# 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.

## Contact Information

Department of Mathematics
University of Chicago
5734 S University Ave
Chicago, IL
60637

Phone: (773) 702-9177

Email: chambers@math.uchicago.edu

Office: Eckhart 325

## 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