This question is inspired by a recent talk by Matt Kahle on random geometric complexes. Some simple notation: let $\mathcal{B} \subset \mathbb{R}^d$ be the unit ball in $d$-dimen …

A finite, two-player, nondegenerate, symmetric game is defined by a nondegenerate $n \times n$ payoff matrix $A$. If player 1 plays strategy $i$ and player 2 plays strategy $j$, t …

There are many mathematical objects that are similar to groups and Cayley graphs of groups but lack homogeneity in some sense. Graphs of webpages with edges corresponding to links …

Let $G$ be a discrete group and let $M$ be a $G$-module. Assume that I have a resolution $$\cdots \rightarrow M_1 \rightarrow M_0 \rightarrow M \rightarrow 0$$ of $M$ by $G$-modul …

Let me begin with an example. Consider the computable function $f(x) = 2x$. A Turing machine can implement this function in $O(|n|)$ steps: simply walk to the end of the input st …

Let $G$ be a semisimple complex Lie group (or perhaps a reductive algebraic group over $\mathbb{C}$) and $V$ an irreducible finite-dimensional representation of $G$, determined by …

For a smooth projective curve $C$ and $f,g \in k(C)^*$, we have $\text{div}(f)=\text{div}(g)$ iff $f=ag$ for some nonzero constant $a$. Is this still true for higher dimension smoo …

For a real number $\alpha$, let the irrationality measure $\mu(\alpha) \in \mathbb{R}\cup {\infty}$ be defined as the supremum of all real numbers $\mu$ such that $$ \left| \alpha …

I am planing to study Kirillov's orbit method. I have seen Kirillov's method in several branch of mathematics, for instance, functional analysis, geometry, .... Why is this theory …

Hi, Is there a continuous function $H:\mathbb{R}\times\mathbb{R}\longrightarrow\mathbb{R}$ satisfying $H(w,c)=H(-w,c+w)$? Thanx.

This is a problem from my exam on functional analysis. I did only trivial case and now I'm just curious about another cases. Let $T : H \rightarrow H$ is a linear continuous unit …

Suppose I have a sequence of stochastic processes $X_{N}(t)$, $N=1,2,3,\ldots$ with mean zero and that I know for every fixed $t$, the random variable $X_{N}(t)$ converges in law t …

Nota bene: all rings are supposed commutative with $1$ and all ring homomorphism should be unital. Let $B$ be the set of truth values {True, False}. For a formula $\phi$ denote by …

Suppose $\delta$ is an inaccessible cardinal, and $\mathbb{P}$ is the Levy Collapse $\text{Col}(\kappa, \delta)$ which adds a surjection from $\kappa \to \delta$ (for some regular …

For probably twenty years, category theorists have known of some objects in the Platonic universe called "(weak) $\infty$-categories", in which there are $k$-morphisms for all $k\i …