Hi, I'm not sure if you can help me with this, but I'm currently looking for an upper bound on the real part of the roots of a polynomial with real coefficients. In other words, I have a polynomial $a_n x^n + a_{n - 1} x^{n - 1} + ... + a_1 x + a_0 = 0$ where $a_0, a_1, \dots, a_{n}$ are real ...

Single-use tags automatically expire after a few months. This is arguably the right thing when the tag is a misspelling (though I'd prefer some way of reviewing the process — but this post is not about that). However, if the tag was clearly deliberate, the default should be not to delete it. I pr...

Let $X$ be a complex minimal surface of general type, id est $K_X$ is big and nef. It is well-known that $\displaystyle\int_X3c_2(X)-c_1(X)^2\geq0$, and the equality holds if and only if $X$ is uniformized by $\mathbb{B}\subset\mathbb{C}^2$ (the open ball). Ever in this case: $X$ does not contain...

The corners theorem of Ajtai and Szemerédi states that if $A\subseteq[N]^2$ is corner-free, i.e. there are no $x,y,h\in\mathbb{N}$ with all of $(x,y),(x+h,y),(x,y+h)$ in $A$, then $|A|=o(N^2)$. The standard proof of this theorem is to apply the triangle removal lemma that follows from Szemerédi's...