Sarthak Chimni : Counting subrings of $\mathbb{Z}^n$ of non zero co-rank

Posted by Alina Carmen Cojocaru , part of the Number Theory Seminar.

At

Oct. 11, 2019, 9:30 a.m.

In

1227 SEO

Abstract

In this talk I will report on a joint work with Gautam Chinta and Ramin Takloo-Bighash in which we study subrings of $\mathbb{Z}^{n+k}$, of $(n+k)$-tuples of integers, of co-rank $k$. We relate the number of subrings $R$ such that the torsion subgroup of $\mathbb{Z}^{n+k}/R$ is of size $r$ to the number of full rank subrings of $\mathbb{Z}^n$ of index $r$.

The seminar lasts 80 minutes (9:30am-10:50am).