**13**

votes

**0**answers

454 views

### What are some examples of weak ω-categories?

As is usual, let's say an (n, k)-category is something with
objects, morphisms, 2-morphisms, ..., n-morphisms, such that all
j-morphisms for j > k are invertible, everything meant in the
weak sense. ...

**7**

votes

**0**answers

123 views

### Nice applications of Liouville's theorem

I need a big list of nice-looking and simple applications of Liouville's theorem on geodesic flow in Riemannian geometry.
Please help.
Examples:
A Riemannian manifold with finite volume does not ...

**7**

votes

**0**answers

1k views

### “Must read ”papers on analytic number theory

Question: What would be some must-read
papers for an aspiring analytic number
theorist? In other words, what are the papers that any analytic number theorist would have read? (Background: ...

**5**

votes

**0**answers

134 views

### List of finitely presented groups with undecidable word problem

Is there any reasonably updated list of (representative) examples of finitely presented groups with undecidable word problem?
By "representative" I mean "avoiding obvious redundancy", i.e. examples ...

**5**

votes

**0**answers

226 views

### What will be the consequences if second Hardy-Littlewood conjecture turns out to be true?

It is generally believed that the Second Hardy-Littlewood Conjecture is false. But it has not been proved (or disproved) yet. My question is,
What would be the consequences if Second ...

**4**

votes

**0**answers

193 views

### Quotations about the class number formula, etc.

I'm looking for interesting and/or expressive quotations from mathematicians about the class number formula. I'm interested both in quotations from historical mathematicians and from modern ...

**2**

votes

**0**answers

120 views

### What other axioms for set theory can be written in the form: “If mathematical structures $X$ and $Y$ are equipotent, then they're isomorphic”?

The "injective continuum function hypothesis" (ICF) is the following statement.
ICF (Version 0). For all cardinal numbers $\kappa$ and $\nu$, we have $2^\kappa = 2^\nu \rightarrow \kappa = \nu.$
...

**2**

votes

**0**answers

93 views

### Non-negative, monotone polynomial sequences without combinatorial interpretation

I am wondering what sequences of integers there are, that are known to grow polynomially, are non-negative, monotone but lacks a combinatorial interpretation.
By combinatorial interpretation, they ...

**2**

votes

**0**answers

131 views

### Isoperimetric inequality, isodiametric inequality, hyperplane conjecture… what are the inequalities of this kind known or conjectured?

I duplicate here a question I asked on math.stackexchange.
Question: Which inequalities similar to the famous isoperimetric inequality is known?
conjectured?
I recently learned about some ...

**2**

votes

**0**answers

244 views

### Forgetting extra structure inducing Symmetries

This is a major edit of the original post after receiving helpful comments.
It is often the case when one adds additional structure to make a problem more tractable. When one attempts to forget this ...

**1**

vote

**0**answers

76 views

### Examples of noncommutative Bezout domains

I would like to see some (or many!) examples of noncommutative Bezout domains (one-sided principal ideals sum to one-sided principal ideals). I've read somewhere that it's not easy to find an example ...

**1**

vote

**0**answers

379 views

### applications of gauss-bonnet theorem

In wikipedia,I was pretty amazed to find a proof of fundamental theorem of algebra
using gauss bonnet theorem.I think given how central it is to mathematics with its far reaching generalizations like ...

**1**

vote

**0**answers

269 views

### Applications of the class number formula, etc.

This is a big list of applications of the class number formula and its generalizations. I'll start:
The solution to Gauss's class number problem for imaginary quadratic fields, and more generally ...

**0**

votes

**0**answers

48 views

### The set of (property) elements of a locally compact group is closed

For which properties $(P)$ is the following statement known to be true?
In any locally compact group $G$, the elements of $G$ that satisfy $(P)$ form a closed subset of $G$. In other words, the ...