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1d
answered Are there exactly solvable CFTs?
Feb
3
revised What mathematical treatment is there on the renormalization group flow in a space of Lagrangians?
updated more references
Feb
3
revised What mathematical treatment is there on the renormalization group flow in a space of Lagrangians?
updated reference and prived URL
Jan
25
awarded  Good Answer
Nov
30
answered How are the real-space RG transformations defined?
Nov
19
comment Is there a similar theory as for symmetric polynomials, that deals with polynomials on the entries of matrices that are symmetric in both dimensions?
I mean Pouzet conjectured that some statement A about invariant rings implies B which is the graph satisfies the graph isomorphism property, i.e., it is the only one up to isomorphism with the same unordered list with repetition of subgraphs with one less vertex. Now Thiery proved that (A implies B) is false. So my question is what remains of the "sound" "general setup"? Are there precise viable substitutes for Pouzet's conjecture written somewhere in the literature?
Nov
19
comment Is there a similar theory as for symmetric polynomials, that deals with polynomials on the entries of matrices that are symmetric in both dimensions?
@Dima: thanks but when I checked my copy of Dersken-Kemper what they say about the connection graph isomorphism pbm<->invariant rings does not sound good. Pouzet's conjecture to this effect was shown to be false by Thiery. So is there still a precise viable connection in the literature?
Nov
17
awarded  Nice Answer
Nov
12
comment Is there a similar theory as for symmetric polynomials, that deals with polynomials on the entries of matrices that are symmetric in both dimensions?
@Dima: what you said about bipartite graphs sounded very interesting, but did not have enough details for me to understand it well. What specific problem from the theory of bipartite graphs could one solve if one had a good enough description of the invariant ring that the OP is asking about? References would be appreciated.
Nov
12
answered Is there a similar theory as for symmetric polynomials, that deals with polynomials on the entries of matrices that are symmetric in both dimensions?
Nov
11
answered Can a general binary sextic form be put into the following form?
Nov
11
comment Involutions of binary sextic forms
My paper with Chipalkatti refers to my co-author's article on the degree 18 of the binary quintic, not sextic. The latter is due to Hermite. I actually don't know who first discovered the degree 15 invariant for sextics. What kind of info would you like on this degree 15 invariant?
Sep
22
comment Name for an orthogonal decomposition of $L^2 (\mathbb{R}^2; \mathbb{C})$
yes. I always wondered also about combinatoric vs combinatorial...
Sep
22
answered Name for an orthogonal decomposition of $L^2 (\mathbb{R}^2; \mathbb{C})$
Sep
22
comment The Guinand-Weil explicit formula without entire function theory
another very nice introductory reference for the explicit formula is the article "The explicit formula in simple terms" by Jean-Francois Burnol available here arxiv.org/abs/math/9810169
Sep
18
awarded  Nice Answer
Sep
14
comment Wavelet-like Schauder basis for standard spaces of test functions?
@Pedro: indeed othogonality would have to be sacrificed. Thanks for pointing out the LP wavelets from Meyer's book. I will have a look.
Sep
11
comment Examples of major theorems with very hard proofs that have NOT dramatically improved over time
I don't know if it is simpler but there seems to be a more "conceptual" proof arxiv.org/abs/1305.0926 by Maculan which relates the result to GIT and Arakelov geometry.
Sep
11
answered Examples of major theorems with very hard proofs that have NOT dramatically improved over time
Sep
10
comment Uniform definition of $S(\mathbb{R})$ and $S(\mathbb{Q}_p)$
other issue with "subspace of $L^1\cap L^2$, Fourier stable, dense and nuclear": nuclearity with respect to which topology?