3 problems

Let $A$ be a homogeneous $k$-algebra, and consider the maximal degrees of the syzygies in a graded free resolution of $A$. Herzog–Srinivasan conjecture. The degree of $A$ is bounde…

Let $F\colon \mathbb{R}^n \to \mathbb{R}^m$ be a fully connected neural network classifier with $\ell$ hidden layers of widths $n_1,\ldots,n_\ell \geq n$, logistic sigmoid activati…

For permutations $v,w\in S_n$ with $v\leq w$, let $P_{v,w}(q)$ be the Kazhdan–Lusztig polynomial and let $H_{v,w}(q)$ be the local $h$-polynomial of the Schubert variety $X_w$ at…