MathOverflow Weekly Newsletter
MathOverflow Weekly Newsletter

Top new questions this week:

The view from inside of a mirrored tetrahedron

Suppose you were standing inside a regular tetrahedron $T$ whose internal face surfaces were perfect mirrors. Let's assume $T$'s height is $3{\times}$ yours, so that your eye is roughly at the ...

mg.metric-geometry convex-polytopes billiards visualization reflection-groups  
asked by Joseph O'Rourke 35 votes
answered by Ryan Budney 46 votes

Fermat's last theorem over larger fields

Fermat's last theorem implies that the number of solutions of $x^5 + y^5 = 1$ over $\mathbb{Q}$ is finite. Is the number of solutions of $x^5 + y^5 = 1$ over $\mathbb{Q}^{\text{ab}}$ finite? Here ...

ag.algebraic-geometry nt.number-theory arithmetic-geometry algebraic-number-theory diophantine-equations  
asked by Pablo 23 votes
answered by Alex B. 10 votes

Underlying idea for (automorphic) L-function?

To preface, I am a student of automorphic representation theory, and I know full well the definition of the L-function attached to an automorphic representation. I am intending to give a talk on the ...

nt.number-theory automorphic-forms big-picture l-functions  
asked by WSL 21 votes
answered by Myshkin 9 votes

When is a topological space the homotopy colimit of an open covering?

Suppose that $X$ is a topological space and $\left(U_i \to X\right)$ is an open cover. We can associate to it the Cech diagram of this cover $$C_U:\Delta^{op} \to Top.$$ I know that for many good ...

at.algebraic-topology homotopy-theory simplicial-stuff  
asked by David Carchedi 15 votes
answered by Marc Hoyois 14 votes

Can all $L^2$ holomorphic functions on a domain vanish at a particular point?

Let $\Omega \subset \mathbb{C}^n$. Is it possible that there is a point $p \in \Omega$ such that every $f \in A^2(\Omega) = L^2(\Omega) \cap \mathcal{O}(\Omega)$ has a zero at $p$? The space ...

complex-geometry cv.complex-variables several-complex-variables  
asked by Steven Gubkin 15 votes
answered by David Speyer 5 votes

Is there a cotangent bundle of a stable $\infty$-category?

Let $C$ be a stable $\infty$-category. Is there any categorical construction $C \mapsto T^* C$, where $T^* C$ is another stable $\infty$-category, that specializes to the following? When $C$ is the ...

ag.algebraic-geometry triangulated-categories quivers  
asked by David Treumann 15 votes

A game of stones

How I arrived at this question is a rather long story having to do with the honors calculus class I am teaching. At this point it's sheer curiosity on my part. Here is the game. ...

co.combinatorics  
asked by Liviu Nicolaescu 14 votes
answered by David Eppstein 12 votes

Greatest hits from previous weeks:

Examples of unexpected mathematical images

I try to generate a lot of examples in my research to get a better feel for what I am doing. Sometimes, I generate a plot, or a figure, that really surprises me, and makes my research take an ...

soft-question big-list experimental-mathematics visualization  
asked by Per Alexandersson 95 votes
answered by Terry Tao 98 votes

What is convolution intuitively?

If random variable $X$ has a probability distribution of $f(x)$ and random variable $Y$ has a probability distribution $g(x)$ then $(f*g)(x)$, the convolution of $f$ and $g$, is the probability ...

pr.probability ca.analysis-and-odes intuition  
asked by Kim Greene 81 votes
answered by Terry Tao 94 votes

Can you answer these?

State of the art in the theory of integer sequences

I was going through N.J.A. Sloane's 'Encyclopedia of Integer Sequences'. In it are discussed many tricks that are used to determine the recursive definition or explicit formula for a given sequence. ...

sequences-and-series big-picture integer-sequences  
asked by Vijay Konnur 3 votes

Many integral points on quartic models of elliptic curve via differences of squares

Pick fourth power free integer $n$ ($p^4$ doesn't divide $n$). Represent $n$ as difference of possibly negative integer squares $n=v_i^2-u_i^2$. The goal is to find quadratic polynomial with integer ...

nt.number-theory elliptic-curves experimental-mathematics  
asked by joro 4 votes

spectral sequence of a bicomplex equipped with a group action

Let $(A_1^\bullet,\partial_1)$ and $(A_2^\bullet,\partial_2)$ be complexes of $\mathbb{C}$-vector spaces. We suppose that $(A_1^\bullet,\partial_1)$ and $(A_2^\bullet,\partial_2)$ are equipped with ...

at.algebraic-topology homological-algebra  
asked by Yeping Zhang 4 votes
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