**16**

votes

**3**answers

3k views

### Finite type/finite morphism

I am not too certain what these two properties mean geometrically. It sounds very vaguely to me that finite type corresponds to some sort of "finite dimensionality", while finite corresponds to ...

**0**

votes

**1**answer

462 views

### probability mass function fitting

I have a probability mass function of some experimental data who's log looks like the following: (please ignore the fact that it is not normalized)
![alt text][1]
[image shack image removed]
...

**8**

votes

**1**answer

496 views

### Triangulations of polytopes and tilings of zonotopes

Consider a set $A = \{ a_1,a_2,\ldots, a_n \} $ of vectors in $\mathbb{R}^d$, which lie in a common affine hyperplane. Two convex polytopes may be obtained from $A$, namely the convex hull of the ...

**7**

votes

**2**answers

1k views

### What does the nilpotent cone represent?

Notation
Let $\mathfrak g$ be a the Lie algebra of an algebraic group $G\subseteq GL(V)$ over a(n algebraically closed) field $k$ (I'm actually thinking $G=GL_n$, so $\mathfrak g=\mathfrak{gl}_n$). ...

**-2**

votes

**1**answer

462 views

### Conjugate vertices and distinguishing properties

Motivation (added)
A finite $n$-set is uniquely described (up to isomorphism) by a single population number $n$.
A finite $n$-set with $k$ predicates is uniquely described (up to isomorphism) by ...

**9**

votes

**2**answers

1k views

### How should I think about delooping?

When talking about the Eilenberg-Maclane space $K(G,n)$, we usually restrict our attention to the situation where $G$ is abelian. In that case, we get $\Omega K(G,n)=K(G,n-1)$, so we can call ...

**6**

votes

**1**answer

633 views

### Do I need to know what an infinity-Gerstenhaber algebra is, and if so, what is it?

I am in the following situation. I have two (rather explicit and specific) dg commutative algebras $R,S$ over a field of characteristic $0$. In fact, $S$ is an $R$-algebra, in that I have a map $R ...

**3**

votes

**2**answers

493 views

### Dimension of moduli space in Lagrangian Floer homology

Let $(M,\omega)$ be symplectic manifold with $\omega=c_{1}=0$ on
$\pi_{2}M$. Let $\Lambda\subseteq M$ be Lagrangian submanifold.
Let $H:M\times S^{1}\rightarrow\mathbf{R}$ be Hamiltonian and $J$
be ...

**8**

votes

**2**answers

866 views

### Character of the Basic Representation for Affine E_8 in Terms of Jacobi Theta Functions

When $\mathfrak g$ is a complex, simple, simply laced Lie algebra of rank r then the (specialized) character of the basic representation for the corresponding affine Lie algebra $\hat {\mathfrak g}$ ...

**3**

votes

**1**answer

312 views

### Finiteness of normalization of Noetherian normal domain

I have the following question:
Let $A$ be an integrally closed Noetherian domain, $K$ its field of fractions. let $L$ be a finite extension of $K$, and $B$ the integral closure of $A$ inside $L$. Is ...

**3**

votes

**2**answers

382 views

### Modules of finite support

I'm reading Dwyer and Fried's paper "Homology of free abelian covers, I". In it, they make the following claim, which I'm having trouble verifying.
Let $F$ be a field and $A = F[x_1^{\pm ...

**2**

votes

**1**answer

245 views

### Modules with small support have big depth - reference wanted

Hello,
I would appreciate an exact reference / proof of the following fact, which I am almost able to prove, but not really:
Let $A$ be a regular Noetherian comm. ring, of finite Krull dimension. ...

**7**

votes

**1**answer

2k views

### Motivation for equivariant sheaves?

Hello everyone;
i'm looking for a motivation for equivariant sheaves (see http://ncatlab.org/nlab/show/equivariant+sheaf) ~ Why are we interested in them?
More explicitely: Can I think of ...

**1**

vote

**4**answers

757 views

### a complex borel measure, whose Fourier transform goes to zero

I have $\mu$ a complex borel measure on $\mathbb(R)$, whose Fourier transform goes to zero as $ \xi$ goes to $ \infty$. I need to prove that $ |\mu|$(singleton) = 0.
Should I approach $\mu$ by a ...

**4**

votes

**2**answers

2k views

### How to think like a set (or a model) theorist.

Kenneth Kunen in his “The Foundations of Mathematics” writes:
‘Set theory is the study of models of ZFC’ (p. 7)
‘Set theory is the theory of everything’ (p. 14)
With (1) Kunen is pointing to a ...

**9**

votes

**2**answers

950 views

### Christoffel symbols on a Lie group in Riemann normal coordinates

Consider a coordinate patch around the identity element in a Lie group given by the exponential mapping (Riemann normal coordinates). We have a Levi-Civita connection corresponding to the ...

**4**

votes

**1**answer

2k views

### What is Floer homology of a knot?

I've heard that there are different theories providing knot invariants in form of homologies. My understanding is that if you embed knot in a special way into a space, there is a special homology ...

**8**

votes

**0**answers

457 views

### SFT gluing on chain level in Floer homology?

I came across a new type of gluing in the FOOO paper http://arxiv.org/abs/1002.1660 (maybe not so new to experts). The situation is as follows: one considers a relative (to lagrangian) class and ...

**4**

votes

**2**answers

1k views

### How should I find a tutor for math-overflow level mathematics? [closed]

Searching for maths tutors online finds people willing to teach up to A-level. I'm looking for help at a more advanced level.
At the moment I'm trying to teach myself category theory from downloaded ...

**8**

votes

**0**answers

402 views

### Degenerate moduli spaces in Floer homology

Let $(W,\omega)$ be a closed symplectially aspherical symplectic
manifold, and fix a Hamiltonian $H\in C^{\infty}(W\times S^{1};\mathbb{R})$
and a compatible almost complex structure $J$ on $W$. Given ...

**1**

vote

**0**answers

117 views

### Non-regular (Non-coherent) subdivisions of a polygon.

There are many papers and books which study about the regular subdivision of a convex lattice polytope.
My question is about "Non"-regular subdivisions of a 2-dimensional convex lattice polygon.
I ...

**5**

votes

**1**answer

467 views

### Comparison of Local and Global Duality

Hello!
I'd like to understand the relation between the following two theorems:
The "global" duality for projective schemes, as explained in [Hartshorne]: If $X$ is an equidimensional projective ...

**0**

votes

**0**answers

18 views

### largest subgroup of $Out(\hat{F_2})$ which preserves the Nielsen invariant

Let $x,y$ be generators for the free group $F_2$. It's known that $Aut(F_2)$, and hence $Out(F_2)$ preserves the conjugacy class of the subgroup $\langle[x,y]\rangle$ generated by $[x,y]$ (This ...

**3**

votes

**0**answers

99 views

### Commuting diagram, algebraic cycles and K-theory

What is the easiest way to see the veracity of the following commutative diagram?$$\require{AMScd}
\begin{CD}
K(X) \otimes K(Y) @>\text{ch}(-) \otimes \text{ch}(-)>> A(X, \mathbb{Q}) \otimes ...

**2**

votes

**2**answers

59 views

### Basic question about discrete minimal surfaces

Let $P$ be a convex polygon with $n > 3$ vertices $v_1, \ldots, v_n \in \mathbb{R}^2$, let $x$ be a point in the interior of $P$, and let $u$ be a function with prescribed values at the vertices of ...

**7**

votes

**0**answers

139 views

### Tangent space of Hilbert scheme

We have the following theorem:
Let $X$ be a projective scheme over an algebraically closed field $k$, and $Y \subset X$ a closed subscheme with Hilbert polynomial $P$. Then$$T_{[Y]}\text{Hilb}_P (X) ...

**1**

vote

**0**answers

71 views

### Rank of the Jacobian of a family of hyperelliptic curves of genus 2

Assume tha $C$ be the hyperelliptic curve $y^2 = (x-a_1)\cdots (x-a_5)$ of genus $g=2$ and $a_i \in \mathbb{Z}$ and we know that the integers $a_i$ has the form $a_i= d_1^2 - d_i^2$ for some positive ...

**0**

votes

**0**answers

145 views

### How do mathematicians find the underlying idea? [on hold]

While reading through the lecture notes here (http://www.math.ucla.edu/~tao/resource/general/131ah.1.03w/week2.pdf , page 22, last paragraph), I came across the following " Thus there must be some ...

**0**

votes

**0**answers

28 views

### Bounding Expected Value of a piecewise function [on hold]

Let X and Y to be two independent random variables with known pdfs. Get a bound for the expected value of the following expression in terms of $E[X]$, $E[Y]$, VAR[X] and VAR[Y]:
\begin{equation}
...

**-2**

votes

**0**answers

103 views

### Flower Arrangements [on hold]

We have a $n\times m$ grid with $k$ flowers (not necessarily distinct). The grid is assumed to have horizontal and vertical symmetry. What is the value of $A(n,m,k)$, where $A(n,m,k)$ is the number of ...

**93**

votes

**16**answers

22k views

### Mathematical software wish list

Like many other mathematicians I use mathematical software like SAGE, GAP, Polymake, and of course $\LaTeX$ extensively. When I chat with colleagues about such software tools, very often someone has ...

**6**

votes

**0**answers

83 views

### A “universally non Hypercomplete” $\infty$-topos?

My question is :
Is there a classifying $\infty$-topos for $\infty$-connected objects ? Does this $\infty$-topos has a nice description (as an $\infty$-category ) ?
What I mean by $\infty$-connected ...

**2**

votes

**1**answer

127 views

### Theorems that tell if an explicit analytical solution is possible for nonlinear PDEs

Are there any theorems that tell if a particular nonlinear PDE can be solved explicitly by analytical methods?
Where analytical methods I refer to methods such as power series or any methods that use ...

**0**

votes

**0**answers

66 views

### When do block sequences yield disjoint subspaces?

Let $X$ be a Banach space having a (unconditional, normalized) Schauder basis $(e_n)_n$. Suppose that $Y$ and $Z$ are (closed) block subspaces of $X$ having normalized block bases (with respect to ...

**1**

vote

**1**answer

91 views

### Number of binary sequences in which the number of $(1, 1)$ and $(0, 0)$ is prespecified

Consider a binary sequence $\mathbf{a}_n$ consisting of 1s and 0s.
Let us denote by $f(\mathbf{a}_n)$ the number of $(1, 1)$ and $(0, 0)$ in $\mathbf{a}_n$; I am not sure whether there is a formal ...

**0**

votes

**0**answers

70 views

### constructing koenigs function

My question is rather simple and I hope someone has some sort of an answer. I am looking for a simple yes or no answer, and a reference if anyone has one.
We have a holomorphic function $f$ defined ...

**1**

vote

**0**answers

59 views

### Calculations about the normal bundle of embedding of symmetric products

Suppose $C^{(d)}$ is the $d$-th symmetric product of a curve, embed it in $C^{(d+s)}$ by $E\to E+sP_0$ where $P_0$ is a fixed point. The normal bundle of this embedding is denoted by $N$.
Suppose ...

**8**

votes

**1**answer

112 views

### Detecting positive endomaps of the formal reals

A locale is a sort of "formal topological space", which "may not have enough points to separate its open sets". For instance, there is a "locale of all real numbers that are both rational and ...

**4**

votes

**1**answer

47 views

### Self-concordant function for dual cone

I wonder if there is any existing result for self-concordant function in the literature about the following question.
Suppose $f$ is a self-concordant barrier function of a proper cone $K$ (pointed, ...

**70**

votes

**52**answers

22k views

### Which popular games are the most mathematical?

I consider a game to be mathematical if there is interesting mathematics (to a mathematician) involved in
the game's structure,
optimal strategies,
practical strategies,
analysis of the game ...

**64**

votes

**16**answers

6k views

### What makes four dimensions special?

Do you know properties which distinguish four-dimensional spaces among the others?
What makes four-dimensional topological manifolds special?
What makes four-dimensional differentiable manifolds ...

**28**

votes

**0**answers

849 views

### Grothendieck's Period Conjecture and the missing p-adic Hodge Theories

Singular cohomology and algebraic de Rham cohomology are both functors from the category of smooth projective algebraic varieties over $\mathbb Q$ to $\mathbb Q$-vectors spaces. They come with the ...

**62**

votes

**16**answers

5k views

### When are two proofs of the same theorem really different proofs

Many well-known theorems have lots of "different" proofs. Often new proofs of a theorem arise surprisingly from other branches of mathematics than the theorem itself.
When are two proofs really the ...

**54**

votes

**12**answers

4k views

### Counterexamples in PDE

Let us compile a list of counterexamples in PDE, similar in spirit to the books Counterexamples in topology and Counterexamples in analysis. Eventually I plan to type up the examples with their ...

**29**

votes

**8**answers

4k views

### Motivation for and history of pseudo-differential operators

Suppose you start from partial differential equations and functional analysis (on $\mathbb R^n$ and on real manifolds). Which prominent example problems lead you to work with pseudo-differential ...

**4**

votes

**0**answers

105 views

### $A_\infty$ structure on sum of twists of structure sheaf

Fix $n$ and let $P^n$ be projective $n$-space. Let $S = k[x_0, \dots, x_n]$. Set $A^0 = \bigoplus_{d \ge 0} H^0(P^n, \mathcal{O}(d))$ and $A^n = \bigoplus_{d < -n} H^n(P^n, \mathcal{O}(d))$.
I ...

**345**

votes

**2**answers

26k views

### Polynomial bijection from $\mathbb Q\times\mathbb Q$ to $\mathbb Q$?

Is there any polynomial $f(x,y)\in{\mathbb Q}[x,y]{}\ $ such that $f:\mathbb{Q}\times\mathbb{Q} \rightarrow\mathbb{Q}$ is a bijection?

**7**

votes

**2**answers

320 views

### Generalized Tannakian Duality?

By the classical theory of Tannakian duality we know that every $k$-linear rigid abelian tensor category ($k$ a field) which has a fibre functor to $\mathrm{Vec}_k$ (finite dim. vector spaces over ...

**2**

votes

**1**answer

379 views

### Non-trivial topological line bundles over cartesian product of manifolds not coming from a pullback

Let $X$ and $Y$ be connected smooth manifolds. Let $L$ be a topological real line
bundle over $X\times Y$. Then we know that the isomorphism class of such a line bundle is determined by its first ...

**18**

votes

**8**answers

6k views

### Applications for p-Sylow subgroups theorem

I have searched for such a question and didn't find it. I recently had a presentation in which I introduced $p$-Sylow subgroups and proved Sylow's theorems. I will have another one soon, concerning ...