Otis Chodosh

I'm a second year mathematics graduate student at Stanford University. Before this, 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 Winter 2013.

Along with Sander Kupers, I'm currently running a student seminar on positive scalar curvature. We usually meet at 5pm on Tuesdays in 381-U. Notes from the talks will be posted here as they become available.

I'm currently co-organizing the Student Geometry and Analysis seminar with Nick Haber. 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.

• Spectral Geometry (Taught by Richard Schoen, Winter 2012)

  Notes from Rick Schoen's course on spectral geometry. The notes are in progress, contact me if you'd like a copy.

• Geometric Measure Theory (Taught by Brian White, Spring 2012)

  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.

• A Lack of Ricci Bounds for the Entropic Measure on Wasserstein Space Over the Interval (2011)

  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]

• Optimal Transport and Ricci Curvature: Wasserstein Space Over the Interval (2011)

  This is my Part III essay, supervised by Clément Mouhot. It contains an introduction to the theory of optimal transport and Wasserstein space, with a particular focus on the space of probability measures on the unit interval. This is followed by a discussion about the use of optimal transport and displacement convexity in giving a synthetic definition of lower Ricci bounds. Using these ideas, we examine the possibility that the space of probability measures over a manifold with non-negative Ricci would inherit this property (as is the case with sectional curvature). We show that, despite heuristics to the contrary, this does not hold with a particular choice of reference measure, and discuss the possibility and ramifications of finding such a measure. A condensed version, containing the part about possible Ricci bounds for Wasserstein space over the interval can be found in the above paper. [arXiv:1105.2883]

• Infinite Matrix Representations of Isotropic Pseudodifferential Operators (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). Methods and Applications of Analysis, vol. 18, no. 4, pp. 351-372 (2011). [arXiv:1101.4459] [Published Version] [MR 2965982]

• Infinite Matrix Representations of Classes of Pseudodifferential Operators (2010)

  This is my undergraduate honors thesis, supervised by András Vasy. In it, we examine the representation of pseudodifferential operators on the torus via their action on complex exponential functions, which allows us to view them as an infinite matrix. We give necessary and sufficient conditions on the decay on and off the diagonal of the matrix in order for an operator to be a pseudodifferential operator of a prescribed order. Additionally, we prove a similar result about isotropic pseudodifferential operators on the real line.