I'm a second year mathematics graduate student 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 am not teaching during Spring 2013.
I'm currently co-organizing the Student Geometry and Analysis seminar with Chris Henderson. This year we will be focusing on the (vaguely defined) topic: "general methods in PDE." A schedule of upcoming talks is available at the website. We usually meet on Fridays at 4pm in 381-T. If you are interested in attending or talking, please contact me or Nick.
Along with Sander Kupers, I ran a student seminar on positive scalar curvature in 2012-2013. Some notes from the talks have been posted here.
Notes from Brian White's course on minimal surfaces (in progress). These were a joint effort with Christos Mantoulidis. Last updated: May 20, 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.
- 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 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. [arXiv:1303.2983]
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] [Published Version] [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] [Published Version] [MR 2965982]
This is my undergraduate honors thesis, supervised by András Vasy.