Joseph Breen
About
Welcome! I am currently a fourth 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 my 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)
Teaching
Math 32B: Calculus of Several Variables (Spring 2020)
YouTube channel: Joe Breen Math. This will be the (likely) hub for recorded discussion sections, review sessions, and other pre-recorded 32B video content I make.
Discussion section info: Video content from the discussions will be posted on my YouTube channel afterwards; this may be from recorded snippets of the live sections, or rerecordings of examples after the fact. Anyone is welcome to watch! I may also post notes from each discussion section here.
Office hours: Office hours will not be recorded. Anyone is welcome to tune in! Ask math questions, lurk in the background if you want, or tune in just to chat in case you're feeling lonely.
SMC: Thursday 11am-12pm. Zoom link: TBD
Helpful 32B links:
- Recent links:
- Old links: (these are notes and problems I wrote a long, long time ago, but could be relevant)
Helpful links for courses I am not teaching right now:
YouTube channel: Joe Breen Math. This has some video content for 31B and 32A, including some prerecorded videos about topics as well as recordings of livestreamed final review sessions for both courses.
Math 31B:
- Extra practice problems:
- Miscellaneous links and notes:
- Unhelpful but interesting links:
Math 32A:
- Extra practice problems:
- Miscellaneous notes:
Previous teaching:
- 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