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# Number Theory Seminar

“Integer-Valued Polynomials on 3 × 3 Matrices” Presented by: Asmita Sodhi

#### Time

In this talk we will visit (or revisit, as the case may be) the world of integer-valued polynomials, first defining them for a subset of the integers, as well as defining Bhargava’s p-orderings and $p$-sequences. We will then see how the idea of maximal orders can allow us to extend Bhargava’s tools to the noncommutative case of integer-valued polynomials over the ring $M_n(\mathbb{Z})$ of $n\times n$ integer matrices. In particular, we will examine the case of the $3\times 3$ matrices.