WEDNESDAY SEPTEMBER 7, 2016.   SH room 1013B

Speaker: Jonathan Lopez

Title: A classification of small operators using graph theory               (joint work with Terry Bisson)

Time: 2:30pm

Abstract: Given a real n \times m matrix X, its operator norm is defined by

    \[||X|| = \max_{||v||=1} ||Xv||.\]

We consider a matrix “small” if it has non-negative integer entries and its operator norm is less than 2. These matrices correspond to bipartite graphs with spectral radius less than 2, which can be classified as disjoint unions of Coxeter graphs. Our goal here is to see these known results as part of a general program of classification of “small” objects, as in classification.

Speaker: Peter Maceli

Title: Graph theory and its place in mathematics

Time: 3:00pm

Abstract: Graph theory is a young and exciting area of discrete mathematics. For our purposes, a graph is just a bunch of dots together with lines or curves joining certain pairs of these dots. Though at first glance graphs may seem like simple objects to study, the field of graph theory contains some of the deepest and most beautiful mathematics of the last fifty years. Being an extremely visual field, many problems in graph theory are easily stated, yet have complex solutions with far reaching implications and applications. Graph theory arises in fields such as computer science, linguistics, chemistry, game theory, and many others. In this talk we will touch on a number of problems in graph theory that could lead to student projects.