Colloqiuim- Matroids and the combinatorics of matrix rank

Title: Matroids and the combinatorics of matrix rank

Speaker:  Louis Deaett, Quinnipiac University

Date and Time: Friday, April 26, 2:00-3:00pm

Place: Rome 206

Abstract :  Combinatorial matrix theory regards a matrix as a combinatorial object by considering patterns in the rectangular grid of its entries.  From this point of view, we may impose combinatorial conditions on a matrix and ask what these imply about its properties as an operator.  Here we focus on the rank.  The question of what values are possible for the rank of a matrix satisfying certain combinatorial conditions has been studied in a variety of contexts, motivated by a variety of applications.  We survey some of these, and introduce recent work that examines how matroid theory can shed light on the situation.

Bio: Louis Deaett earned his Ph.D. in 2009 at the University of Wisconsin–Madison under the supervision of Richard Brualdi.  He completed a postdoctoral fellowship at the University of Victoria, and is now an associate professor of mathematics at Quinnipiac University.  His interests lie primarily in the intersection of linear algebra and combinatorics.