MathOverflow Weekly Newsletter
MathOverflow Weekly Newsletter

Top new questions this week:

Producing finite objects by forcing!

It is a trivial fact that forcing can not produce finite sets of ground model objects. However there are situations, where we can use forcing to prove the existence of finite objects with some ...

reference-request lo.logic set-theory ho.history-overview forcing  
asked by Mohammad Golshani 27 votes
answered by Joel David Hamkins 11 votes

Graduate program applications that require questionnaires and other non-letter material

In the December 2014 AMS Notices, a letter to the editor (http://www.ams.org/notices/201411/rnoti-p1311.pdf) by Deconinck and Medlock addresses the problem of (math) graduate programs requiring letter ...

soft-question big-list career  
asked by KConrad 22 votes
answered by KConrad 6 votes

Unstable homotopy groups of spheres beyond Toda's range

In 1962 Toda published his book "Composition methods in homotopy groups of spheres", which contains computations of $\pi_{n+k}(S^n)$ for $k\le 19$ and $n\le 20$. The values of these groups are ...

reference-request at.algebraic-topology homotopy-theory  
asked by Mark Grant 20 votes
answered by Ryan Budney 17 votes

Cantor's theorem for presheaves?

Some years back (before MathOverflow was born), Tom Leinster asked an interesting question at the $n$-Category Café which I don't recall ever seeing an answer for: Does there exist a ...

ct.category-theory  
asked by Todd Trimble 15 votes

ULU Decomposition of a matrix

Let $g \in GL_n(\mathbb{F}_q)$. Is it true that we can always write $g = u_1lu_2$, where $u_1$ and $u_2$ are upper-triangular and $l$ is lower-triangular? Note that I'm not requiring that the matrices ...

gr.group-theory rt.representation-theory matrices  
asked by Scott Andrews 15 votes
answered by Andrei Smolensky 10 votes

The letters of the word "ART"

Edit: According to the Gelfand duality between topological spaces and commutative $C^{*}$algebras, I add some new tags. So the question is that what is the structure of $ Ext (A,A)$ where $A$ is ...

gn.general-topology oa.operator-algebras c-star-algebras operator-theory extension  
asked by Ali Taghavi 14 votes
answered by Will Sawin 3 votes

Joyal's letter to Grothendieck

Mostly out of curiosity: Where do I find Joyal's letter to Grothendieck in which he defines a model structure on simplicial sheaves? The question was already asked in this MO post, but that ...

reference-request model-categories  
asked by Helene Sigloch 14 votes
answered by Alexander Campbell 16 votes

Greatest hits from previous weeks:

Are there other nice math books close to the style of Tristan Needham?

Hello, I've been very positively impressed by Tristan Needham's book "Visual Complex Analysis", a very original and atypical mathematics book which is more oriented to helping intuition and insight ...

books math-communication big-list  
asked by Marco 81 votes
answered by L J 25 votes

Computer Algebra Errors

In the course of doing mathematics, I make extensive use of computer-based calculations. There's one CAS that I use mostly, even though I occasionally come across out-and-out wrong answers. After ...

computer-algebra big-list  
asked by Kevin O'Bryant 65 votes
answered by Dan Piponi 119 votes

Can you answer these?

Algorithm to minimally connect line segments in Euclidean plane

Suppose you have finitely many line segments in the Euclidean plane. How do you "connect them to form one chain of line segments of minimal length?" More formally and generally, what I'm looking for ...

graph-theory linear-programming convex-optimization integer-programming  
asked by Xoph 3 votes

An extension of group schemes admitting Neron models

Let $R$ be a discrete valuation ring, $K$ its field of fractions, and $$ 0 \rightarrow G_K' \rightarrow G_K \rightarrow G_K'' \rightarrow 0$$ a short exact sequence of smooth $K$-group schemes of ...

ag.algebraic-geometry algebraic-groups group-schemes neron-models  
asked by Question Mark 4 votes

invariant measures of the expanding maps on the circle

I would be very happy to know about original references for the following results; For the expanding map $x \mapsto mx$ on the circle, (with $m$ some integer greater than 1) (1) There exist ...

reference-request ds.dynamical-systems ergodic-theory  
asked by user20471 2 votes
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