Former Courant Instructor / PIRE Fellow at the Courant Institute at New York University.
Email: lagatta at cims dot nyu dot edu
Office: 927 Warren Weaver Hall
Office Phone: 212-992-9920
Office Hours: TBA
I apply methods and ideas from differential geometry and analysis to problems arising from probability and statistical mechanics. My main object of study is a model of random geometry called Riemannian first-passage percolation (FPP). In many respects, the model is similar to lattice FPP models at macroscopic scales. Consequently, techniques from that setting (entropy-energy estimates, shape theorem, Busemann functions) can be adapted to this situation with little difficulty. Locally, however, the model is very different, and requires different tools to deal with the continuum. To study minimizing geodesics, I study how random metrics evolve under the geodesic flow, how the length-minimization property changes under small perturbations of metrics, and I use estimates of continuous disintegrations coming from the theory of probability on Banach spaces.
I am also interested in dynamical systems, particularly when the law governing the dynamics is uncertain. I also collaborate with political scientists at NYU.
• T. LaGatta and J. Wehr. Geodesics of Random Riemannian Metrics. Communications in Mathematical Physics, accepted for publication, 2013.
• T. LaGatta. Continuous Disintegrations of Gaussian Processes. Theory of Probability and Its Applications, 57:1 (2012), 192-203.
• T. LaGatta and J. Wehr. A Shape Theorem for Riemannian First-Passage Percolation. J. Math. Phys., 51(5), 2010.
• A. Little, J. Tucker and T. LaGatta. Elections, Protest, and Alternation of Power. arXiv preprint 1302.0250, submitted for publication, 2013.
• A. Smith, T. LaGatta and B. Bueno de Mesquita. Prizes, Groups and Pivotal Voting in a Poisson Voting Game. arXiv preprint 1106.3102, submitted for publication, 2012.
• T. LaGatta and J. Wehr. Geodesics of Random Riemannian Metrics: Supplementary Material. arXiv preprint 1206.4940, 2013.
• D. Sanders and T. LaGatta. An Efficient Algorithm for the Lorentz Lattice Gas. Work in progress, 2013.
• Curvature, with pretty pictures of geodesics in various different environments.