I'm a third year graduate student studying mathematics at Stanford University. My advisor is Simon Brendle.
Before graduate school at Stanford, I completed Part III of Cambridge's Mathematical Tripos, where I was a member of Churchill College. Prior to my stint in the UK, I was an undergraduate math and physics major at Stanford.
My office is 381-D in the math department (building 380).
My email is "ochodosh [at] math.stanford.edu."
I will not be teaching in Fall Quarter 2013.
I'm currently co-organizing the Student Geometry and Analysis seminar with Alessandro Carlotto and Chris Henderson. This year we will be holding a learning seminar on elliptic regularity, following the book Elliptic Partial Differential Equations by Han and Lin. The schedule is available here. For more information, or to participate, please contact one of the organizers. A list of talks from previous years is available at the website.
Notes from Brian White's course on minimal surfaces. These were a joint effort with Christos Mantoulidis. Last updated: June 11, 2013.
Notes for several (expository) talks I gave in Rafe Mazzeo's course "Classics in Analysis." The notes are on linearization stability of scalar curvature and the Einstein equations in the sense of Fischer-Marsden.
Notes from Brian White's course on flat chains. Last updated: September 27, 2012.
- Summer 2013: I supervised a SURIM group studying Faber-Krahn type inequalities. I was also the TA for Michael Eichmair's course at the PCMI graduate summer school in geometry and analysis.
- Fall 2012: I was the TA for Ravi Vakil and Ruth Starkman's course THINK 37: "Education as Self-Fashioning: Rigorous and Precise Thinking."
- Summer 2012: Along with Yanir Rubinstein, I supervised a SURIM group studying optimal transport.
- Spring 2012: I was the WIM (Writing in the Major) component grader/CA for András Vasy's Math 171 course on real analysis.
We define a notion of renormalized volume of an asymptotically hyperbolic manifold and prove a sharp volume comparison theorem for metrics with scalar curvature at least -6. [arXiv:1305.6628]
We show that expanding Kähler-Ricci solitons which have positive holomorphic bisectional curvature and are asymptotic to Kähler cones at infinity must be the U(n)-rotationally symmetric expanding solitons constructed by Cao. [arXiv:1304.0277]
We show that an expanding gradient Ricci soliton with positive sectional curvature which is asymptotic to a (round) cone at infinity in a certain sense must be rotationally symmetric. To appear in Calculus of Variations and Partial Differential Equations. [arXiv:1303.2983] [Journal]
We show that the entropic measure on the Wasserstein space over the interval does not have (generalized) Ricci lower bounds, contrary to what one would expect from various heuristics.
Journal of Functional Analysis, vol. 262, no. 10, pp. 4570-4581 (2012). [arXiv:1111.0058] [Journal] [MR 2900478]
This is my Part III essay, supervised by Clément Mouhot. A condensed version may be found in the above paper. [arXiv:1105.2883]
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).
Methods and Applications of Analysis, vol. 18, no. 4, pp. 351-372 (2011). [arXiv:1101.4459] [Journal] [MR 2965982]
This is my undergraduate honors thesis, supervised by András Vasy.