Santa Clara University

Mathematics and Computer Science department

Colloquium Series

Winter 2012

Unless otherwise noted, talks will be at 3:50 PM in O'Connor 204.  Also, there will be refreshments before each talk in O'Connor 31 at 3:40 PM.

Tuesday January 24, O'Connor 204

Speaker: Rick Scott, Santa Clara University

Title: Groups with Cayley graph isomorphic to a cube, part I

Abstract: Groups are algebraic objects that capture the notion of symmetry in mathematics. One way to study a group is from the geometric perspective of its Cayley graph -- a collection of vertices and labeled edges that exhibits the symmetries of the group. In this talk we will consider groups whose Cayley graphs are cubes. We will give a combinatorial characterization of these groups in terms of generators and relations and describe a correspondence between such groups and certain decorated graphs. The talk will start with a gentle introduction to groups and Cayley graphs, including definitions and examples.

Tuesday, January 31, O'Connor 204

Speaker: Colin Hagemeyer, Santa Clara University

Title: Groups with Cayley graph isomorphic to a cube, part II

Abstract: Representation theory studies groups by relating a group to specific matrix groups which may share many of the properties of the original group (technically speaking a representation is a homomorphism from a group to a matrix group). This allows one to use what we know about linear mappings to better understand groups. Importantly, each representation of a group may be decomposed into a number of (possibly different) irreducible representations of that specific group. In this talk we will look at how representation theory relates to groups with Cayley graph isomorphic to a cube, and specifically will associate with each decorated graph a geometric representation based off of its Cayley graph. We will show that this representation must always be reducible (ie. can be decomposed into more than one irreducible representation).

If you have a disability and require a reasonable accommodation,
please call/email Rick Scott 408-554-4460/rscott at scu dot edu (or
use 1-800-735-2929 TTY—California Relay).

Abstracts of previous talks are available here.
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