| Name: | Elliot Glazer |
|---|---|
| Email: | eglazer (at) reu (dot) dimacs (dot) rutgers (dot) edu |
| Office: | Hill 323 |
| School: | Rutgers University |
| Project: | K-theory and Grothendieck classes of T-stable varieties (tentative title) |
| Advisor: | Anders Buch, Department of Mathematics, Rutgers University |
I met with Professor Buch to discuss subjects I should read about before the start of the REU. I read about modules, group representations, and varieties from Algebra (Artin). I continued my reading on modules in Abstract Algebra (Dummit and Foote), from which I also learned the definitions of the tensor product of modules and exact sequences.
Moved into my apartment and attended orientation. Had two meetings with Professor Buch and Gyu Eun. In the first meeting, Professor Buch introduced some of the basic notation and definitions relating to our project, in particular the K-homology and K-cohomology of a ring. In the second meeting, we learned more background and terminology, and were told our particular problem involving multidimensional matrices. Learned more background material from Gyu Eun. Read through Professor Buch's notes and attempted his exercises. Gave our initial presentation describing the subject and problem. Read about homogeneous coordinates to understand projective space better.
I read through Gyu Eun's notes on the project. These notes clarified the notation and terminology Professor Buch had presented to us in our meetings. This helped me to better understand graded rings and modules, short exact sequences of representations, the Grothendieck group of T-representations, and how these all relate. Met with Gyu Eun to discuss the basic terms and exercises. We had our third meeting with Professor Buch, where he discussed graded vector spaces and the computation of Grothendieck classes.