Gregory R. Chambers

Since September 2014, I have been an L. E. Dickson Instructor at the University of Chicago. I completed my PhD at the University of Toronto in June 2014 under the supervision of Alexander Nabutovsky and Regina Rotman.

Beginning in July 2017, I will be an assistant professor at Rice University.

My research is in metric geometry and geometric analysis. I am particularly interested in quantitative topology, min-max theory, isoperimetric inequalities, stability estimates for geometric inequalities, and symmetrizations and their applications.

My CV can be downloaded here.

Contact Information

Publications

Submitted

  1. Area of convex disks, with C. Croke, Y. Liokumovich, and H. Wen
    arXiv:1701.06594
  2. Quantitative nullhomotopy and rational homotopy type, with F. Manin, and S. Weinberger
    arXiv:1611.03513
  3. Quantitative null-cobordism, with D. Dotterrer, F. Manin, and S. Weinberger
    arXiv:1610.04888
  4. Existence of minimal hypersurfaces in complete manifolds of finite volume, with Y. Liokumovich
    arXiv:1609.04058
  5. A note on the affine-invariant plank problem
    arXiv:1604.00456

Published

  1. Monotone homotopies and contracting discs on Riemannian surfaces, with R. Rotman
    Journal of Topology and Analysis, to appear, arXiv:1311:2995
  2. Optimal sweepouts of a Riemannian 2-sphere, with Y. Liokumovich
    Journal of the European Mathematics Society, to appear, arXiv:1411:6349
  3. Proof of the Log-Convex Density Conjecture
    Journal of the European Mathematics Society, to appear, arXiv:1311.4012
  4. Ergodic properties of folding maps on spheres, with A. Burchard and A. Dranovski
    Discrete and Continuous Dynamical Systems - Series A 37(3):1183-1200 (2017), DOI 10.3934/dcds.2017049, arXiv:1509.02454
  5. Isoperimetric regions in \(\mathbb{R}^n\) with density \(r^p\), with W. Boyer, B. Brown, A. Loving, and S. Tammen
    Analysis and Geometry in Metric Spaces 4(1):236-265 (2016), DOI 10.1515/agms-2016-0009, arXiv:1504:01720
  6. Splitting a contraction of a simple curve traversed \(m\) times, with Y. Liokumovich
    Journal of Topology and Analysis (2016), DOI 10.1142/S1793525317500157, arXiv:1510.03445
  7. Geometric stability of the Coulomb energy, with A. Burchard
    Calculus of Variations and PDE 54(3):3241-3250 (2015), DOI 10.1007/s00526-015-0900-8, arXiv:1407.1918
  8. Perimeter under multiple Steiner symmetrizations, with A. Burchard
    Journal of Geometric Analysis (2015) 25:871, DOI 10.1007/s12220-013-9448-z, arXiv:1209.4521
  9. Converting homotopies to isotopies and dividing homotopies in half in an effective way, with Y. Liokumovich
    Geometric and Functional Analysis (2014) 24:1080, DOI 10.1007/s00039-014-0283-6, arXiv:1311.0779