Anthony Thompson: Curriculum Vitae Personal Information:

• Full Name: Anthony Charles Thompson
• Born: April 4, 1937
• Citizenship: Canadian (since 1974), British
• Marital Status: Married, 3 Children
• Education:
  B.Sc. University College, London 1959 (1st Class Honours in Mathmatics)
  Ph.D. Newcastle Upon Tyne 1963 Supervisor: F. F. Bonsall
  Thesis: Generalizations of the Perron-Frobenius Theorum to Operators Mapping a Cone Into Itself

Professional Experience:

• Instructor, Yale University 1962 - 63
• Lecturer, University College Swansea 1963 - 66
• Assistant & Associate Professor, Dalhousie 1966 - 1980
• Professor, Dalhousie University 1980 - Present
  Chairman of Dept. of Mathematics, Statistics and Computing Science, Dalhousie University 1980 - 83

Teaching Experience:

• I have taught a wide variety of undergraduate classes including Calculus, Advanced Calculus, Real Analysis, Linear Algebra, Differential Geometry, Complex Analysis, Problems in Geometry, General Topology, Set Theory, Theory of Metric Spaces, Introductory Probability Theory, Covexity Theory, Mathematics for Liberal Arts, a special Summer School class in Transformational Geometry (for High School teachers); and graduate classes in Analysis (Measure Theory, Functional Analysis, Locally Convex Spaces, etc).

Publications: Refereed Publications are marked with *

• *On certain contraction mappings in a partially ordered vector space, Proc. Amer. Math. Soc. (1963) 438-443. MR 26 6727 (wrongly attributed to a namesake).
• *On the eigenvalues of some not-necessarily-linear transformations, Proc. London Math. Soc. (3) 15 (1965) 577-598. MR 32 364.
• *(with M. Edelstein) Contractions, isometries and some properties of inner product spaces, Indagationes Math. 29 (1967) 326-331. MR 36 5672.
• *A spectral theorem for positive operators, J. London Math. Soc. 44 (1969) 485-495. MR 38 6385.
• *(with S. Swaminathan) On the size of sets and some fixed point theorems, Comm. Math. Univ. Carolinae 12 (1971) 537-549. MR 45 4236.
• *(with M. Edelstein) Some results on nearest points and support properties of convex sets in c₀, Pacific J. Math. 40 (1972) 553-560. MR 46 7855.
• *(With M.S. Vijaya Kumar) An order preserving representation theorem for Banach algebras and some examples, Glasgow Math. J. 14 (1973) 128--135. MR 49 1119.
• *(with F.F. Bonsall) Banach algebra elements whose spectra intersect R⁺, Proc. Edin. Math. Soc. 19 (1974) 59-69. MR 49 9630.
• *An equiperimetric property of Minkowski circles, Bull. London Math. Soc. 7 (1975) 271-272. MR 52 4138.
• *(with J.R. Betts) Three remarks on the measurement of unit spheres, Canad. Math. Bull. 18 (1975) 485-488. MR 54 5802.
• *Isometric embedding in Hilbert space, Nieuw Arch. Wisk. (3) 25 (1977) 161-168. MR 58 7047.
• *(with R.D. Holmes) N-dimensional area and content in Minkowski spaces, Pacific. J. Math. 85 (1979), 77--110. MR 81k 52023.
• Distances, circles and pi, Dalhousie J. of Undergraduate Math.} (1976) 12-19.
• (with K. Dunn and P.N. Stewart) Transformational Geometry, Notes for Math. 105 at Dalhousie (1977).
• (with E. Klein) Theory of correspondences, including applications to Mathematical Economics (xi+256pp) Wiley-Interscience. (vol 2 in Canad. Math. Soc. Monograph Series) (1984). MR 86a 90012.
• *(with K. Johnson) The isoperimetric map in Minkowski spaces. Colloq. Math. Soc. Janos Bolyai 48, Intuitive Geometry (Sofok, 1985), North-Holland, Amsterdam-New York (1987). MR 88i 52011.
• *A theorem about affine maps in Banach spaces, Geom. Dedicata 39 (1991) 93-97. MR 92f 52005.
• *(with M. Edelstein and K. Johnson) On the isometric dissection problem of convex sets, Studia Sci. Math. Hungar., 27 (1992) 273-277. MR 94f 52022.
• *Applications of various inequalities to Minkowski geometry, Geom. Dedicata, 46 (1993) 215-231. MR 94g 52006.
• *(with M.T. McGregor) On real polynomial forms and inequalities related to triangles, C. R. Math Rep., Acad. Sci. Canada 15 (1993) 249-254. MR 94i 26007.
• *Odd magic powers, Amer. Math Monthly, 101 (1994) 339-342. MR 95b 05040.
• Member, Editorial Board for: Kaleidoscopes, Canadian Math. Soc. 50th Anniversary Volume of H.S.M. Coxeter's selected works, Wiley, C.M.S. Monograph Series (1995). MR 96f 01041.
• *(with A.A. Thompson) The divergence theorem and the Laplacian in Minkowski spaces, Geom. Dedicata 63 (1996) 159-170. MR 97j 52007.
• *Minkowski Geometry, Encyclopedia of Mathematics and its Applications, vol 63 Cambridge University Press, (1996) (xvi + 346 pp). MR 97f 52001.
• *On Benson's definition of area in Minkowski space, Canad. Math. Bull. 42 (2) (1999) 237-247. MR 00g 52004.
• *Geometric means of ellipsoids and other convex bodies, (accepted) Rend. Circ. Mat. Palermo (1999) (14 ms pp)

Research Interests:

• Convexity theory and functional analysis with particular interest in the geometry of normed spaces; metric properties of finite dimensional normed spaces.

Administrative Experience:

• Have served on numerous department, faculty, and university committees including the chairmanship of the Department's Graduate Students Committee and the Faculty's Committee on Studies. Secretary of the Dalhousie Faculty Association 1978-79. Chairman of a large and diverse department 1980-83. Negotiator for the Dalhousie Faculty Association, 1986 & 88.

Other Experience:

• Member of Canadian Mathematical Society, London Mathematical Society, American Mathematical Society
• Two Ph.D. students and 11 M.Sc. students have completed their theses under my direction at Dalhousie.
• 1972 - 73 Sabbatical Leave, University of Edinburgh, Scotland
• 1979 - 80 Sabbatical Leave, Nanjing University, China
• 1983-84 Sabbatical Leave, (and Leave of Absence) University of Toronto, Canada
• 1990-91 Sabbatical Leave , Albert-Ludwigs University, Freiburg, Germany
• I have served as a member of the Canadian Mathematics Society Education Committee; a member of the Task Force of the Provincial Department of Education revising the Mathematics Curriculum for Grades 9-12 in N.S.; a Member of the Board of the Canadian Math. Society; a Member of the Canad. Math. Soc. Olympiad Committee responsible for setting and marking the Canadian Math. Olympiad Exam (86-89); Chairman of the Scientific Committee for the C.M.S. Summer Meeting in Halifax, 1990. the Canadian Mathematics Society Human Rights Committee; the Canadian Mathematics Society Publications Committee; I act as reviewer for both Mathematical Reviews and Zentralblatt fur Mathematik.

Research Grants:

• NSERC Research Grant 1993-1996, $12,000
• NSERC Research Grant 1996-2000, $24,000
• NSERC Research Grant 2000-2004, $28,000
• NSERC Conference Grant 1996, $9,000