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pro vyhledávání: '"Wood, Melanie Matchett"'
Autor:
Wood, Melanie Matchett
We consider the probability theory, and in particular the moment problem and universality theorems, for random groups of the sort of that arise or are conjectured to arise in number theory, and in related situations in topology and combinatorics. The
Externí odkaz:
http://arxiv.org/abs/2301.09687
Autor:
Sawin, Will, Wood, Melanie Matchett
Cohen, Lenstra, and Martinet have given conjectures for the distribution of class groups of extensions of number fields, but Achter and Malle have given theoretical and numerical evidence that these conjectures are wrong regarding the Sylow $p$-subgr
Externí odkaz:
http://arxiv.org/abs/2301.00791
Autor:
Nguyen, Hoi H., Wood, Melanie Matchett
In this paper we study the cokernels of various random integral matrix models, including random symmetric, random skew-symmetric, and random Laplacian matrices. We provide a systematic method to establish universality under very general randomness as
Externí odkaz:
http://arxiv.org/abs/2210.08526
Autor:
Sawin, Will, Wood, Melanie Matchett
The moment problem in probability theory asks for criteria for when there exists a unique measure with a given tuple of moments. We study a variant of this problem for random objects in a category, where a moment is given by the average number of epi
Externí odkaz:
http://arxiv.org/abs/2210.06279
For $2 \leq d \leq 5$, we show that the class of the Hurwitz space of smooth degree $d$, genus $g$ covers of $\mathbb P^1$ stabilizes in the Grothendieck ring of stacks as $g \to \infty$, and we give a formula for the limit. We also verify this stabi
Externí odkaz:
http://arxiv.org/abs/2203.01840
Autor:
Sawin, Will, Wood, Melanie Matchett
For $G$ and $H_1,\dots, H_n$ finite groups, does there exist a $3$-manifold group with $G$ as a quotient but no $H_i$ as a quotient? We answer all such questions in terms of the group cohomology of finite groups. We prove non-existence with topologic
Externí odkaz:
http://arxiv.org/abs/2203.01140
We determine the average size of the 3-torsion in class groups of $G$-extensions of a number field when $G$ is any transitive $2$-group containing a transposition, for example $D_4$. It follows from the Cohen--Lenstra--Martinet heuristics that the av
Externí odkaz:
http://arxiv.org/abs/2110.07712
Akademický článek
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Autor:
Wang, Weitong, Wood, Melanie Matchett
The goal of this paper is to prove theorems that elucidate the Cohen-Lenstra-Martinet conjectures for the distributions of class groups of number fields, and further the understanding of their implications. We start by giving a simpler statement of t
Externí odkaz:
http://arxiv.org/abs/1907.11201
We consider the distribution of the Galois groups $\operatorname{Gal}(K^{\operatorname{un}}/K)$ of maximal unramified extensions as $K$ ranges over $\Gamma$-extensions of $\mathbb{Q}$ or $\mathbb{F}_q(t)$. We prove two properties of $\operatorname{Ga
Externí odkaz:
http://arxiv.org/abs/1907.05002