**Nikolai Vavilov**

St. Petersburg State University, Russia

July 18, 2013

**A closer look at weight diagrams**:
The talk presents recent enhancements of the representation theoretic and geometric methods in the study of exceptional groups. In the
lectures at TIFR in 2011, and in the previous lectures this week in the framework ATM Workshop on Classical and Non-stable Algebraic K-Theory I sketched the use of minimal modules for calculations in exceptional groups over rings. Essentially, I explained, that weight
diagrams are an efficient substitute of matrices, when you deal with an individual column or row of a matrix. However, applications at the level of K_2 and more sophisticated applications at the level of K_1 require more. I outline some new results, which indicate that with the use of weight diagrams you can do much more, and easily calculate with several columns and/or rows of elements of exceptional groups. I mention several current or potential applications, such as stability for K_1 and K_2, description of subnormal subgroups, overgroups of subsystem subgroups, structure of not necessa