Arithmetic statistics of rational matrices of bounded height

2:00 pm, Wednesday, 1st May

Abstract

Consider the set of matrices whose entries are rational numbers of height at most H. In this talk, we present several bounds related to the arithmetic statistics of this set, e.g., on the number of matrices with a fixed rank or determinant or characteristic polynomial. These results can be seen as analogues to several known results on the statistics of integer matrices of bounded height. Joint work with Vivian Kuperberg (ETH Zürich), Alina Ostafe and Igor E. Shparlinski.