Richard Elman

Richard Elman is a Professor of Mathematics at the University of California, Los Angeles (UCLA), affiliated with the Department of Mathematics. His research focuses on algebraic structures, particularly quadratic forms, Witt rings, and their connections to algebraic geometry and Galois cohomology. He has authored foundational texts like Lectures in Algebra and contributed to topics such as elliptic curves, linear algebraic groups, and cohomological dimensions. His work bridges abstract algebra with geometric and topological methods, influencing both pure and applied mathematical research.

Elman's research interests include advanced algebraic theories such as quadratic form theory, Witt ring structure, and the interplay between algebraic geometry and number theory. He has explored topics like cohomological dimensions of fields, étale cohomology, and the classification of quadratic forms over various fields. His publications often address problems at the intersection of algebraic structures and geometric interpretations.

His recent work (2019) continues the development of abstract algebraic frameworks, while earlier contributions (2008, 2006) delve into geometric and cohomological aspects of quadratic forms. Notable projects include studies on elliptic curves over local fields and the structure of Witt rings. Elman has also engaged in interdisciplinary efforts, such as public health research on reducing environmental tobacco smoke exposure in communities.

Though no specific student or grant information is provided in the text, his extensive publication record indicates sustained academic contributions. His office is located in the Mathematical Sciences Building at UCLA, and he can be reached via email at rse@math.ucla.edu.