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location Oxford, United Kingdom
age 51
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May
21
comment Will this be a case of self plagiarism or will it annoy the referee?
Yet another option is to include the parts with proofs from P1 as an appendix to P2. An appendix is meant to be for referees. As P1 is not yet published, this seems the most appropriate.
May
19
comment Looking for reference or proof to some facts stated on Anand Pillay's book
if your 2-dimensional closed sets have at least 3 elements then one doesn't need any group actions and infiniteness, it's just pure synthetic geometry to show that you sill get an affine or projective geometry.
May
19
comment Cardinality of non-integer points in the translation of the Minkowski sum of convex hull.
counting integer points in $mP+nQ$ is quite famous question, related to mixed volumes. Perhaps you can use it to get $|S|$...
May
19
comment Looking for reference or proof to some facts stated on Anand Pillay's book
you need infiniteness to avoid a sporadic example related to the Mathieu group $M_{22}$, I suppose. Well, I don't know how to deal with the case of 2-dimensional closed sets (a.k.a. lines) being of size 2, and locally being an infinite projective plane.
May
19
comment Looking for reference or proof to some facts stated on Anand Pillay's book
2.1.11 is also a result that is very old, at least in geometric terms (I don't know what an "infinite homogeneous" means though). Does it mean that the rank is infinite?
May
19
comment Looking for reference or proof to some facts stated on Anand Pillay's book
2.1.12 is a classical result in projective geometry, any good book should have it. e.g. see math.stackexchange.com/questions/549099/… for a list of books.
May
19
comment Is any F-stable maximal torus contained in some F-stable Borel subgroup?
I'm voting to close this question as it has been answered in the comments
May
16
comment Extreme points of convex hull of Minkowski sum
it seems you do not understand what conv(X) is.
May
16
comment Extreme points of convex hull of Minkowski sum
you are not reading it right.
May
16
comment Extreme points of convex hull of Minkowski sum
@Cusp : if $Q$ is a point $a$ then $P+Q$ is just $P$ shifted by the vector $a$, and the vertices of $P+Q$ are the vertices of $P$ shifted by $a$, and this is what I claim.
May
16
comment Extreme points of convex hull of Minkowski sum
pictures speak for themselves here: en.wikipedia.org/wiki/Minkowski_addition
May
16
comment Extreme points of convex hull of Minkowski sum
@AnthonyQuas : this is also an exercise :-)
May
16
comment Extreme points of convex hull of Minkowski sum
$ext(P+Q)$ will be $conv(\{a_i+b_j\mid 1\leq i\leq p, 1\leq j\leq q\})$. It is an exercise.
May
8
comment What is the complexity of intersecting two matrix algebras over a finite field?
The only hope seems to be to compute (partial) decompositions (using Meataxe, see e.g. homepages.warwick.ac.uk/~mareg/download/papers/bham_95/…) of the representations of the groups generated by $\mathcal{A}$ and $\mathcal{B}$, and hope they have small factors only. Then linear algebra becomes faster.
May
7
comment What is the complexity of intersecting two matrix algebras over a finite field?
Computational representation theory of groups is harder than linear algebra (this is a metatheorem :-)). My bet is that in general there cannot be a speedup hoped for in the question.
May
5
comment If the quotient of an algebraic space $X$ by a finite group is a scheme, is $X$ a scheme?
I'm voting to close this question as off-topic because it has been answered in the comments
May
2
comment A table for irreducible integral representation of finite cyclic groups
table? A theorem, perhaps...
May
1
comment Do unit quaternions at vertices of a regular 4-simplex, one being 1, generate a free group?
wouldn't this imply that the multiplicative group of quaternions contains a free group on 4 symbols? This is rather surprising to me.
Apr
30
comment the complex representations of $B(2, \overline{\mathbb{F}_p})$
and what is $B(2,F)$ ? And what is the Mackey method you mention - provide a reference...
Apr
30
comment Number of matrices with given Smith normal form
this is essentially about counting presentations of a f.g. Abelian group with a given upper bound on size.