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 (possibly old) CV: (pdf)
You can find and contact me at:
- Office: MS 3915C
- 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)
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.
Teaching
This fall, I'm an instructor for Math 32AH. We will primarily use
the CCLE webpage for all course material. If you're a former student wanting to sneak into my office hours to say hi or to get some help, please do! During my 32AH office hours I will prioritize 32AH students, but if there are no 32AH questions I'm happy to help anybody. Also, I'll have an open office hour where 32AH students are on equal footing with everyone else in terms of priority.
The Zoom link for all office hours is
https://ucla.zoom.us/j/95564988610?pwd=cERZZ1g2NGdobkUzYW5SdkxBSXZEQT09 and the schedule is:
32AH-priority office hours:
- Monday 7pm - 8:30pm PST
- Tuesday 3pm - 4:30pm PST
- Wednesday 12pm - 1pm PST
- Thursday 6pm - 7pm PST
- Friday 10am - 11am PST
Open office hour:
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 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)
Previous teaching:
- Spring 2020: Math 32B: Calculus of Several Variables
- Winter 2020: Math 32A: Calculus of Several Variables and Math 31B: Integration and Infinite Series
- Fall 2019: Math 31B: Integration and Infinite Series and Math 31A: Differential and Integral Calculus
- Summer 2019: CEED Summer Bridge Math 31B
- Spring 2019: Math 31B: Integration and Infinite Series
- Winter 2019: Math 31B: Integration and Infinite Series
- Fall 2018: Math 31B: Integration and Infinite Series
- Spring 2018: Math 115AH: Honors Linear Algebra and Math 33A: Linear Algebra and Applications
- 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
- 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