Fedor (Fedya) Manin

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

I am a Research Visiting Assistant Professor (postdoc) in mathematics at the Ohio State University. I got my PhD in 2015 at the University of Chicago, where my advisor was Shmuel Weinberger; from 2015 to 2017 I was at the University of Toronto.

email: manin.4 osu edu
   (add appropriate punctuation)
office: MA 318

Department of Mathematics
231 W. 18th Ave.
Columbus, OH 43210
USA


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

All my papers can also be found on the arXiv.
  1. Integral and rational mapping classes,
    (with Shmuel Weinberger)
    arXiv preprint arXiv:1802.05784 (February 15, 2018).
  2. Plato's cave and differential forms,
    arXiv preprint arXiv:1801.00335 (December 31, 2017).
  3. Quantitative nullhomotopy and rational homotopy type,
    (with Greg Chambers and Shmuel Weinberger)
    arXiv preprint arXiv:1610.03513 (November 10, 2016);
    accepted for publication in Geometric and Functional Analysis (GAFA).
  4. Quantitative null-cobordism,
    (with Greg Chambers, Dominic Dotterrer, and Shmuel Weinberger)
    arXiv preprint arXiv:1610.04888 (October 16, 2016).
  5. Volume distortion in homotopy groups,
    (based on about two-thirds of my PhD thesis, which also has some other stuff in it)
    Geometric and Functional Analysis (GAFA), Vol. 26 Issue 2 (April 2016) pp 607–679.
  6. 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

At the moment, I am teaching MATH 2568, Linear algebra, sections 0020 and 0075. Course information can be found here and on Carmen.

At the University of Toronto, I taught: At the University of Chicago, I taught: