(add appropriate punctuation)
office: Physical Geography room 205D
Department of Mathematics
40 St. George St., Room 6290
Toronto, ON M5S 2E4 CANADA
I am mostly motivated by problems in quantitative geometry and topology. 20th-century topology has produced a trove of results asserting the existence of certain objects---for example, homotopy classes of maps, cobordisms, embeddings of manifolds. However, these algebraic results place no bounds, or very large bounds, on how complicated such objects must be. In some cases, as in anything connected to fundamental groups, such objects may even be uncomputably large in general. In other cases, they may be polynomial or even linear in size in terms of some available data.
Such questions are similar in nature, but not identical, to the question: how computationally difficult are such objects to produce? Here again, one may consider both computability and computational complexity.
Geometric group theory, when thought of as the study of fundamental groups of spaces, is motivated by a similar philosophy, and forms part of my range of interests.
Quantitative nullhomotopy and rational homotopy type,
(with Greg Chambers and Shmuel Weinberger)
arXiv preprint arXiv:1610.03513.
The complexity of nonrepetitive
edge coloring of graphs,
(based on undergraduate research with Chris Umans in 2006–2007)
arXiv preprint arXiv:0709.4497.
Like most mathematicians, I prefer to give talks on the blackboard. For very short talks, though, this can be infeasible, and so I've occasionally given slide talks.
At the 50th Spring
Topology and Dynamics Conference in Waco, Texas, I highlighted a geometric
group theory aspect of my paper “Volume distortions in homotopy groups”:
At the 2016
Workshop in Geometric Topology in Colorado Springs, I spoke about an
ongoing project with Shmuel Weinberger studying geometric bounds on smooth and
PL embeddings of manifolds:
A draft proof of “Gromov's theorem for diagrams” is available upon request.
In 2016–2017 I am teaching MAT137Y1, Calculus!. I taught the same course in 2015–2016.At the University of Chicago, I taught:
- MATH 152–153, Calculus II and III (2014–2015)
- MATH 196, Linear algebra (Winter 2014 and Spring 2012)
- MATH 195, Mathematical methods for the social sciences (a multivariable calculus class; Fall 2013, Winter 2013, Fall 2012)
- MATH 131–132, Elementary functions and calculus I and II (2011–2012)