Fedor Manin

2013 photo
A proof that the Earth is not simply connected
(Potosí Department, Bolivia, August 2013)

I am a postdoctoral fellow in mathematics at the University of Toronto. I got my PhD at the University of Chicago, where my advisor was Shmuel Weinberger.

email: manin math toronto edu
   (add appropriate punctuation)
office: Physical Geography room 205D

Department of Mathematics
Bahen Centre
40 St. George St., Room 6290
Toronto, ON M5S 2E4
CANADA


Research Interests

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.

Papers

Quantitative nullhomotopy and rational homotopy type,
(with Greg Chambers and Shmuel Weinberger)
arXiv preprint arXiv:1610.03513.

Quantitative null-cobordism,
(with Greg Chambers, Dominic Dotterrer, and Shmuel Weinberger)
arXiv preprint arXiv:1610.04888.

Volume distortion in homotopy groups,
Geometric and Functional Analysis (GAFA), Vol. 26 Issue 2 (April 2016) pp 607–679.

The complexity of nonrepetitive edge coloring of graphs,
(based on undergraduate research with Chris Umans in 2006–2007)
arXiv preprint arXiv:0709.4497.

Presentations

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”:
Directed filling functions and the groups ♢n

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:
Counting embeddings
A draft proof of “Gromov's theorem for diagrams” is available upon request.

Teaching

In 2016–2017 I am teaching MAT137Y1, Calculus!. I taught the same course in 2015–2016.

At the University of Chicago, I taught: