Jay Williams
I am a postdoc at Caltech. My research interests are in descriptive set theory and its application to problems in combinatorial/geometric group theory.
You can contact me at jaywill x caltech y edu, where x=at and y=dot.
My office is Sloan 256.
Teaching info:
This spring I am teaching Math 6c. The webpage is here.
Previous courses:
Here are links to the websites for previous courses I taught at Caltech.
- Math 1a, Freshman Mathematics, Fall 2014. This covered calculus up to around the Fundamental Theorem of Calculus, but was more proof-based than calculation-based, as is the custom here at Caltech. Homeworks and solutions are linked to on the page.
- Math 116c, Topics in Set Theory, Spring 2014. Course notes were taken by students and are linked to on the page.
- Math 116b, Introduction to Set Theory, Winter 2014. Course notes and homeworks are linked to on the page. I also have typed-up solutions for the homeworks, which you can contact me for.
- Math 116a, Introduction to Model Theory, Fall 2013.
- Math 6c, Introduction to Discrete Mathematics. I followed the course notes linked to on the page, which come from earlier versions of the course.
- Math 191b, Section 2, Introduction to Geometric Group Theory, Winter 2013.
Publications and preprints
- Countable Borel quasi-orders, my thesis.
- Universal countable Borel quasi-orders, J. Symb. Logic, (2014) 79 (3): 928-954. This is a streamlined version of the results from my thesis, and probably makes for a better read. The material in the final section is not in my thesis.
- The bi-embeddability relation for finitely generated groups, J. London Math. Soc., (2013) 88 (2): 501-522.
This is joint work with Simon Thomas.
- The bi-embeddability relation for finitely generated groups II, submitted for publication. This is joint work with Simon Thomas.
- Isomorphism of finitely generated solvable groups is weakly universal, J. Pure Appl. Alg., 219 (2015), no. 5, 1639–1644.
- Chain conditions, elementary amenable groups, and descriptive set theory, submitted for publication. This is joint work with Phillip Wesolek.
I occasionally blog about math here. Occasionally.