16
votes
3answers
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
1answer
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
1answer
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
2answers
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
1answer
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
2answers
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
1answer
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
2answers
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
2answers
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
1answer
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
2answers
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
1answer
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
1answer
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
4answers
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
2answers
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
2answers
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
1answer
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
0answers
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
2answers
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
0answers
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
0answers
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
1answer
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
0answers
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
0answers
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
2answers
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
16answers
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
0answers
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
1answer
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
0answers
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
1answer
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
0answers
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
0answers
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
1answer
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
1answer
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
52answers
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
16answers
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
0answers
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
16answers
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
12answers
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
8answers
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
0answers
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
2answers
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
2answers
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
1answer
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
8answers
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 ...

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