Karen Smith, University of Michigan, will be the Earle Raymond Hedrick Lecturer at MAA MathFest 2015 in Washington, D.C. The title of her Hedrick Lecture Series is Algebra Over Finite Fields.
Hedrick Lecture 1
Wednesday, August 5, 9:30 AM - 10:20 AM, Marriott Wardman Park, Salon 2/3
Starting with a little trick I learned in third grade to check my multiplication homework, I'll share my fascination with algebra as it grew through middle school, high school, college and eventually led to research in characteristic p rings. Along the way, I'll point out the importance of many mentors and teachers who led me to eventually pursue my career in mathematics.
Hedrick Lecture 2
Friday, August 7, 9:30 AM - 10:20 AM, Marriott Wardman Park, Salon 2/3
In the second talk, I will explain how doing algebra over finite fields can deepen our understanding of geometry. Specifically, I'll discuss how understanding solutions to polynomials over finite fields can help understand the geometry of algebraic varieties defined by real or complex polynomials. Miraculously, rings of characteristic p have some very special properties that can be powerful tools in analyzing them, often replacing tools like integration for real manifolds.
Hedrick Lecture 3
Saturday, August 8, 9:30 AM - 10:20 AM, Marriott Wardman Park, Salon 2/3
In the third talk, I will explain some of these recent tools in “characteristic p” algebra---specifically Frobenius splitting and related tools--- which have made an impact on different areas of math, including the minimal model program for complex algebraic varieties and cluster algebras in combinatorics/representation theory. Some of this work is joint work with my PhD students and post-docs.
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