Nathaniel Eldredge

PhD, University of California – San Diego, 2009.
Area of Study: Mathematics

MA, University of California – San Diego, 2005.
Area of Study: Mathematics

BS, Harvey Mudd College, 2003.
Area of Study: Mathematics

Associate Professor, University of Northern Colorado
School of Mathematical Sciences (2018-Present)

Assistant Professor, University of Northern Colorado
School of Mathematical Sciences (2013-2018)

Postdoctoral Associate/Visiting Assistant Professor, Cornell University
(2009-2013)

Associate Instructor, University of California, San Diego
(2008-2009)

Teaching Assistant, University of California, San Diego
(2003-2009)

Areas of Interest

• Probability theory and stochastic processes
• Stochastic, functional and geometric analysis
• Probability and analysis on sub-Riemannian manifolds and Lie groups
• Partial differential equations, heat kernel analysis, and functional inequalities

Probability theory, stochastic and geometric analysis

I am interested in analysis and probability on spaces with interesting geometry, especially sub-Riemannian manifolds, Lie groups, and infinite-dimensional spaces.  My work particularly focuses on stochastic processes and partial differential equations on these spaces, and functional inequalities for their solutions and heat kernels.

• F. Baudoin and N. Eldredge. Transportation inequalities for Markov kernels and their applications. Electron. J. Probab. 26(45):1–30, 2021.
• N. Eldredge, M. Gordina and L. Saloff-Coste. Left-invariant geometries on SU(2) are uniformly doubling. In press, Geom. Funct. Anal. 28(5):1321–1367, 2018.
• N. Eldredge. On complex H-type Lie algebras. Le Matematiche 73(1):155-160, 2018.
• N. Eldredge. Strong hypercontractivity and strong logarithmic Sobolev inequalities for log-subharmonic functions on stratified Lie groups. Nonlinear Analysis 168:1–26, 2018.
• N. Eldredge, L. Gross and L. Saloff-Coste. Strong hypercontractivity and logarithmic Sobolev inequalities on stratified complex Lie groups. Trans. Amer. Math. Soc. 370(9):6651–6683, 2018.
• B. K. Driver, N. Eldredge and T. Melcher. Hypoelliptic heat kernels on infinite-dimensional Heisenberg groups. Trans. Amer. Math. Soc. 368:989–1022, 2016.
• N. Eldredge and L. Saloff-Coste. Widder’s representation theorem for symmetric local Dirichlet spaces. J. Theoret. Probab. 27(4):1178–1212, 2014.
• N. Eldredge. Gradient estimates for the subelliptic heat kernel on H-type groups. J. Funct. Anal. 258(2):504–533, 2010.
• N. Eldredge. Precise estimates for the subelliptic heat kernel on H-type groups. J. Math. Pures. Appl. 92(1):52–85, 2009.