-1
votes
1answer
30 views
How to start Game theory?
Hi everybody,
I recently got interested in Game Theory but I don't know where should I start.
Can anyone recommend any references and textbooks?
And what are the prerequisites of …
0
votes
1answer
26 views
Montague’s Reflection Principle and Compactness Theorem
Here's a question I can't answer by myself: The Reflection Principle in Set Theory states for each formula $\phi(v_{1},...,v_{n})$ and for each set M there exists a set N which ext …
2
votes
0answers
49 views
additive structure in a small multiplicative group of a finite field?
Let $p$ be a prime. Given a positive integer $n$, does there exist a
$\beta$ in an extension of $F_p$ such that
1) If $F_p[\beta] = F_{p^N}$, then $N > n^n$; ( $\beta$ lies in a …
2
votes
2answers
77 views
Triangles, squares, and discontinuous complex functions
Is there some onto function $f:$ $\mathbb{C}$ $\rightarrow$ $\mathbb{C}$
such that for each triangle $T$ (with its interior), $f(T)$ is a
square (with interior, too) ?
I would have …
2
votes
1answer
69 views
Occurrence of the trivial representation in restrictions of Lie group representations
Suppose $G$ is a semisimple group, and $V_{\lambda}$ is an irreducible finite-dimensional representation of highest weight $\lambda$. Suppose $H \subset G$ is a semisimple subgrou …
3
votes
3answers
93 views
Does the Baker-Campbell-Hausdorff formula hold for vector fields on a (compact) manifold?
Consider a compact manifold M. For a vector field X on M, let $\phi_X$ denote the diffeomorphism of M given by the time 1 flow of X.
If X and Y are two vector fields, is $\phi_X \ …
3
votes
3answers
216 views
Integer points (very naive question)
Well, I don't have any notion of arithmetic geometry, but I would like to understand what arithmetic geometers mean when they say "integer point of a variety/scheme $X$" (like e.g. …
0
votes
0answers
16 views
How to generate correlated random binary data
Suppose I have a column of random binary numbers. I would like to find a way to generate a second column with the same number of cases that has a specified correlation with the ini …
-1
votes
0answers
78 views
tangent bundle and orientation [closed]
Let M is a smooth manifold, TM is tangent bundle. We know TM is Manifold too.
How to make TM orientable?
2
votes
1answer
161 views
Is there a name for this property of a topology?
This property seems like it should have a nice name, but I can't find one anywhere. Does anyone know a name for this?
For each non-empty open set $U$, there exist proper open s …
0
votes
0answers
7 views
Is there a good reference for the relationship between the Yangian and formal based loop group?
For every finite dimensional semi-simple Lie group $\mathfrak{g}$, we have a loop algebra $\mathfrak{g}[t,t^{-1}]$. This loop algebra has a natural invariant inner product by taki …
10
votes
0answers
87 views
Cayley graphs of finitely generated groups
Let $\approx$ be the binary relation on the class of finitely generated groups
such that $G \approx H$ iff $G$ and $H$ have isomorphic (unlabeled nondirected)
Cayley graphs with r …
3
votes
0answers
45 views
Is there a sensible notion of abstract constructible space?
In the past by the term "variety" people understood a subset of projective space locally closed for the Zariski topology. Now we have a more natural notion of abstract algebraic va …
10
votes
3answers
200 views
Mathematical symbols, their pronunciations, and what they denote: Does a comprehensive ordered list exist?
Often, certain symbols in mathematics denote different things in different fields. Is there any sort of ordered list that will tell you what a certain symbol means in alphabetical …
4
votes
2answers
78 views
Choice function for Borel sets?
Let's say we want to define a choice function for certain particular subsets $S \subset2^{\mathbb{R}}$, i.e. we want a function $c:S \rightarrow \mathbb{R}$ such that $c(X)\in X$ f …
