David W. Lewis (mathematician)

David W. Lewis (21 February 1944 in Douglas, Isle of Man—20 August 2021 in Dublin) was a Manx mathematician known for his contributions to quadratic forms theory. He spent his entire career at University College Dublin (UCD), where he was head of the Department of Mathematics (now the School of Mathematics and Statistics) from 1999 until 2002. After his retirement in 2009 he remained research active for many years.

Education and career
Lewis attended Douglas High School where he developed an interest in physics and astronomy, and ultimately mathematics. He attended the University of Liverpool, and after completing his BSc degree in 1965 commenced doctoral studies in topology under the guidance of CTC (Terry) Wall. When his PhD funding ended in 1968, he started as assistant lecturer at the UCD Mathematics Department, while continuing the work on his doctoral thesis, shifting from topology to algebra and specifically to the area of quadratic and hermitian forms.

During his first decade of lecturing at UCD, he completed his PhD thesis, Hermitian Forms over Algebras with Involution, under the supervision of Professor Wall and was awarded a doctorate by the National University of Ireland in 1979. He received a DSc from NUI in 1992, and served as head of the Department of Mathematics there from 1999 until 2002.

He supervised 4 PhDs and authored one monograph.

Books

 * 1991 – Matrix Theory, World Scientific Publishing Co., Inc., River Edge, NJ.
 * 2000 – Quadratic Forms and Their Applications, AMS (Contemporary Mathematics 272). Proceedings of the Conference on Quadratic Forms and Their Applications, July 5–9, 1999, University College Dublin, edited by David Lewis with Eva Bayer-Fluckiger & Andrew Ranicki)

Selected papers

 * 2013 (with A. Cortella) "Sesquilinear Morita Equivalence and Orthogonal Sum of Algebras with Antiautomorphism", Comm. Algebra 41, no. 12, 4463–4490.
 * 2007 (with S.A.G. De Wannemacker) "Structure theorems for AP rings", J. Algebra 315, no. 1, 144–158.
 * 2003 (with T. Unger) "A local-global principle for algebras with involution and Hermitian forms", Math. Z. 244, no. 3, 469–477.
 * 2000 (with S. McGarraghy) "Annihilating polynomials, étale algebras, trace forms and the Galois number", Arch. Math. (Basel) 75, no. 2, 116–120.
 * 1993 (with Jean-Pierre Tignol) "On the signature of an involution", Arch. Math. (Basel) 60, no. 2, 128–135.
 * 1987 – "Witt rings as integral rings", Invent. Math. 90, no. 3, 631–633.
 * 1985 – "Periodicity of Clifford algebras and exact octagons of Witt groups", Math. Proc. Cambridge Philos. Soc. 98, no. 2, 263–269.
 * 1982 – "New improved exact sequences of Witt groups", J. Algebra 74, no. 1, 206–210.
 * 1977 – "Forms over real algebras and the multisignature of a manifold", Advances in Math. 23, no. 3, 272–284.