I took the liberty of creating the upper-bounds tag, and of retagging the linked upper-bonds question.

Given $\gamma \in [0, 1)$, an integer $N \ge 2$, and a decreasing null sequence of positive numbers $e_1,e_2,\ldots,e_t,\ldots$, I'm interested in estimating the sum $S_N := \sum_{t=1}^N\gamma^t e_{N-t}$. Question What is a good upper bound for $S_N$ for large $N$ ? Observations Empirically, ...

Let $a,b \in (0, 1)$ and $N \ge 1$, and consider the incomplete gamma function $x \mapsto \Gamma(1-a,x)$. Question Is there a simple bound (involving 'simple function's) for the expression $\Gamma(1-b,\log(a))-\Gamma(1-b,N\log(a))$ ? Motivation Ultimately, I'm interesting in bounding the sum ...

Recently I dug up some biographical details of Lindsay Burch, of Hilbert-Burch Theorem fame, whose few papers have had quite an impact on commutative algebra. This made me curious about the first women who obtained PhDs in abstract algebra in the US and Britain. Question 1: Who was the first wom...

I am still studying Deligne and Illusie's paper (https://eudml.org/doc/143480), and I am again stuck, this time on pages 262/263. Assume $X\longrightarrow S$ is a smooth morphism of $\mathbb{F}_{p}$-schemes, then $\operatorname{Lif}(X,\tilde{S})$ is the gerbe of liftings to $\tilde{S}=S(\mathbb{Z...

I've just stumbled on something that seems either too good to be true, or else too good for me not to have heard of it before. It has to do with the basepoint forgetting map $$ u: [A, M] \to \langle A, M \rangle, $$ where $A$ is a pointed space, $M$ is a topological monoid, and $\langle A, M\ran...

Let $M$ be an abelian monoid. For sake of simplicity we shall assume that in $M$ the cancellation law holds true. With this last assumption we define the group completion $G$ of $M$ as $$G:=M\times M/\sim$$ where $(a,b)\sim (a',b')$ if and only if $a+b'=a'+b$. It has been quite surprizing find ou...

The question is from the definition of to topological group. I can find an example such that the inversion map is continuous but the group operation is not continuous, but I cannot find an example such that the group operation is continuous but the inversion map is not continuous. I guess that su...

Do we know any problem in NP which has a super-linear time complexity lower bound? Ideally, we would like to show that 3SAT has super-polynomial lower bounds, but I guess we're far away from that. I'd just like to know any examples of super-linear lower bounds. I know that the time hierarchy the...