## Biography

David Lewis is Professor of Mathematics at U.C.D.

He is a native of the Isle of Man and is a graduate of Liverpool University.

He was awarded the degree of D.Sc. by the National University of Ireland in 1992 on the basis of published work.

His research interests are in the areas of quadratic and hermitian forms and algebras with involutions.

He was the local co-ordinator of the Dublin node of the

European Union TMR network project on `K-theory,linear algebraic groups and related structures', 1997-2002,

and also local co-ordinator for the RTN network KTAGS on " Algebraic K-theory, linear algebraic groups and related structures", 2002-2006. See the above web link

## Professional

## Publications

### Books

Eva Bayer-fluckiger, David W. Lewis, and Andrew Ranicki (editors); (2000) Quadratic forms and their applications. Providence, Rhde Island: American Mathemtical Socety, Contemporary Mathematics Series No 272. [Details] |

Lewis, D.W.; (1991) Matrix Theory. River Edge N.J: World Scientific Publishing Co. [Details] |

### Peer Reviewed Journals

D.W.Lewis, C.Scheiderer, and T.Unger; (2001) 'The weak Hasse principle for central simple algebras with involution'. Documenta Mathematica, :241-251. [Details] |

I.Dejaiffe, D.W.Lewis, and J-P.Tignol; (2000) 'Witt equivalence of central simple algebras with involution'. Rendiconti Del Circolo Matematico Di Palermo, Series Ii, 49 :325-342. [Details] |

Lewis, D.W. with J-P Tignol; (1999) 'Classification theorums for central simple, algebras with involution'. Manuscripta Mathematica, 100 :259-276. [Details] |

Lewis, D.W.; (1997) 'A note on trace forms and involutions of the first kind'. Expositiones Mathematicae, 7 :265-272. [Details] |

Lewis, D.W.; (1997) 'Hankel matrices and quadratic forms'. Linear and Multilinear Algebra, 42 :349-363. [Details] |

Lewis, D.W.; (1997) 'Congruence of skew-hermitian matrices'. Irish Mathematics Society Bulletin, 39 :6-9. [Details] |

Lewis, D.W.; (1996) 'Trace forms, Kronecker sums and the shuffle matrix'. Linear and Multilinear Algebra, 40 :221-227. [Details] |

Lewis, D.W.; (1996) 'Scaled trace forms of central simple algebras'. Bulletin of the Belgian Mathematical Soc.-Simon Stevin, 3 :281-294. [Details] |

Lewis, D.W.; (1995) 'Matrices in perfect condition'. Irish Mathematics Society Bulletin, 34 :30-34. [Details] |

Lewis, D.W.; (1994) 'Trace forms of central simple algebras'. Mathematische Zeitschrift, 215 :367-375. [Details] |

Lewis, D.W. with Jan Van Geel; (1994) 'Quadratic forms isotropic over the function field of a conic'. Indagationes Mathematicae, 5 :325-329. [Details] |

Lewis, D.W.; (1994) 'David Hilbert and the theory of algebraic invariants'. Irish Mathematics Society Bulletin, 33 :42-54. [Details] |

Lewis, D.W. with J-P. Tignol; (1993) 'On the signature of an involution'. Archive Der Mathematik, 60 :128-135. [Details] |

Lewis, D.W. with J-P Tignol; (1993) 'Square class groups and Witt rings of central simple algebras'. Journal of Algebra, 154 :360-376. [Details] |

Lewis, D.W.; (1992) 'Annihilating polynomials and positive forms'. CANADIAN MATHEMATICS BULLETIN, 35 :103-107. [Details] |

Lewis, D.W.; (1990) 'The level of a Witt ring'. LINEAR AND MULTILINEAR ALGEBRA, 27 :163-165. [Details] |

Lewis, D.W., Critchley, H.R.; (1990) 'Engineering mathematics for the 1990s, report on the I.M.S. / S.E.F.I. meeting'. IRISH MATHEMATICS SOCIETY BULLETIN, 25 :13-16. [Details] |

Lewis, D.W.; (1990) 'Sums of squares in Witt rings'. JOURNAL OF PURE AND APPLIED ALGEBRA, 69 :67-72. [Details] |

Lewis, D.W.; (1990) 'Units in Witt rings'. COMMUNICATIONS IN ALGEBRA, 18 :3295-3306. [Details] |

Lewis, D.W.; (1989) 'New proofs of the structure theorems for Witt rings'. EXPOSITIONES MATHEMATICAE, 7 :83-88. [Details] |

Lewis, D.W.; (1989) 'Hermitian forms over odd-dimensional algebras'. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 32 :139-145. [Details] |

Lewis, D.W.; (1989) 'Levels of quaternion algebras'. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 19 :787-792. [Details] |

Lewis, D.W.; (1988) 'Sums of hermitian squares'. JOURNAL OF ALGEBRA, 115 :466-480. [Details] |

Lewis, D.W.; (1987) 'Witt rings as integral rings'. Inventiones Math, 90 :631-633. [Details] |

Lewis, D.W.; (1987) 'On the level'. IRISH MATHEMATICS SOCIETY BULLETIN, 19 :33-48. [Details] |

Lewis, D.W.; (1987) 'Levels and sublevels of division algebras'. PROCEEDINGS ROYAL IRISH ACADEMY, SECTION A, 87 :103-106. [Details] |

Lewis, D.W.; (1985) 'Sums of squares in central simple algebras'. MATHEMATISCHE ZEITSCHRIFT, 190 :497-498. [Details] |

Lewis, D.W.; (1985) 'Periodicity of Clifford algebras and exact octagons of Witt groups'. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL, 98 :263-269. [Details] |

Lewis, D.W.; (1985) 'A note on Clifford algebras and central division algebras with involution'. GLASGOW MATHEMATICAL JOURNAL, 26 :171-176. [Details] |

Lewis, D.W.; (1985) 'A determinantal identity for skewfields'. Linear Algebra Appl, 71 :213-217. [Details] |

Lewis, D.W.; (1985) 'Hermitian forms and von Neumann regular matrices, in Report on the Dublin Matrix Theory Conference, March 1984'. Linear Algebra Appl, 68 :243-274. [Details] |

Lewis, D.W.; (1984) 'The Merkurjev-Suslin theorem'. IRISH MATHEMATICAL SOCIETY NEWSLETTER, 11 :29-37. [Details] |

Lewis, D.W.; (1983) 'Exact sequences of equivariant forms'. Enseignement Math, 29 :45-51. [Details] |

Lewis, D.W.; (1983) 'An exact square of graded modules over a graded Witt ring'. PROCEEDINGS ROYAL IRISH ACADEMY, SECTION A, 83 :179-187. [Details] |

Lewis, D.W.; (1983) 'Some canonical pairings of Witt groups of forms'. JOURNAL OF ALGEBRA, 81 :508-520. [Details] |

Lewis, D.W.; (1982) 'Quaternionic skew-hermitian over a number field'. JOURNAL OF ALGEBRA, 74 :232-240. [Details] |

Lewis, D.W.; (1982) 'New improved exact sequences of Witt groups'. JOURNAL OF ALGEBRA, 74 :206-210. [Details] |

Lewis, D.W.; (1982) 'Equivariant K-theory and forms over twisted group rings'. JOURNAL OF PURE AND APPLIED ALGEBRA, 25 :303-310. [Details] |

Lewis, D.W.; (1982) 'The isometry classification of hermitian forms over division algebras'. Linear Algebra Appl, 43 :245-272. [Details] |

Lewis, D.W.; (1980) 'A product of hermitian forms over quaternion division algebras'. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY, 22 :215-220. [Details] |

Lewis, D.W.; (1979) 'Frobenius algebras and hermitian forms'. JOURNAL OF PURE AND APPLIED ALGEBRA, 14 :51-58. [Details] |

Lewis, D.W.; (1979) 'A note on hermitian and quadratic forms'. BULLETIN OF THE LONDON MATHEMATICS SOCIETY, 11 :265-267. [Details] |

Lewis, D.W.; (1977) 'Forms over real algebras and the multisignature of a manifold'. Advances in Math, 23 :272-284. [Details] |

Lewis, D. & S.DeWannemacker; (2007) 'Structure Theorems for AP-rings'. Journal of Algebra, :144-158. [Details] |

Lewis, D.W., Mahmoudi, M., Tignol, J-P., Villa, O.; (2006) 'Decomposable quadratic forms and involutions'. JOURNAL OF ALGEBRA, 298 :612-629. [Details] |

Lewis, D.W.; (2006) 'Involutions and anti-automorphisms of algebras'. BULLETIN OF THE LONDON MATHEMATICS SOCIETY, 38 :529-545. [Details] |

Lewis, D.W.; (2006) 'Quaternion algebras and the algebraic legacy of Hamilton'. IRISH MATHEMATICS SOCIETY BULLETIN, 57 :41-64. [Details] |

David W.Lewis, Thomas Unger, and Jan Van Geel; (2005) 'The Hasse principle for similarity of hermitian forms'. Journal of Algebra, 285 (1):192-212. [Details] |

D.W.Lewis; (2004) 'Anti-automorphisms of the second kind'. Contemporary Mathematics, 344 :257-264. [Details] |

D.W.Lewis and T.P.Unger; (2003) 'A local-global principle for algebras with involution and hermitian forms'. Mathematische Zeitschrift, 244 :469-477. [Details] |

Lewis, D.W.; (2003) 'To the Glory of God, Honour of Ireland, and Fame of America a biographical sketch of Francis D. Murnaghan'. Proceedings of the Royal Irish Academy, 103 . [Details] |

Lewis, D.W.; (2003) 'Involutions and anti-automorphisms of central simple algebras'. Journal of Pure and Applied Algebra, 182 :253-261. [Details] |

D.W.Lewis; (2003) 'Involutions and anti-automorphisms of central simple algebras'. Journal of Pure and Applied Algebra, 182 :253-261. [Details] |

Lewis, D.W.; (2002) 'The life and work of Fergus Gaines (1939-2001)'. Irish Mathematics Society Bulletin, 48 . [Details] |

Lewis, D.W.; (2001) 'Annihilating polynomials for quadratic forms'. International Journal of Mathematics, 27 :449-455. [Details] |

Lewis, D.W. & Sean McGarraghy; (2000) 'Annihilating polynomials, étale algebras, trace forms and the Galois number'. Archive Der Mathematik, 75 :116-120. [Details] |

## Research

### Research Interests

Research Profile The research interests of Professor Lewis are in the general areas of algebra and topology, and more specifically in the algebraic theory of quadratic and hermitian forms, and in the theory of algebras with involution. He was manager of the Dublin branch of the European Union TMR network on "Algebraic K-theory and Linear Algebraic Groups" 1997-2002, and manager of the Dublin branch of the European Union Research Training Network KTAGS on "K-theory, Linear Algebraic Groups and Related Topics" 2002-2006. He co-organized international mathematics conferences on "Quadratic forms and their applications" in UCD, 4 -11 July 1999, and on "K-theory, algebraic groups and related structures" in UCD, 5 - 8 July 2004. He is the author of approximately 60 mathematical papers appearing in international journals, one textbook on matrix theory, and is co-editor of one book in the AMS Contemporary Mathematics series. |