For the Luke of Math

This website is for the math parts of Luke Wolcott.   It is an exhibition of my mathematical interests and work, cast into the internet with the hope of establishing connections with like-minded thinkers.  If something catches your eye, I encourage you to email me: luke [dot] wolcott [at] gmail [dot] com.
In June 2012, I finished my PhD in mathematics at the University of Washington, in Seattle.  I worked with John Palmieri, in algebraic topology, and I'm pretty proud of my dissertation, which integrates mathematics and metamathematics.  Then I was at the Instituto Superior Technico in Lisbon, Portugal, on a postdoc with Dan Christensen of the University of Western Ontario.  Then I worked for a year at Insight Link Consulting in Berlin, while continuing my research, for example with a long research visit at the University of Bielefeld.  For two years I was a Visiting Assistant Professor at Lawrence University, WI, a small liberal arts college.  As of August 2016, I'm a Lecturer at the University of Southern California.  This website is up-to-date as of May 2017.
On these pages you'll find various attempts to give insight into the process and experience of doing mathematics.  How do we learn, understand, create/discover, and communicate mathematics?  I've used video, discussion groups, music, performance art, a blog, and written a book exploring these questions.
Current projects -- short summaries of what I'm working on these days
Past projects -- documentation of past projects
Talks -- titles, abstracts, and slides
Publications and preprints -- list with up-to-date PDFs
Art collaborations -- descriptions and documentation of collaborations with artist Elizabeth McTernan
Consulting -- link to site of Insight Link Consulting

This website is also an attempt at articulating the challenging subject matter of mathematics.  In various places, I've written up short answers and long answers to the question "What is....?"  The "short" answers are aimed at strangers to mathematics; the "long" answers are aimed at acquaintances of mathematics.  There are several such essays on the Past Projects page.  Here are a few.
What is algebraic topology?  (short answer)   (long answer)
What's so interesting about algebraic topology?   (short answer)   (long answer)
illustrations by Shannon Wallace
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