# Questions tagged [reference-request]

This tag is used if a reference is needed in a paper or textbook on a specific result.

12,408 questions
Filter by
Sorted by
Tagged with
101 views

### Does this theorem on tangential quadrilateral have a name?

Let $ABCD$ be a quadrilateral, $P$ be a point in the plane let $E$, $F$ be the projections of the incenters of triangles $\triangle CPB$, $\triangle BPA$ onto $PB$ respectively; Let $G$, $H$ be the ...
77 views

### Orlik-Solomon algebra and hyperplane complements in positive characteristic

Let $k$ be an algebraically closed field of characteristic $p\geq 0$, $\underline H:=\{H_1,\dots, H_m\}$ a set of hyperplanes in $\mathbb A_k^n$ and $X:=\mathbb A^n-(\bigcup H_i)$. Given a ring $R$ ...
336 views

### Reference for the Brauer-Nesbitt theorem

In Wikipedia's article on the Brauer-Nesbitt theorem, they state that given a group $G$ and a field $E$, two semisimple representations $\rho_1,\rho_2 : G\longrightarrow \operatorname{GL}_n(E)$ are ...
36 views

### proper : (proper + $\omega^\omega$-bounding) = generic : x

If $P$ is a forcing notion, $A \subseteq P$ (usually an antichain), $q\in P$, then I write $A\cap q$ for the set of all conditions in $A$ which are compatible with $q$. For a proper forcing notion $P$,...
129 views

### Amenability, growth and asymptotic dimension

I recently found this question on MSE, relating growth of groups with whether they are amenable, elementary amenable or not. I would like to know if there is an extra relation to finite or infinite ...
83 views

### Stability of super vector bundles

A super vector bundle is a $\mathbb{Z}_2$-graded bundle, see for example "Heat Kernels and Dirac Operators" of Berline-Vergne-Getzler section 1.3. Does it exist an adapted notion of ...
140 views

### What is this optimization problem called

Let $X$ be a set and $\mathcal{F}$ be a set of functions $f:X \to \Bbb{R}$ (for my purposes, it is fine to assume both sets are finite). For a probability distribution $\mu$ on $\mathcal{F}$, we ...
65 views

### A formula involving the heat kernel on the universal cover of a punctured plane

I am looking for the earliest reference to the following formula: $$\int_0^\infty\tilde{P}(1,e^{i\alpha},t)\frac{dt}{t}=\frac{1}{\pi \alpha^2},\quad \alpha>0,$$ where $\tilde{P}(x,y,t)$ is the ...
296 views

### Product of vertex degrees of an edge in a planar graph

Let $G$ be a planar graph, which we may assume to be a triangulation, with vertex set $V$ and edge set $E$. Suppose the minimum vertex degree is at least 3, and suppose any two distinct edges share at ...
175 views

### Unions=colimits in categories

The basic way to define a partial map $X\rightharpoonup Y$ in a category is as a span $X\hookleftarrow U\to Y$ in which the first map (the support) is mono and we call the second evaluation. These are ...
96 views

### Reference request: probabilistic models on climate (change)

I am looking for probabilistic models to address climate change. Are they known in the existing literature? I have found the post Math behind climate modeling. concerning PDE models. Many thanks for ...
98 views

88 views

67 views

### Equivalence between smoothly regular and analytically regular

I think the following statement is true. Let $M$ be a real analytic manifold. Let $S \subset M$ be an analytic or semianalytic subset. A point $p \in S$ is called smoothly regular resp. analytically ...
89 views

### Premeasurability of affiliated operators for type $\textrm{III}$ von Neumann algebras

$\DeclareMathOperator\dom{dom}$If $M\subset B(H)$ is a semifinite von Neumann algebra with faithful, normal, semifinite trace $\tau$, then a closed operator $T:H\rightarrow H$ intertwining the action ...
236 views

### Geometry book recommendation

Context and mathematical maturity: I have knowledge of the usual engineering math courses, meaning differential+integral+vector calculus, linear algebra, probability and statistics, etc. and some pure ...