Polarization of Monomial Ideals

Isaac Cook

Polarization of monomial ideals is a technique in abstract algebra with powerful applications. The use of polarization provides combinatorial tools that allow for the study of monomial ideals in polynomial rings by analyzing square-free monomials. In this talk, we will provide a brief overview of the basics of abstract algebra so that we can discuss the properties of polarization. We will conclude with a discussion of real-world applications of polarization.

• Isaac Cook graduated as valedictorian from Liberty High School in 2019. He is a senior in the dual degree mathematics and engineering program with minors in biology and chemistry. Isaac is a member of Lander's Honors College, works as a consultant in the Writing Center on campus, and acts a youth leader at his local church.