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location  Oxford, United Kingdom  
age  50  
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2d

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Invariant planes of a nilpotent matrix with two Jordan blocks of size two
The 2dimensional subspaces are parametrised by the points on a quadric $Q$ in $P^5$, via Plucker coordinates. You can write down how $N$ acts there, and take the fixed vectors of linear map which satisfy the quadratic relation defining $Q$. Thus you will have them parametrised by the intersection of $Q$ and the linear subspace of fixed points. 
Aug 24 
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Real solutions for systems of monomial equations
this is a particular case of a problem involving binomial ideals; the latter are quite wellstudied, in the context of toric varieties. 
Aug 18 
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How to prove a Proposition of Rouquier?
how can it be so that some statements in the text indicate that it's not clear how to prove some other statement in the same text?! 
Aug 18 
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What is the minimal girth of a cayley graph for Alt(n) in which the girth relator is not a proper power?
6? Why? Why not 42? :) 
Aug 18 
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What is the minimal girth of a cayley graph for Alt(n) in which the girth relator is not a proper power?
from topology point of view, you might want to disregard length 2 loops. 
Aug 13 
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Linkage between homotopy equivalence and identification of algorithms
this is called "univalent foundations of mathematics", see e.g. homotopytypetheory.org 
Aug 8 
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Possible degrees of faithful projective representations of $\mathrm{PSL}(k,q)$ and $\mathrm{Sp}(2k,q)$ over complex numbers
The poster most probably doesn't have access to Magma. (well, the same computations can be done in GAP (gapsystem.org), which is free...) 
Aug 6 
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When polynomial GI implies polynomial (edge) colored GI?
other questions are harder :) 
Aug 6 
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When polynomial GI implies polynomial (edge) colored GI?
the explicit generators are trivial to find. Indeed, the action on the degree 2 vertices is just the action of $S_n$ on pairs {[12],[13],..,[pq]...}, for p<q. 
Aug 6 
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When polynomial GI implies polynomial (edge) colored GI?
Actually if you read details in A052565 you'll see that it is n! for n>3. 
Aug 6 
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When polynomial GI implies polynomial (edge) colored GI?
The case $n=3$ is exceptional, as the resulting graph is hexagon, so you get 12. Then for all $n\geq 4$ you should just get $n!$. 
Aug 6 
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When polynomial GI implies polynomial (edge) colored GI?
OK; then please write "the subdivision", not just "subdivision". Anyhow, I am sure that the automorphism group of such a graph is easy to describe for any $n$. (not sure though what you mean by "tractable to compute"  by some particular algorithm? Or do you mean "describe"?) 
Aug 6 
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When polynomial GI implies polynomial (edge) colored GI?
Do you mean a particular subdivision of $K_n$? (I have trouble reading English with missing articles). In your description, you seem to have defined a family of subdivisions for a given $n$, not just one particular. 
Aug 6 
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When polynomial GI implies polynomial (edge) colored GI?
How is A052565 relevant here? What are these numbers counting? 
Aug 5 
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Software tools for mediumscale systems of polynomial equations
yes, I agree that it's quite probable that the exact original polynomials have a common real 0. IMHO trying numerical methods to improve upon 2*10^9 is pretty much pointless here. 
Aug 5 
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Software tools for mediumscale systems of polynomial equations
SQP most probably will terminate in a local minimum. I'd be surprised if any restarts from such a minimum are attempted. 
Aug 3 
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Software tools for mediumscale systems of polynomial equations
as you have a sum squares cost function to optimise, I suppose the most natural method will be one based on semidefinite programming (a.k.a. Lasserre hierarchies). Did you try these? 
Aug 3 
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Software tools for mediumscale systems of polynomial equations
your link does not seem to work; it leads to the URL raw.githubusercontent.com/alexflint/polygamy/master/out/… which does not show up. 
Jul 31 
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Smallest Connected Graph for Given Degree Sequence
ok, i edited the question as to make it clear here. 
Jul 31 
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Smallest Connected Graph for Given Degree Sequence
ok, but what are you minimizing? 