I am a Veblen Instructor in the math department at Princeton and the IAS.
My research interests include geometric analysis and PDE. My email is ochodosh AT math DOT princeton DOT edu.
I previously spent a year at Cambridge as a postdoc. I recieved my Ph.D. from Stanford in 2015, advised by Simon Brendle and co-advised by Michael Eichmair. Before graduate school at Stanford, I completed Part III of Cambridge's Mathematical Tripos, where I was a member of Churchill College. Before that, I was an undergraduate math and physics major at Stanford.
During Fall 2018, I am teaching MAT192, a multivariable calculus course for engineering students (integrated with a first-year physics sequence, PHY192). See my past teaching here.
Expository/lecture Notes are available here.
On the topology and index of minimal surfaces II (with Davi Maximo),
A splitting theorem for scalar curvature (with Michael Eichmair and Vlad Moraru),
to appear in Comm. Pure Appl. Math. [arXiv:1804.01751]
Characterization of large isoperimetric regions in asymptotically hyperbolic initial data (with Michael Eichmair, Yuguang Shi, and Jintian Zhu),
Minimal surfaces and the Allen–Cahn equation on 3-manifolds: index, multiplicity, and curvature estimates (with Christos Mantoulidis),
Curvature estimates and sheeting theorems for weakly stable CMC hypersurfaces (with Costante Bellettini and Neshan Wickramasekera),
Asymptotically flat three-manifolds contain minimal planes (with Daniel Ketover),
Adv. Math., vol. 337, pp. 171–192 (2018). [arXiv:1709.09650] [Journal]
On far-outlying CMC spheres in asymptotically flat Riemannian 3-manifolds (with Michael Eichmair),
Global uniqueness of large stable CMC surfaces in asymptotically flat
3-manifolds (with Michael Eichmair),
Isoperimetry, scalar curvature, and mass in asymptotically flat Riemannian 3-manifolds (with Michael Eichmair, Yuguang Shi, and Haobin Yu),
submitted. [arXiv:1606.04626] [Oberwolfach Report]
Time-periodic Einstein–Klein–Gordon bifurcations of Kerr (with Yakov Shlapentokh-Rothman),
Comm. Math. Phys., vol. 356, no. 3, pp. 1155–1250 (2017). [arXiv:1510.08025] [Journal] [MR 3719550]
Stationary axisymmetric black holes with matter (with Yakov Shlapentokh-Rothman),
to appear in Comm. Anal. Geom. (2018) [arXiv:1510.08024]
Area-minimizing surfaces in asymptotically flat three-manifolds (with Michael Eichmair).
This result was included with this paper for publication. [arXiv:1510.07406]
Minimal hypersurfaces with bounded index (with Daniel Ketover and Davi Maximo),
Invent. Math., vol. 209, no. 3, pp. 617–664 (2017). [arXiv:1509.06724] [Journal] [MR 3681392]
Effective versions of the positive mass theorem (with Alessandro Carlotto and Michael Eichmair),
Invent. Math., vol. 206, no. 3, pp. 975–1016 (2016). [arXiv:1503.05910] [Journal] [MR 3573977]
On the maximum curvature of closed curves in negatively curved manifolds (with Simon Brendle),
Canad. Math. Bull., vol. 58, no. 4, pp. 713–722 (2015). [Local Version] [Journal] [MR 3415662]
On the topology and index of minimal surfaces (with Davi Maximo),
J. Differential Geom., vol. 104, no. 3, pp. 399–418 (2016). [arXiv:1405.7356] [Journal] [Oberwolfach Report][MR 3568626]
Isoperimetric structure of asymptotically conical manifolds (with Michael Eichmair and Alexander Volkmann),
J. Differential Geom., vol. 105, no. 1, pp. 1–19 (2017). [arXiv:1503.05181] [Journal] [MR 3592692]
Large isoperimetric regions in asymptotically hyperbolic manifolds,
Comm. Math. Phys., vol. 343, no. 2, pp. 393–443 (2016). [arXiv:1403.6108] [Journal] [MR 3477343]
Slowly converging Yamabe flows (with Alessandro Carlotto and Yanir Rubinstein),
Geom. Topol., vol. 19, no. 3, pp. 1523–1568 (2015).
[arXiv:1401.3738] [Journal] [MR 3352243] [Errata]
On discontinuity of planar optimal transport maps (with Vishesh Jain, Michael Lindsey, Lyuboslav Panchev and Yanir Rubinstein), J. Topol. Anal., vol. 7, no. 2, pp. 239–260 (2015). This research was carried out by our group mainly during a 2012 SURIM REU. [arXiv:1312.2929] [Journal] [MR 3326301]
A volume comparison theorem for asymptotically hyperbolic manifolds (with Simon Brendle),
Comm. Math. Phys., vol. 332, no. 2, pp. 839–846 (2014). [arXiv:1305.6628] [Journal] [MR 3257665]
Rotational symmetry of conical Kähler-Ricci solitons (with Frederick Tsz-Ho Fong),
Math. Ann., vol. 364, no. 3, pp. 777–792 (2016). [arXiv:1304.0277] [Journal] [MR 3466851]
Expanding Ricci solitons asymptotic to cones,
Calc. Var. Partial Differential Equations, vol. 51, no. 1–2, pp. 1–15 (2014). [arXiv:1303.2983] [Journal] [MR 3247379]
A lack of Ricci bounds for the entropic measure on Wasserstein space over the interval, J. Funct. Anal., vol. 262, no. 10, pp. 4570–4581 (2012). A condensed version of my Part III essay. [arXiv:1111.0058] [Journal] [MR 2900478]
Infinite matrix representations of isotropic pseudodifferential operators,
Methods Appl. Anal., vol. 18, no. 4, pp. 351–372 (2011). A condensed version of my undergraduate thesis (also including an application of the result to prove a commutator characterization for isotropic pseudodifferential operators similar to the one proven by Beals for standard pseudodifferential operators).
[arXiv:1101.4459] [Journal] [MR 2965982]