Gregory R. Chambers

I am an assistant professor in the Department of Mathematics at Rice University. Before coming to Rice, I was an L. E. Dickson Instructor at the University of Chicago, and a graduate student at the University of Toronto before that.

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

Teaching

I am not teaching in the fall 2017 semester. In the spring 2018 semester, I am teaching MATH 356: Abstract Algebra 1 and MATH 521: Advanced Topics in Real Analysis.

Publications

Submitted

  1. Constructing monotone homotopies and sweepouts, with E. W. Chambers, A. de Mesmay, T. Ophelders, and R. Rotman
    arXiv:1704.06175
  2. Area of convex disks, with C. Croke, Y. Liokumovich, and H. Wen
    arXiv:1701.06594
  3. Quantitative nullhomotopy and rational homotopy type, with F. Manin, and S. Weinberger
    arXiv:1611.03513
  4. Quantitative null-cobordism, with D. Dotterrer, F. Manin, and S. Weinberger
    arXiv:1610.04888
  5. Existence of minimal hypersurfaces in complete manifolds of finite volume, with Y. Liokumovich
    arXiv:1609.04058
  6. 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