Joseph Breen
About
Welcome! I am currently a first year Ph.D. student in the department of mathematics at UCLA. I graduated with a B.A. in mathematics from Northwestern University in 2016. Broadly speaking, my research interests are in analysis and the study of partial differential equations.
Here is a copy of my current 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 (Fall 2017):
Previous teaching:
Writing
Coursework:
- Lectures in Harmonic Analysis (pdf)
- This is a monograph on harmonic analysis, adapted from my own lectures notes taken during Monica Visan's Winter 2017 247A and Spring 2017 247B courses. It is currently a work in progress, and was last updated on June 29, 2017. Strictly chronological (and unpolished!) versions of the notes are available here:
- - 247A Notes (pdf) (last updated: May 30, 2017)
- - 247B Notes (pdf) (last updated: May 30, 2017)
Papers and Expositions:
- 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.
Teaching and Educational Materials:
Here are some notes that I wrote while teaching multivariable and vector calculus at Northwestern.
- Understanding the Dot Product and the Cross Product (pdf)
- Line and Surface Integrals (pdf)
- Green's Theorem (pdf)
- The Theorems of Vector Calculus (pdf)