Joseph Breen
About
Welcome! I am currently a second year Ph.D. student in the department of mathematics at UCLA. I graduated with a B.A. in mathematics from Northwestern University in 2016.
Here is a copy of a fairly recent CV: (pdf)
You can find and contact me at:
- Office: MS 3915C
- E-mail: josephbreen@ucla.edu
Research and Publications
- On the sign characteristic of Hermitian linearizations in DL(P). Joint work with M. Bueno, S. Ford, and S. Furtado. Linear Algebra and its Applications, 519 (2017), 73-101. (link)
Teaching
Current teaching (Spring 2018):- Math 115AH: Honors Linear Algebra
- Office hours: Tuesday 3-4, Wednesday 4-5
- Some extra "challenge" exercises, updated through the quarter: (pdf)
- Math 33A: Linear Algebra and Applications
- Office hours: Thursday 11-12
- SMC: Tuesday 11-12
Previous teaching:
- Winter 2018: Math 31B: Integration and Infinite Series and Math 31B: Integration and Infinite Series
- Fall 2017: Math 31B: Integration and Infinite Series and Math 31AL: Differential and Integral Calculus Laboratory
- Spring 2017: Math 31B: Integration and Infinite Series
- Winter 2017: Math 31B: Integration and Infinite Series
- Fall 2016: Math 31B: Integration and Infinite Series
Writing
- Lectures in Harmonic Analysis (pdf)
- An incomplete work on harmonic analysis, adapted from my own lectures notes taken during Monica Visan's Winter 2017 247A and Spring 2017 247B courses.
- Fredholm Operators and the Family Index (pdf)
- My undergraduate senior thesis, written under the advisement of Ezra Getzler.
- An Introduction to Index Theory (pdf)
- An expository version of some of the above senior thesis.
- Path Connectedness and Invertible Matrices (pdf)
- Notes prepared for a lecture I gave for the Northwestern Undergraduate Math Society in the spring of 2016.