School of Mathematical Sciences

University College Dublin


Homepage of  Professor David Lewis
Photo of David Lewis






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' 
and also  local co-ordinator for  the RTN network KTAGS on " Algebraic K-theory, linear algebraic groups and related structures", which is  essentially a  continuation of the previous TMR network. See the above web link

Past and Present Ph.D. students

Thomas Unger - "Quadratic forms and central simple algebras with involution" (2000)
Sean McGarraghy - "Annihilating polynomials and exterior powers for quadratic forms" (2001)
Stefan De Wannemacker  - "Annihilating polynomials and Stirling numbers of the second kind"  (2006)
Ronan Flatley (started 2005, jointly supervised with T. Unger)

 

Publications of David W. Lewis up to Sept 2006

    1. Forms over real algebras and the multisignature of a manifold, Advances in Math. 23 (1977), 272-284.
    2. Frobenius algebras and hermitian forms, J. Pure and Applied Algebra 14 (1979), 51-58.
    3. A note on hermitian and quadratic forms, Bull. London Math. Soc.11 (1979), 265-267.
    4. A product of hermitian forms over quaternion division algebras, J. London Math. Soc 22 (1980), 215-220.
    5. Quaternionic skew-hermitian over a number field, J. Algebra 74 (1982), 232-240.
    6. New improved exact sequences of Witt groups, J. Algebra 74 (1982), 206-210.
    7. The isometry classification of hermitian forms over division algebras, Linear Algebra Appl. 43 (1982), 245-272
    8. Equivariant K-theory and forms over twisted group rings, J. Pure and Applied Algebra 25 (1982), 303-310.
    9. Exact sequences of equivariant forms, Enseignement Math.29 (1983), 45-51.
    10. Some canonical pairings of Witt groups of forms, J. Algebra 81 (1983), 508-520.
    11. An exact square of graded modules over a graded Witt ring, Proc. Royal Irish Acad. Sect. A 83 .(1983), 179-187.
    12. The Merkurjev-Suslin theorem, Irish Math. Soc. Newsletter 11 (1984), 29-37.
    13. Sums of squares in central simple algebras, Math. Zeitschrift 190 (1985), 497-498.
    14. A note on Clifford algebras and central division algebras with involution, Glasgow Math. Journal 26 (1985), 171-176.
    15. Hermitian forms and von Neumann regular matrices, in Report on the Dublin Matrix Theory Conference, March 1984, Linear Algebra Appl. 68 (1985), 243-274.
    16. A determinantal identity for skewfields, Linear Algebra Appl. 71 (1985), 213-217.
    17. Periodicity of Clifford algebras and exact octagons of Witt groups, Math. Proc.Cambridge Phil. Soc. 98 (1985), 263-269.
    18. Witt rings as integral rings, Inventiones Math. 90 (1987), 631--633.
    19. Levels and sublevels of division algebras, Proc. Royal Irish Acad. Sect. A 87 .(1987), 103-106.
    20. On the level, Irish Math. Soc. Bull. 19 (1987), 33-48.
    21. Sums of hermitian squares, J. Algebra 115 (1988), 466-480.
    22. New proofs of the structure theorems for Witt rings, Expositiones Math.7 (1989), 83-88.
    23. Hermitian forms over odd-dimensional algebras, Proc. Edinburgh Math. Soc. 32 (1989), 139-145.
    24. Levels of quaternion algebras, Rocky Mountain J. Math. 19 (1989), 787-792.
    25. The level of a Witt ring, Linear and Multilinear Algebra 27 (1990), 163-165.
    26. Units in Witt rings, Comm. Algebra 18 (1990), 3295-3306.
    27. Sums of squares in Witt rings, J. Pure and Applied Algebra 69 (1990), 67-72.
    28. (with R.H.Critchley), Engineering mathematics for the 1990s, report on the I.M.S. / S.E.F.I. meeting, Irish Math. Soc. Bull. 25 (1990), 13-16.
    29. Matrix Theory, World Scientific Publishing Co., River Edge N.J., (1991), 298pp.
    30. Annihilating polynomials and positive forms, Canadian Math.Bull. 35 (1992), 103-107
    31. Trace forms and splitting fields of central simple algebras, Univ. de Caen Seminaire - Théorie des nombres, Année 1991-1992, 1-8
    32.(with J-P. Tignol), Square class groups and Witt rings of central simple algebras, J. Algebra 154 (1993), 360-376.
    33.(with J-P. Tignol), On the signature of an involution, Arch. Math.60 (1993), 128-135.
    34. Trace forms of central simple algebras, Math. Zeitschrift 215 (1994), 367-375.
    35. (with Jan Van Geel), Quadratic forms isotropic over the function field of a conic, Indag. Math.(N.S.) 5 (1994), 325-339.
    36. David Hilbert and the theory of algebraic invariants, Irish Math. Soc. Bull. 33 (1994), 42-54.
    37. (with J.F. Morales), The Hasse invariant of the trace form of a central simple algebra, Théorie des nombres, Années1992/93-93/94, Publ. Math.Besancon, 8pp.
    38. Matrices in perfect condition, Irish Math. Soc. Bull. 34 (1995), 30-34.
    39. (with D.W. Hoffmann and J. Van Geel), Minimal forms for function fields of conics, Proc.Symposia Pure Math. 58, part 2, (Amer. Math.Soc. Providence R.I)., 227-237.
    40. Trace forms, Kronecker sums and the shuffle matrix, Linear and Multilinear Algebra 40 (1996), 221-227.
    41. Scaled trace forms of central simple algebras, Bull. Belg.Math.Soc.Simon Stevin 3 (1996), 281-294
    42. A note on trace forms and involutions of the first kind, Expositiones Math.7 (1997), 265-272.
    43. Hankel matrices and quadratic forms, Linear and Multilinear Algebra 42 (1997), 349-363.
    44. Congruence of skew-hermitian matrices Irish Math. Soc. Bull. 39 (1997), 6-9.
    45. The angle between adjacent faces of a Platonic solid, Int. J. Math.Ed.in Science and Technology 29 (1998), 125-128
    46.(with J-P. Tignol), Classification theorems for central simple, algebras with involution, (with an appendix by R.Parimala), Manuscripta Math.100 (1999), 259-276.
    47. Levels of quaternion algebras - a survey, Théorie des nombres, Années1996/97-1997/98, Publ. Math.. Besancon, 9pp.
    48.(with Sean McGarraghy), Annihilating polynomials, étale algebras, trace forms and the Galois number, Arch. Math.75 (2000), 116-120.
    49. (with I. Dejaiffe and J-P. Tignol), Witt equivalence of central simple algebras with involution, Rend. Circ. Mat. Palermo (2) 49 (2000), 325-342.
    50. The Witt semigroup of central simple algebras with involution, Semigroup Forum 60 (2000), 80-92.
    51. (edited with Eva Bayer-Fluckiger and Andrew Ranicki), Quadratic forms and their applications, Contemporary Mathematics 272, American Math.Soc., Providence R.I., (2000), 311pp.
    52. Annihilating polynomials for quadratic forms, Int.J. Math. and Math.Science. 27 (2001), 449-455.
    53. (with C. Scheiderer and T. Unger), The weak Hasse principle for central simple algebras with involution, Documenta Mathematica, Quadratic Forms LSU (2001), 241-251.
    54. (with T.J.Laffey), The life and work of Fergus Gaines (1939-2001), Irish Math.Soc.Bulletin 48 (2002), 11-15.
    55. "To the Glory of God, Honour of Ireland, and Fame of America", a biographical sketch of Francis D. Murnaghan, Math. Proc. Royal Irish Acad.103A (2003), 101-112.
    56. (with T.Unger), A local-global principle for algebras with involution and hermitian forms, Math. Zeitschrift 244 (2003), 469 - 477.
    57. Involutions and anti-automorphisms of central simple algebras, J.Pure and Applied Algebra 182 (2003), 253-261.
    58. Anti-automorphisms of the second kind, Algebraic and Arithmetic Theory of Quadratic Forms, Contemporary Mathematics 344, (2004), 257-264.
    59. (with T.Unger and J.Van Geel), The Hasse principle for similarity of hermitian forms, J.Algebra 285 (2005), 196-212.
    60. (with M.Mahmoudi, J-P.Tignol and O.Villa), Decomposable quadratic forms and involutions, J. Algebra 298 (2006), 612-629.
    61. Involutions and anti-automorphisms of algebras, Bull. London Math. Soc.38 (2006), 529-545.
    62. Quaternion algebras and the algebraic legacy of Hamilton, Irish Math Soc.Bull. 57 (2006), 41-64.



Links

Mathematics and the Isle of Man

My Official UCD homepage




Telephone: +353-1-716 2579
Fax: +353-1-716 1196
email: david.lewis@ucd.ie

School of Mathematical Sciences
Last updated  27 October 2006 by david.lewis@ucd.ie