MathOverflow Weekly Newsletter
MathOverflow Weekly Newsletter

Top new questions this week:

Connectedness in the language of path-connectedness

Is there a topological space $(C,\tau_C)$ and two points $c_0\neq c_1\in C$ such that the following holds? A space $(X,\tau)$ is connected if and only if for all $x,y\in X$ there is a ...

gn.general-topology point-set-topology  
asked by Dominic van der Zypen 22 votes
answered by Helene Sigloch 17 votes

On a drawing in Dixmier's Enveloping Algebras

This image comes from Dixmier's book, 'Enveloping Algebras' ('Alg├Ębres enveloppantes'). Dixmier writes that The curves shown on p. XIV have their origin in the study of U(sl(3)). They are ...

rt.representation-theory lie-groups lie-algebras  
asked by Jimmy Dillies 16 votes
answered by Jim Humphreys 8 votes

What are the applications of operator algebras to other areas?

Question: What are the applications of operator algebras to other areas? More precisely, I would like to know the results in mathematical areas outside of operator algebras which were proved by ...

oa.operator-algebras big-list gm.general-mathematics  
asked by Sébastien Palcoux 14 votes
answered by Nik Weaver 16 votes

Are there any natural differential operators besides $d$?

Let $\lambda = (\lambda_1, \ldots, \lambda_r)$ and $\mu = (\mu_1, \ldots, \mu_r)$ be partitions such that $\mu_j = \lambda_j +1$ for one index $j$ and $\mu_i = \lambda_i$ for all other $i$. Then there ...

dg.differential-geometry rt.representation-theory differential-operators  
asked by David Speyer 13 votes
answered by Vladimir Dotsenko 12 votes

Is there a natural bijection from $\mathbb{N}$ to $\mathbb{Q}$?

In a conversation where it came up that the Pythagoreans probably found an enumeration of the rational numbers I erroneously remarked that Georg Cantor found a natural bijection from $\mathbb{N}$ to ...

nt.number-theory lo.logic set-theory  
asked by Frode Bjørdal 13 votes
answered by Vladimir Dotsenko 26 votes

Enumeration of $0-1$ matrices with determinant $1$

Has the number $f(n)$ of $n \times n$, $0{-}1$ matrices whose determinant is $+1$ been enumerated? E.g., for $n{=}2$, there are $f(2)=3$ such matrices: $$ \left( \begin{array}{cc} 1 & 0 \\ 0 ...

co.combinatorics matrices finite-groups  
asked by Joseph O'Rourke 13 votes
answered by Gerhard Paseman 2 votes

Is $\sum_{k=1}^{n} \sin(k^2)$ bounded by a constant $M$?

I know $\sum_{k=1}^{n} \sin(k)$ is bounded by a constant. How about $\sum_{k=1}^{n} \sin(k^2)$?

real-analysis sequences-and-series  
asked by npbool 12 votes
answered by Terry Tao 22 votes

Greatest hits from previous weeks:

why study Lie algebras?

I don't mean to be rude asking this question, I know that the theory of Lie groups and Lie algebras is a very deep one, very aesthetic and that has broad applications in various areas of mathematics ...

dg.differential-geometry lie-groups lie-algebras differential-equations  
asked by Olivier Bégassat 57 votes
answered by Deane Yang 74 votes

Examples of common false beliefs in mathematics

The first thing to say is that this is not the same as the question about interesting mathematical mistakes. I am interested about the type of false beliefs that many intelligent people have while ...

big-list mathematics-education  
asked by gowers 452 votes
answered by Tilman 372 votes

Can you answer these?

Interesting triple integral

Some time ago I stumbled on an alleged identity $$\int\limits_0^\infty \frac{dx}{x} \int\limits_0^x \frac{dy}{y} \int\limits_0^y \frac{dz}{z} [\sin{x}+\sin{(x-y)}-\sin{(x-z)}-\sin{(x-y+z)}]= ...

ca.analysis-and-odes integration  
asked by Zurab Silagadze 4 votes

Finitely generated projective modules over the algebra of sections of the Clifford bundle

Consider a (pseudo-)Riemannian manifold $(M,g)$ and the corresponding Clifford bundle $Cl_g(T^*M)$. Let $R$ be the algebra of sections of $CL_g(T^*M)$, with point-wise multiplication. What are the ...

dg.differential-geometry riemannian-geometry clifford-algebras  
asked by Igor Khavkine 4 votes

Nekrasov-Okounkov hook length formula

I am now reading the paper An explicit expansion formula for the powers of the Euler Product in terms of partition hook lengths by Guo-Niu Han. The author rediscovered what he calls ...

nt.number-theory modular-forms symmetric-group algebraic-combinatorics young-tableaux  
asked by Dianbin Bao 8 votes
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