## [PAST EVENT] Mathematics Colloquium: Nicholas Werner (State University of New York at Westbury)

February 15, 2019
2pm - 3pm
##### Location
Jones Hall, Room 302
200 Ukrop Way
Williamsburg, VA 23185Map this location
##### Access & Features
• 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.

Eric Swartz