6 papers
A geometric approach to the density of rank-metric codes
Shamil Asgarli, Lian Duan, Nathan Kaplan +1
We study the asymptotic density of -point-free linear sections of geometrically irreducible projective varieties over finite fields. We then apply these results to ra…
Sandpile groups of random bipartite graphs and families of distributions with the same moments
Jason Fulman, Nathan Kaplan, Deepesh Singhal +1
Recently, there has been significant interest in applying the method of moments developed by Wood and others to study distributions of finite abelian groups that arise in number th…
A mod determinant criterion for Cohen--Lenstra convergence of random -adic matrices with prescribed zero patterns
Hyungmin Jang, Nathan Kaplan, Jungin Lee +1
We study the distribution of cokernels of Haar-random matrices over the -adic integers with prescribed zero patterns, motivated by the Cohen--Lenstra heuristics. A central featu…
The shape of a random numerical semigroup
Maria Bras-Amorós, Nathan Kaplan, Deepesh Singhal
We study statistical properties of random numerical semigroups of a given genus. We analyze the graph of a typical numerical semigroup, understood as a function from t…
The probability of isomorphic group structures of isogenous elliptic curves over finite fields
John Cullinan, Nathan Kaplan
Let l be a prime number and let E and E' be l-isogenous elliptic curves defined over Q. In this paper we determine the proportion of primes p for which E(F_p) is isomorphic to E'(F…
The probability of non-isomorphic group structures of isogenous elliptic curves in finite field extensions, II
John Cullinan, Shanna Dobson, Linda Frey +5
Let and be 2-isogenous elliptic curves over $\Q$. Following \cite{ck}, we call a good prime \emph{anomalous} if $E(\F_p) \simeq E'(\F_p)$ but $E(\F_{p^2}) \not \simeq…