Joseph Breen
About
Welcome! I am currently a fifth year Ph.D. student in the department of mathematics at UCLA working under the advisement of Ko Honda. I graduated with a B.A. in mathematics from Northwestern University in 2016. My research interests are in contact and symplectic geometry.
Here is a copy of a (probably old) CV: (pdf)
You can find and contact me at:
- Office: previously MS 3915C, currently my bedroom
- E-mail: josephbreen@ucla.edu
Preprints and Publications
- Morse-Smale Characteristic Foliations and Convexity in Contact Manifolds. Preprint, 2019. (arXiv link)
- 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
In Spring 2021, I am an instructor for Math 115A. We will primarily be using
the CCLE webpage.
Course notes: pdf, updated through Lecture 6.
Office hour link: https://ucla.zoom.us/j/95564988610?pwd=cERZZ1g2NGdobkUzYW5SdkxBSXZEQT09.
115A office hours: Anyone can attend these office hours, but the priority rankings are as follows: my 115A students, then other 115A students, then the rest of the world.
- Sunday 3pm-4pm
- Monday 7pm-8:30pm
- Tuesday 2pm-3pm
- Wednesday 11am-12pm and 9pm-10pm
- Thursday 1pm-2pm
- Friday 9am-10am
Open office hour: Anyone can attend this office hour with equal priority!
Helpful links for courses I am not teaching right now:
YouTube channel: Joe Breen Math. There are many videos about Math 32B on this channel, as well as some for 31B and 32A, including some prerecorded videos about topics as well as recordings of livestreamed final review sessions for all three courses.
Math 32AH:
- In Fall 2020, I was the instructor for Math 32AH. I wrote a fairly extensive set of notes on what we covered in the course, linked here: Advanced Differential Multivariable Calculus. Currently a work in progress, but it does contain everything we covered in the course.
- All of my lectures were recorded, and they are available in a private playlist. If you want access to the recordings, just let me know.
Math 31B:
- Extra practice problems:
- Miscellaneous links and notes:
- Unhelpful but interesting links:
Math 32A:
- Extra practice problems:
- Miscellaneous notes:
Math 32B:
In Spring 2020 I was a TA for an online 32B course, and throughout the quarter I made many videos about 32B. Here is a link to the full playlist of videos. They start out low-quality, but as I became a better video editor they improve over time.
- Recent links:
- Old links: (these are notes and problems I wrote a long, long time ago, but could be relevant)
Music
Perhaps my main contribution to the world of math is mathematical music.
Here is a link to a YouTube playlist of all of the songs I've made so far, which includes songs about
the Fourier transfom,
knot theory,
contact geometry,
calculus, and more.
Writing
- Liouville and Weinstein Domains (pdf)
- A set of notes based on a lecture I gave in Math 234: Contact Geometry.
- 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.
Other