## Student Algebra & Combinatorics

•  Joshua Ruiter, Michigan State
•  Root systems - a powerful tool for classification
•  09/30/2019
•  4:30 PM - 5:30 PM
•  C304 Wells Hall

Root systems arose historically as a tool for classifying semisimple Lie algebras, but they can also be understood without that context. I will describe several concrete examples of root systems, with plenty of pictures. I will describe how to associate a special graph called a Dynkin diagram to a root system, and briefly describe the classification of root systems. If time allows, I will describe some of the applications to classifying semisimple Lie algebras and reductive algebraic groups. All you need to know to understand my talk is how to compute dot products on $\mathbb{R}^n$.

## Contact

Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science