[PAST EVENT] Mathematics Colloquium: Nicholas Werner (State University of New York at Westbury)
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- Open to the public
Mathematics Colloquium: Nicholas Werner (State University of New York at Westbury)
TITLE: Reachable Pairs in Digraphs and Zero Pattern Matrix Rings
ABSTRACT: This talk will discuss two closely related problems, one in graph theory and one involving matrix rings. Given vertices $u$ and $v$ in a directed graph (digraph) $\Gamma$, we say that the ordered pair $(u, v)$ is a reachable pair if there exists a path of directed edges from $u$ to $v$. One may ask: if the digraph $\Gamma$ has $n$ vertices, then how many reachable pairs could $\Gamma$ contain? To answer this question, we translate it into an algebraic form and consider the problem of counting the number of nonzero entries in certain rings of $n \times n$ matrices.
No prior knowledge will be assumed, and the talk should be accessible to undergraduates. This is joint work with Eric Swartz.