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Minicourse: Algebraic Structures and Closure Operations, Dr. Janet Vassilev.

Since the 20th century many commutative algebraists have studied individual closure operations such as the radical, integral closure, tight closure, and others. Some of these closures have lead to breakthroughs in classifying singularities and have resulted in shorter proofs to difficult theorems like the Briancon-Skoda Theorem. Through this workshop we will solidify the students' understanding of algebraic structures and introduce the notion of closure operation on the algebraic structures we discuss.
In particular, a closure operation on a ring R is a function mapping the set of ideals R to itself which is extensive, idempotent and order preserving. In this week the students will be introduced to the foundations of algebraic structures and closures and will gain some insight into elegant and powerful uses of these tools. We will use lecture, interactive games, discovery exercises and brainstorming sessions in groups, and motivate the material in part by coding theory.
One of our goals is to strengthen the students abstract and deductive reasoning skills, as well as clear oral and written presentation skills, in a fun and entertaining manner.

Professor Vassilev has been composing and grading the Math Contest since 2008, She has advised several undergraduate and graduate students on research projects, and is another of our most beloved teachers. In June 2011, she was awarded the William P. and Heather W. Weber Award for Teaching Excellence.