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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).
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