3,211 reputation
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bio website people.virginia.edu/~aa4cr/…
location University of Virginia
age
visits member for 4 years, 5 months
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I am a mathematical physicist working on:

• Constructive quantum field theory.

• Rigorous renormalization group methods.

• Mathematical statistical mechanics.

• Combinatorics related to Feynman diagrams and cluster expansions.

• Classical invariant theory, and applications of the classical symbolic method to problems in algebraic geometry and representation theory.


Dec
18
answered References: Solutions of the Bethe Ansatz Equations
Dec
18
revised Generalization of Pascal's Theorem to Higher Dimensions
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Dec
18
answered Not especially famous, long-open problems which anyone can understand
Dec
18
comment New proofs to major theorems leading to new insights and results?
I think that's a good answer to the question, although not quite accurate. The first proof for SL2 by Gordan was not a monstrous explicit calculation but a monstrous algebro-combinatorial proof with a double induction on trees decorated by collections of covariants. Hilbert managed to find a new proof which applied to SLn as well.
Dec
15
revised What are examples of good toy models in mathematics?
fixed typo
Dec
15
answered What are examples of good toy models in mathematics?
Dec
8
comment what characterizes a characteristic function of a probability measure in separable Hilbert spaces?
alternatively if you want the theorems like Bochner and Levy continuity to read exactly like in finitely-many dimensions, ie., without extra hypotheses like (ii), then you need to abandon Hilbert and Banach spaces and work with duals of nuclear spaces, like $S'(\mathbb{R}^d)$ or $\mathbb{R}^{\mathbb{N}}$.
Dec
5
comment Rationality of moduli spaces of rational curves
@Piotr: where did the SL2 action go?
Dec
4
revised Rationality of moduli spaces of rational curves
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Dec
4
revised What is a cumulant really?
fixed typo
Dec
4
revised Generalization of Pascal's Theorem to Higher Dimensions
edited tags
Dec
4
answered Rationality of moduli spaces of rational curves
Dec
4
comment Generalization of Pascal's Theorem to Higher Dimensions
@Mostafa: thanks. I don't know if there has been progress since the SW paper, but as far as I know this is indeed open and perhaps hopeless. You should try to have a look at the paper by Turnbull and Young. Unfortunately it is difficult to find. Google Books has a digitized version of Transactions of the Cambridge Philosophical Society, vol 23, where the article is, but it is not accessible to the public. I was reading the reprinted version in the collected works of Alfred Young. The reason I was interested in these things is because of trying to find symbolic formulas for catalecticants.
Dec
4
revised Generalization of Pascal's Theorem to Higher Dimensions
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Dec
3
comment Generalization of Pascal's Theorem to Higher Dimensions
The CB theorem generalizes Pascal's in the projective plane, but do the results or conjectures in the Eisenbud-Green-Harris article help answer the question by Mostafa for ten points and a quadric in $\mathbb{P}^3$?
Dec
3
revised Generalization of Pascal's Theorem to Higher Dimensions
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Dec
3
revised Generalization of Pascal's Theorem to Higher Dimensions
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Dec
3
revised Generalization of Pascal's Theorem to Higher Dimensions
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Dec
3
revised A monoid-structure on pairs of interlacing polynomials
changed obvious typo: monomial->monoid
Dec
3
revised Generalization of Pascal's Theorem to Higher Dimensions
added 1335 characters in body