My research interests include Geometric Functional Analysis, Probability, Applications to Computer Science, and Scientific Computing. In particular, I am working in the area of Compressed Sensing. My adviser is Roman Vershynin.In collaboration with my adviser we developed a breakthrough greedy algorithm, Regularized Orthogonal Matching Pursuit. This algorithm bridged the gap between the two major approaches in the field, and provides advantages that no other greedy algorithm had been able to. Shortly after, I worked with my colleague Joel Tropp to provide the algorithm Compressive Sampling Matching Pursuit, which is optimal in every important aspect.I have taught a diverse array of courses at the University of California, Davis, the University of Nevada, Reno, and Sacramento City College. These include:UC Davis: Math Circle: Games and Probability, Instructor Math 108 (Abstract Math), Associate Instructor Math 21B (Calculus II), Lead Teaching Assistant Math 16A (Calculus I), Lead Teaching Assistant Math 280: Non-Asymptotic Random Matrix Theory, Teaching Assistant Math 12 (Precalculus), Associate InstructorUniv. of Nevada: Math 124 (College Algebra), Associate Instructor Math 120 (Survey of Math), Associate InstructorSac. City College: Math 100 (Beginning Algebra), Instructor Math 120 (Intermediate Algebra), Instructor Stat 300 (Probability and Statistics), Instructor My research papers as well as other information are available on my website, http://www.math.ucdavis.edu/~dneedell/.