### Mathematics Colloquium

** NIGEL BOSTON
**

UW Madison

**Title:** Some Novel Applications of Algebra

**Date:** Monday, February 11, 2019

**Place and Time:** Room 101, Love Building, 3:35-4:25 pm

**Refreshments:** Room 204, Love Building, 3:00 pm

**Abstract.**
I shall briefly describe three recent examples of how algebra has enabled breakthroughs in problems arising in engineering. The first concerns the shape of entropy regions, a problem motivated by network coding but one that turns out to be equivalent to a question in group theory. The second concerns the Belgian Chocolate Problem, which arises in control theory and turns out to be amenable to algebraic attack, with mysterious connections to the abc conjecture. The third concerns the Power Flow Equations, whose real solutions correspond to operating points for power systems and whose number we can efficiently study via commutative algebra. No assumption of expert knowledge in algebra or engineering will be made.