5
votes
2answers
879 views
Properties of monodromy of a fibration?
Sorry for a loaded question.
I'm not an expert on those things, but I do know that a fibration gives rise to the representations of pointed fundamental group of the base on the co …
4
votes
3answers
932 views
Asymptotics of a hypergeometric series/Taylor series coefficient.
I was planning on figuring this problem out for myself, but I also wanted to try out mathoverflow. Here goes:
I wanted to know the asymptotics of the sum of the absolute values o …
1
vote
2answers
762 views
Algorithms for maximum weighted spanning (connected) dag (directed acyclic graph)
Suppose I have a weighted directed graph, often with symmetric links. I was to compute a maximum weight spanning DAG subgraph that is connected. I can't find any references to anyt …
-1
votes
1answer
434 views
how to formalize a notion of symmetric set difference probability?
I saw in a paper an argument, that seems simple. (Let $\triangle$ be the triangle operator of symmetric set difference between two sets)
It states that if $P(A \triangle B) < \e …
-3
votes
0answers
141 views
How to show that NC1 is a subset of L. [closed]
How to show that NC1 is a subset of L. How to prove that the true quantified boolean formula is not in NC
3
votes
2answers
152 views
one-side estimates for quasi-trigonometric polynomial
Let $f(x)=\Re(\sum_{k=1}^n a_k e^{i\lambda_k x})$ for $0 < \lambda_1 < \lambda_2 < \dots < \lambda_n$ and some complex $a_1$, $a_2$, $\dots$, $a_n$. What is the best (i …
1
vote
1answer
427 views
Abelian varieties of CM type?
Is there any introduction to abelian varieties of CM type?any reference?Like how to construct a abelian varieties given a CM field E?What is the properites of the Mumford Tate grou …
3
votes
1answer
202 views
Semicontinuity and cohomological flatness for algebraic spaces
Let $f \colon X \to S$ be a proper morphism form a seperated algebraic space $X$ to an affine noetherian scheme $S$.
Given a coherent sheaf $F$ on $X$, we know from Knutson's book …
0
votes
2answers
427 views
A hyperbolic PDE with infinite boundary conditions
Given known functions $a(x,y)$ and $b(x,y)$, I have a linear, second-order, hyperbolic PDE for a surface $z(x,y)$. The PDE is of the form:
$z_{xx} - a^2 z_{yy} + ab z_x - b z_y = 0 …
2
votes
1answer
568 views
Ambiguous definition of “nerve of an open covering” on wikipedia?
Let $(U_i)_{i\in I}$ be an open covering of a topological space $X$.
At http://en.wikipedia.org/wiki/Nerve_of_an_open_covering,
the nerve of the open covering is defined as follow …
2
votes
1answer
816 views
Examples of Equivariant Sheaves under Group action
I feel it very unintuitive to understand what an equivariant sheaf is. In the simplest example, L/K is a finite Galois extension, G=Gal(L/K), G acts on Spec L, what are the equivar …
12
votes
1answer
821 views
Analogue of Shimura curves in the symplectic case?
My understanding is this: one can attach 2-d Galois representations to classical modular eigenforms because one can look in the etale cohomology of modular curves. For Hilbert modu …
2
votes
3answers
333 views
Automorphisms of the totally ordered group Z^n with lexicographical order
It is easy to see that the totally ordered group Z (the integers) with the natural order has no non-trivial automorphisms. Is this also true for Z^n with the lexicographical order? …
1
vote
2answers
1k views
The Application of Lanczos Algorithm on Sparse Matrix
I am looking for suitable algorithm to compute the eigenvalues and eigenvectors of a matrix. My matrix is sparse ( think of Finite Element Matrix), and it is very, very big ( think …
10
votes
4answers
593 views
Geometry of the multilagrangian Grassmannian
Let's introduce the following variety $MG(3,6)$, which is a "multisymplectic" analog of a Lagrangian Grassmannian $LG(3,6)$.
Consider a 3-form $\omega = dx1 \wedge dx2 \wedge dx^3 …
