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Given a finite degree $d$ cover of curves $f: X \to \mathbb P^1$, we study $f_* \mathscr O_X$, which is a rank $d$ vector bundle on $\mathbb P^1$, hence can be written as a direct sum of line bundles $f_* \mathscr O_X \simeq \oplus_{i=1}^d \mathscr O(a_i)$. Naively, one might expect that if the…

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Abstract

Let $X$ be an $n \times n$ sparse random symmetric matrix that is a Hadamard product of $G$ and $\Xi$, where $G$ is a Wigner matrix with centered sub-Gaussian entries (the distribution of the diagonals is allowed to be different) and $\Xi$ is a symmetric matrix with i.i.d. Bernoulli $p$ entries…

Abstract

Abstract

Abstract

tba

Abstract

Abstract