2,836 reputation
625
bio website people.virginia.edu/~aa4cr/…
location University of Virginia
age
visits member for 4 years
seen Jul 10 at 22:49

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
comment 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
comment 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
comment Equivalent binary forms
Yes, covariants would be more efficient. Why do you want to avoid them?
Jul
4
comment 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
comment 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
comment 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