David Arends Gieseker (born 23 November 1943 in Oakland, California) is an American mathematician, specializing in algebraic geometry.
Gieseker received from Reed College in 1965 his bachelor's degree and from Harvard University in 1967 his master's degree and in 1970 his Ph.D.
under Robin Hartshorne with thesis Contributions to the Theory of Positive Embeddings in Algebraic Geometry.
Gieseker became in 1975 a professor at the University of California, Los Angeles.
The topics of his research include geometric invariant theory and moduli of vector bundles over algebraic curves.