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.

I am a co-organizer of the Geometry Seminar.

Contact Information

Teaching

During the spring 2025 semester, I am teaching MATH 410: Calculus of Variations and MATH 427/517: Complex Analysis.

Publications

Submitted

  1. Diameter, area, and mean curvature, with J. Marx-Kuo
    arXiv:2412.04636
  2. The cubical relative isoperimetric problem for the cube, with L. Mouillé
    arXiv:2302.04382
  3. A note on Kalai's 3d Conjecture, with E. Portnoy
    arXiv:2211.09215
  4. On minimal higher genus fillings
    arXiv:2202.01342
  5. Uryson width and pants decompositions of hyperbolic surfaces
    arXiv:2207.11874
  6. A note on the affine-invariant plank problem, with L. Mouillé
    arXiv:1604.00456

Published

  1. On the square peg problem with E. W. Chambers, A. de Mesmay, T. Ophelders, and R. Rotman
    Discrete and Computational Geometry, to appear, arXiv:2203.02613
  2. Geodesic nets on non-compact Riemannian manifolds, with Y. Liokumovich, A. Nabutovsky, and R. Rotman
    Journal for pure and applied mathematics (Crelles Journal), vol. 2023, no. 799, 2023, pp. 287-303, DOI 10.1515/crelle-2023-0028
  3. A stability result for Riesz potentials in higher dimensions, with A. Burchard
    Indiana University Journal of Mathematics, to appear, arXiv:2007.11664
  4. The Length of the ROC Curve-a Robust Framework to Discover and Evaluate Biomarkers Corresponding to Improper ROC Curves, with L. E. Bantis, J. V. Tsimikas, M. Capello, S. M. Hanash, and Z. Feng
    Statistics in Medicine, to appear
  5. Constructing monotone homotopies and sweepouts, with E. W. Chambers, A. de Mesmay, T. Ophelders, and R. Rotman
    J. Differential Geom. 119(3): 383-401 (November 2021) DOI 10.4310/jdg/1635368350
  6. Existence of minimal hypersurfaces in complete manifolds of finite volume, with Y. Liokumovich
    Inventiones Mathematicae 219(2020), 179 -- 217 DOI 10.1007/s00222-019-00903-3
  7. Quantitative null-cobordism, with D. Dotterrer, F. Manin, and S. Weinberger
    Journal of the AMS 31(2018), 1165--1203, DOI 10.1090/jams/903
  8. Quantitative nullhomotopy and rational homotopy type, with F. Manin, and S. Weinberger
    Geometric and Functional Analysis 28(2018), 563--588 DOI 10.1007/s00039-018-0450-2
  9. Area of convex disks, with C. Croke, Y. Liokumovich, and H. Wen
    Proceedings of the AMS, to appear, arXiv:1701.06594
  10. Monotone homotopies and contracting discs on Riemannian surfaces, with R. Rotman
    Journal of Topology and Analysis 10(2018) 323--354, DOI 10.1142/S1793525318500103
  11. Optimal sweepouts of a Riemannian 2-sphere, with Y. Liokumovich
    Journal of the European Mathematics Society 21(5):1361-1377 (2019), DOI 10.4171/JEMS/863
  12. Proof of the Log-Convex Density Conjecture
    Journal of the European Mathematics Society 21(8):2301-2332 (2019), DOI 10.4171/JEMS/885
  13. 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
  14. 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
  15. Splitting a contraction of a simple curve traversed \(m\) times, with Y. Liokumovich
    Journal of Topology and Analysis 9(2016) 409--418, DOI 10.1142/S1793525317500157
  16. 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
  17. Perimeter under multiple Steiner symmetrizations, with A. Burchard
    Journal of Geometric Analysis (2015) 25:871, DOI 10.1007/s12220-013-9448-z
  18. 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