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. ...

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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