Mathematics & Computer Science Colloquium: October 8, 2019

Tuesday, October 8, 20194:00PM - Tuesday, October 8, 20195:00PM
At Ruffner 356

What is a partial order? Making use of mathematical hierarchies.

Michael Strayer is in his first year as an Assistant Professor of Mathematics and Computer Science at Hampden-Sydney College. He recently completed his PhD at the University of North Carolina at Chapel Hill, studying certain ways in which partially ordered sets can be used in the mathematical area of Lie algebra representation theory. Outside of math, he enjoys roasting (and drinking!) coffee, golf, and swimming. He and his wife welcomed their first child this past May.

The whole numbers have a familiar order to them: 1 is less than 2 which is less than 3, and so on. Moreover, any two whole numbers can be compared to each other in this order; that is, one will be less than the other. Do orders exist on other collections where two objects can be incomparable? Yes! For example, the CEO of a company is “greater than” every other employee in the company hierarchy, but two employees chosen at random may not be comparable in the hierarchy. A collection with such an order is called a partially ordered set, or poset for short, and it will be the primary focus of this talk. We will explore some basic concepts involving posets, emphasizing examples. We will also show how posets can be used to visually illuminate structure to help solve some interesting but deceptively difficult mathematical problems. The goal will be to always present ideas as visually as possible, and no prior mathematical knowledge will be needed.

Designed for a broad audience, Longwood's Math and Computer Science Colloquium Series explores ideas, developments and careers in the fields of mathematics, computer science and mathematics education. Learn more about the Colloquium Series