bio | website | people.virginia.edu/~aa4cr/… |
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location | University of Virginia | |
age | ||
visits | member for | 4 years |
seen | Jul 10 at 22:49 | |
stats | profile views | 3,072 |
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.
Jul 7 |
awarded | Yearling |
Jul 7 |
comment |
Equivalent binary forms
I was looking for papers which implemented the singular curve idea and I found sciencedirect.com/science/article/pii/S039304401100115X I think their notations mean up to normalization factors $I_1=H$, $I_2=T$, $I_3=U$. They find the implicit equation $F$ for the the signature curve which I wrote in parametric form in my answer. They also have a Maple program at the end of their paper which you may want to run on some examples. I don't know how fast it is. |
Jul 7 |
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Equivalent binary forms
@Tony: You're welcome. BTW, Lemma 16 can be amended simply by restricting the binary forms being compared to the stable locus of forms with roots of multiplicity $<d/2$. As for ideas about an efficient algorithm, the two I proposed in my answer are all I can think of at the moment. Maybe someone else with more expertise in computational invariant theory can propose better ones. Did you try Olver's singular curve method? Why is that not good enough for you? |
Jul 7 |
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Equivalent binary forms
@Tony: in relation to your earlier comment "GL_2(k)-invariants determine the orbits (by definition)", Lemma 16 in arxiv.org/abs/1406.5659 is wrong. Also, for binary forms, Hilbert's Finiteness Theorem (1890) is Gordan's Finiteness Theorem (1868). |
Jul 6 |
revised |
Equivalent binary forms
edited body |
Jul 6 |
reviewed | Approve suggested edit on One or two questions about so-called “absolute” set theories |
Jul 6 |
answered | Equivalent binary forms |
Jul 4 |
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Equivalent binary forms
Yes, covariants would be more efficient. Why do you want to avoid them? |
Jul 4 |
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Equivalent binary forms
I don't know about the subgroup case but for GL you can set up the question as an elimination problem since you get a system of algebraic equations in the entries of $M$. I suppose you could try Groebner bases. If you use instead resultants, my guess is that you will end up with invariants/covariants again. BTW, the difference between invariants and covariants is perhaps not important to you, but it certainly was for the people who invented this subject in the 19th century. |
Jul 4 |
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Equivalent binary forms
You mean if they have the same covariants. I'm sure you know that invariants alone do not distinguish orbits. |
Jul 4 |
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2d Ising model in conformal fields theory and statistical mechanics
Yes. That's what I said. |
Jul 3 |
reviewed | Approve suggested edit on about the structure of components of tensor product if more than one bipartite graph is taken |
Jul 2 |
answered | 2d Ising model in conformal fields theory and statistical mechanics |
Jul 1 |
revised |
Free Boson Correlator $ \langle X(z)X(w) \rangle =- \ln |z - w| $
added 1124 characters in body |
Jun 30 |
revised |
Free Boson Correlator $ \langle X(z)X(w) \rangle =- \ln |z - w| $
added 19 characters in body |
Jun 30 |
answered | Free Boson Correlator $ \langle X(z)X(w) \rangle =- \ln |z - w| $ |
Jun 27 |
reviewed | Approve suggested edit on What does the generating function $x/(1 - e^{-x})$ count? |
Jun 27 |
reviewed | Approve suggested edit on How do you show that $S^{\infty}$ is contractible? |
Jun 27 |
answered | Comparison of Different Types of QFT |
Jun 19 |
reviewed | Approve suggested edit on Simple sheaves are smooth points in the Quot scheme |