PhD Candidate in Mathematics

Boulder, CO 80309-0395

 Office: Math 360 Email: sebastian.bozlee AT colorado.edu

## Notes

• ### Solutions to Recurrence Relations:

These notes derive the fundamental solutions associated to linear homogeneous recurrence relations using linear algebra, including the repeated eigenvalue case. The approach in these notes differs from the usual approach in that I do not use generating functions. Link

• ### Solutions and Elaborations for Weibel's "Introduction to homological algebra"

Weibel's "homological algebra" is a book with a lot of content, but also a lot left to the reader. Here I attempted to fill in some of what's left to the reader: filling in gaps in proofs, performing checks, correcting errors, and doing exercises.

These notes are very much a work in progress, with only solutions for parts of chapters 3, 4, and 8. Feel free to contact me with any corrections. Last updated 1/19/17. Link

• ### Introductory Category Theory Notes

Notes for a series of lectures on category theory for first year graduate students.

Day 1
Day 2
Day 3
• ### Intro to Sheaves and Abelian Categories

Notes for a 2 hour talk introducing sheaves and abelian categories. Aimed at graduate students who have completed a graduate course or two in algebra and topology.

• ### Reference sheets

Notes I wrote while taking these courses:

## Apps

• ### Projective Curve Viewer

Displays algebraic curves in the real projective plane. Available under the terms of the GPL.

Source (Qt Creator Project)

## Publications

• Rank Drops of Recurrence Matrices in Electronic Journal of Linear Algebra, 2015.

Abstract: A recurrence matrix is a matrix whose terms are sequential members of a linear homogeneous recurrence sequence of order k and whose dimensions are both greater than or equal to k. In this paper, the ranks of recurrence matrices are determined. In particular, it is shown that the rank of such a matrix differs from the previously found upper bound of k in only two situations: When (a_j) satisfies a recurrence relation of order less than k, and when the nth powers of distinct eigenvalues of (a_j) coincide.

• Asymptotic equivalence of group actions on surfaces and Riemann-Hurwitz solutions in Archiv der Mathematik, with coauthor Aaron Wootton. 2014.