bio | website | people.virginia.edu/~aa4cr/… |
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location | University of Virginia | |
age | ||
visits | member for | 4 years, 5 months |
seen | yesterday | |
stats | profile views | 3,343 |
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 |
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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 |
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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
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