Algebra Seminar: Tropical mathematics and dynamic programming
1:10p.m. Neill 106W
Abstract: I will introduce the ideas behind the "tropical approach" in mathematics. The tropical semiring uses the set of reals R and the extra element of infinity. But the tropical sum of two numbers is defined as their minimum, and the tropical product of two numbers is their sum. I will provide several examples of the otherwise common operations as defined using tropical arithmetic. Finally, I will illustrate its relevance to discrete mathematics by explaining how to solve the shortest path problem and the integer linear programming problem using tropical arithmetic. If time permits, I will also illustrate how to model the problem of DNA sequence alignment using tropical arithmetic.