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Research Biography

My current postdoc is co-sponsored by Professor Nassif Ghoussoub and Professor Young-Heon Kim at UBC. Our research is in the interesection of optimal transportation, optimal control theory, nonlinear PDE and variational inequalities. We hope our results and new perspectives coming from this mix of subjects will be of interest for many other applications in mathematical physics and even machine-learning.

My PhD was advised by Professor Tim Healey at Cornell University. Our primary research was in nonlinear elasticity, and my dissertation was on the constraints of incompressibility and self-contact in second-gradient elasticity [1], [3],[4]. I developed new techniques to deal with these constraints in the framework of twice differentiable Sobolev deformations, which allowed us to prove global existence of equilibrium solutions. This research involved the calculus of variations, regularity theory for the divergence equation, and variational inequalities.

At Cornell I was also mentored by Professor Alex Vladimirsky. We did research that began with exploring numerical methods for nearly-degenerate 2nd-order Hamilton-Jacobi-Bellman equations. We then worked on probabilistic constraints in optimal stopping problems [2], which we solved by using a Lagrangian relaxation that yields a quasi-variational inequality.

I was an undergraduate at the University of California, Santa Cruz. I wrote an undergraduate thesis under the supervision of Professor Debra Lewis on optimal control theory on Lie groups. Also at UCSC, after graduating I continued research with Professor Dejan Milutinović working on open-loop stochastic control theory [5]. We used computational path-integration techniques to approximate solutions the resulting forward-backward nonlinear PDE.

Publications

  1. Aaron Zeff Palmer. Variations of Deformations with Self-Contact on Lipschitz Domains. Submitted to Set-Valued and Variational Analysis, 2017. (preprint.)
  2. Aaron Zeff Palmer and Alexander Vladimirsky. Optimal Stopping with a Probabilistic Constraint. Submitted to Journal of Optimization Theory and Applications, 2017. (preprint.)
  3. Aaron Zeff Palmer and Timothy J. Healey. Injectivity and Self-contact in Second-Gradient Nonlinear Elasticity. Calculus of Variations and Partial Differential Equations, 2017. (preprint. link. The final publication is available at Springer via http://dx.doi.org/10.1007/s00526-017-1212-y.)
  4. Aaron Zeff Palmer. Incompressibility and Global Injectivity in Second-Gradient Non-Linear Elasticity. PhD thesis, Cornell University, 2016. (available here.)
  5. Aaron Palmer and Dejan Milutinović. A Hamiltonian Approach Using Partial Differential equations for Open-Loop Stochastic Optimal Control. In Proceedings of the 2011 American Control Conference, IEEE, 2011. (pdf.)