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Research Overview

Research Interests

• The limit shape of first-passage percolation, and stochastic homogenization of Hamilton-Jacobi equations
• Directed polymers and KPZ universality
• A generalized, ergodic theoretic approach to geodesic dynamics in first-passage percolation
• Concentration inequalities

Selected Publications

• Stationary random walks on the lattice with J. Chaika. 
• Tracy-Widom fluctuations for perturbations of the log-gamma polymer in intermediate disorder with J. Quastel. 
• Variational formula for the time-constant of first-passage percolation Vol 69, Number 10, Comm. Pure. Appl. Math. DOI:10.1002/cpa.21648 []
• Variational formula for the time-constant of first-passage percolation Ph.D. Thesis, defended May 6, 2014, NYU Courant Institute. 
• Renewal-Reward Process Formulation of Motor Protein Dynamics with B.I. Epureanu. Bulletin of Mathematical Biology. 
• A Stochastic Mechano-Chemical Model for Cooperative Motor Protein Dynamics Co-authored with B.I. Epureanu. Conference proceedings, SMASIS 2008. 
• The Random Walker: Stochastic Mechano-Chemical Models for Motor Proteins Masters Thesis, defended August 15, 2008, University of Michigan.
• Asymptotic Solution for the One Dimensional Euler Equations for Isentropic Flow in a Variable Area Duct Co-authored with K. Balasubramaniam and R.I. Sujith. Conference proceedings, AIAA Fluid Dynamics, June 2007. 
• Prediction of NOx reduction with Exhaust Gas Recirculation using the Flame Temperature Correlation Technique Co-authored with V.C. Sekar, Balaji J., and S.M. Boopathi. Conference proceedings, ECKAME-2006.