
May
1
comment Metrics and completions on the direct limit of matrices of all sizes over arbitrary fields
What exactly do you mean by uniform norm? Do you mean you need to use a different norm on $M_n$ than the two norm/maximum singular value?
Apr
29
revised Metrics and completions on the direct limit of matrices of all sizes over arbitrary fields
edited title
Apr
29
asked Metrics and completions on the direct limit of matrices of all sizes over arbitrary fields
Mar
26
revised Injectivity bounds for complex analytic functions
added 4 characters in body
Mar
26
awarded  Editor
Mar
26
revised Injectivity bounds for complex analytic functions
added 4 characters in body
Mar
26
comment Injectivity bounds for complex analytic functions
I posted an answer. It should clear up your multivariable question. Somehow I think it should encode a basic proof, but I don't know what it is.
Mar
26
answered Injectivity bounds for complex analytic functions
Mar
24
awarded  Supporter
Mar
24
comment Injectivity bounds for complex analytic functions
The theorem is an algebraic criterion for the invertibility of functions. It talks about a precise sense in which having nonsingular derivative on a domain implies that function is injective. (However, there are some provisos here! I'll link to it later when I can upload it! (It's not complicated, I just don't want to do all the TeXing involved again just for MO))
Mar
24
comment Injectivity bounds for complex analytic functions
Somehow you need the series to have the superlinear terms have negative coefficients, That is, take $$F(z) = id(z) - \sum_{|I|\geq 2} a_Iz^I$$ where $a_I\geq 0.$ Further suppose $F$ is defined on some polydisk at 0. If the derivative of $F$ is nonsingular throughout the intersection of polydisk and the positive reals, then $F$ is injective.
Mar
24
comment Injectivity bounds for complex analytic functions
It is some analogue of an algebraic theorem I proved, I wanted to know if it had a simple proof in complex variables. You proof exhibits this fact. In fact it should be that for holomorphic maps $F:\mathbb{C}^n\rightarrow \mathbb{C}^n$ of the form $$F(z)= \text{id}(z) + O(\|z\|^2)$$ that the above holds (for appropriate statements of what the domain could be, some kind of polydisks.) Thank you for your time.