Nathaniel Eldredge

Visiting Assistant Professor of Mathematics
593 Malott Hall
(607) 255-7113
neldredge@math.cornell.edu

Ph.D. (2009) University of California at San Diego

Research Area

geometric analysis, probability theory

I am interested in the study of hypoelliptic partial differential operators, and in particular their heat equations. Lie groups such as the Heisenberg group and its generalizations provide a natural setting, and tools from Riemannian and sub-Riemannian geometry are highly relevant. Recently I have been studying sharp heat kernel estimates, gradient bounds, logarithmic Sobolev inequalities, and other functional inequalities for these operators. I am also interested in the application of probabilistic methods, such as infinite dimensional calculus, to better understand these types of problems.

Selected Publications

Precise estimates for the subelliptic heat kernel on H-type groups, J. Math. Pures. Appl. 92 (2009), 52–85. doi:10.1016/j.matpur.2009.04.011. arXiv:0810.3218v2 [math.AP].

Gradient estimates for the subelliptic heat kernel on H-type groups, J. Funct. Anal (to appear). arXiv:0904.1781v1 [math.AP].