Carmen A. Bruni

Documents

This is my Comprehensive Exam File. As a requirement for obtaining a PhD in mathematics at UBC, one must write and pass a qualifying exam. To prepare for this, I tried to solve as many relevant questions as possible. Here is a copy of the document I created while solving these problems. I would like to thank Faisal al-Faisal and Vince Chan for their help with the problems and correcting the material. As a caveat, I must warn the reader that some solutions might be incorrect and that the file is incomplete. At the very least, this file can serve as a guide for solving problems and provide the statements of the relevant theorems needed to pass the exam.

 

Since posting this file, many other UBC students have been joining to help future students tackle this exam. One such student, Maxime Bergeron has given me his file to post here.

 

A copy of my Masters project on the Riemann-Roch theorem for algebraic curves can be found here.

 

Compute the determinant of the Killing form with respect of the standard basis for the Lie algebra sl(3,C) via brute force.

- MAPLE file.

- Text file

 

Compute the determinant of the Killing form with respect of the standard basis for the Lie algebra sl(n,C). (Uses the fact that this is just 2nTr(xy) via an exercise from class).

- MAPLE file.

- Text file

 

Compute the determinant of the Killing form with respect of the standard basis for the Lie algebra sl(n,C) quickly. (Left as an exercise to the reader to verify its correctness).

- MAPLE file.

- Text file

 

Also, see an updated entry in OEIS on the above.

 

Here is a continuity application I made as a part of the TAAP accreditation program.

 

A copy of the graduate colloquium talk I gave on November 29th, 2012 can be found here.

 

A copy of the talk I gave for CMS in December of 2012 can be found here. The OEIS reference found in this file can be found here.

 

Here is a copy of my CV.

 

 

 

 

 

 

PhD Candidate - Mathematics