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 (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)
Teaching
Current teaching (Fall 2019):- Math 31A: Differential and Integral Calculus
- OFFICE HOURS: Monday 11-12, Thursday 3:30-4:30 (both in MS 3915C)
- SMC: Wednesday 11-1
- Final review session 1: Sunday Dec 8, 6:30-9:00 in Boelter 2760
- Final review session 2: Monday Dec 9, 6:30-9:00 in Boelter 2760
- Finals week office hours: Monday 11-12, Tuesday 9:30-10:30 (both in MS 3915C)
- Entire scanned textbook
- Math 31B: Integration and Infinite Series
- OFFICE HOURS: Monday 12-1, Thursday 2:30-3:30 (both in MS 3915C)
- SMC: Wednesday 11-1
- Final review session 1: Sunday Dec 8, 12:00-2:00 in Boelter 2760
- Final review session 2: Tuesday Dec 10, 6:30-9:30 in Boelter 2760
- Finals week office hours: Monday 12-2, Wednesday 12-1 (both in MS 3915C)
- Helpful links for 31B
- Extra challenging integral problems.
- Extra challenging sequence and series problems.
- Extra challenging power series and Taylor series problems.
- Additional practice problems in solving differential equations with power series.
- My version of a series convergence flowchart.
- A collection of well-written "model" solutions for most types of 31B problems.
- Unhelpful but interesting links for 31B
- Here is a link to a lecture I gave in the UCLA Math graduate student seminar where I did a really, really insane integral.
Previous teaching:
- 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.
- Line and Surface Integrals (pdf)
- Older notes written for a multivariable course I TA'd for at Northwestern.
- The Theorems of Vector Calculus (pdf)
- Older notes written for a multivariable course I TA'd for at Northwestern.