I am an L.E. Dickson RTG Instructor in the mathematics department at the University of Chicago. My faculty mentor is Takis Souganidis. I received my PhD in 2015 from Princeton University under the supervision of Peter Constantin. For a detailed CV, click here.
My research interests lie within analysis and PDE. Specific topics include:
- Hydrodynamics with thermal effects.
- Asymptotic analysis of fluid-like PDE with nonlocal effects.
- Quantifying propagation in reaction-diffusion equations.
- Homogenization for nonlocal evolution equations.
Preprints and Publications:
- Local existence, lower mass bounds, and smoothing for the Landau equation (with C. Henderson and S. Snelson), Journal of the European Mathematical Society, under review; arXiv:1712.07111.
- Front propagation for nonlocal KPP reaction-diffusion equations in periodic media (with P.E. Souganidis), SIAM Journal on Mathematical Analysis, under review; arXiv:1707.00419.
- Improved a priori bounds for thermal fluid equations Transactions of the AMS, under review; arXiv:1611.06431.
- Gradient estimates and symmetrization for Fisher-KPP front propagation with fractional diffusion (with J.-M. Roquejoffre) Journal de Mathématiques Pures et Appliquées, 108 (2017) 399—424.
- Long time dynamics of forced critical SQG (with P. Constantin and V. Vicol) Communications in Mathematical Physics, 335 (2015) 93—141.
- Absence of anomalous dissipation of energy in forced two dimensional fluid equations (with P. Constantin and V. Vicol) Archive for Rational Mechanics and Analysis, 212 (2014) 875—903.
- A Study in the Asymptotic Behavior of Nonlinear Evolution Equations with Nonlocal Operators, PHD thesis, Princeton University (2015).
- Alternating traps in Muller and parity games (with A. Grinshpun, P. Phalitnonkiat, and S. Rubin) Theoretical Computer Science, 521 (2014) 73—91.
- Resolving Shocks in Partial Differential Equations through Mesh Adaptation, 2010
SURF Caltech Report.
- An Ihara formula for partially directed graphs (with R. Perlis) Linear Algebra and its Applications, 431 (2009) 73—85.