CV and Publications of Ted Chinburg

Ted Chinburg                                 Home address:
Department of Mathematics                    506 Rockavon Road
University of Pennsylvania                   Narberth, PA  19072
Philadelphia, PA  19104                      office: 215-898-8340
                                             home:   215-664-8031

EDUCATION

Ph.D. Mathematics    Harvard University  November, 1980
M.A.  Mathematics    Harvard University  June, 1979
B.S.  Mathematics    Harvey Mudd College June, 1975

RESEARCH AREAS

Number theory, arithmetic and hyperbolic geometry

Particular interests:    Galois module structure, values of L-
                         functions, hyperbolic three-manifolds,
                         arithmetic groups, Arakelov theory,
                         capacity theory

HONORS AND GRANTS

NSF grant, 1992 - 2000
NSA grant, Spring 1990
NSF grant, 1982-1989
University of Pennsylvania research grant, 1989
University of Pennsylvania Natural Sciences grant, 1986
MSRI mid-career fellowship, 1986
Sloan fellowship, 1985
Research grants, Cambridge University and Universite de Bordeaux,
1983
NSF postdoctoral fellowship, 1980 - 1981

PROFESSIONAL EXPERIENCE

Visitor, I.H.E.S., Summer 1996
Visitor, University of Meunster, Summer 1995
Visitor, Universit« de Bordeaux, Summer 1994
Visitor, University of Manchester, Summer 1993
Visitor, Universit« de Bordeaux, Summer 1992
Visitor, University of Amsterdam, Summer 1991
Member, MSRI, 1986 - 1987
Visitor, Cambridge University and Universite de Bordeaux, 1983
Member, Institute for Advanced Study, 1982 - 1983
Visitor, I.H.E.S., summers of 1980, 1981, and 1988

ACADEMIC POSITIONS

Professor, University of Pennsylvania, 1989-present
Associate Professor, Columbia University, Barnard College, 1987 -
1989
Assistant Professor, University of Pennsylvania, 1982 - 1987
Acting Assistant Professor, University of Washington, 1981 - 1982

PH.D STUDENTS

  1. S. Bae, Univ. of Penn. Thesis (June, 1988) "Conjectures of Lichtenbaum and Chinburg over Function Fields."
  2. S. Kim, Univ. of Penn. Thesis (June, 1988) "A generalization of Frohlich's Theorem to wildly ramified quaternion extensions of Q ."
  3. D. Solomon, Brown U. Thesis (June, 1988) "Lichtenbaum's Conjecture for Dirichlet characters."
  4. T. Schmidt, Univ. of Penn. Thesis (June, 1989) "Congruences for the values at s = O of quaternionic representations."
  5. T. Costa, Univ. of Penn. Thesis (June, 1989) "Class number congruences and modular forms."
  6. A. Agboola, Columbia University. Thesis (June, 1991), "Abelian varieties and Galois module structure in Global Fields."
  7. M. Rogers, Columbia University. Thesis (June, 1991), "On a Multiplicative-Addictive Galois Invariant."
  8. G. Pappas, Columbia University. Thesis (June, 1992), "The bad reductions of some Hilbert-Blumenthal moduli varieties."
  9. C.F. Lau, University of Pennsylvania. Thesis (June, 1993), "An arithmetic capacity on Grassmanian varieties."
  10. S. Kwon, University of Pennsylvania. Thesis (June 1994), "Galois module structure of tame covers".
  11. C. Xiao, University of Pennsylvania. Thesis (June 1997), "Galois module structure of elliptic curves".
  12. S. Hu, University of Pennsylvania. Thesis (Dec. 1997), "On Eisenstein Cocyles".

SELECTED INVITED TALKS

PUBLICATIONS

A. Research articles published or accepted for publication.

  1. T. Chinburg and M. Henriksen, "Multiplicatively Periodic Rings," Amer. Math. Monthly, Vol. 83 n. 7 (1976), p. 547- 549.
  2. T. Chinburg and M. Henriksen, "Sums of k-th powers in the ring of polynomials with integer coefficients," Acta Arith. 29 (1976), p. 227-250. Research announcement, Bull. Amer. Math. Soc., Vol. 81, #1 (1975), p. 107-110.
  3. "`Easier' Waring problems for commutative rings," Acta Arith. 35 n. 4 (1979), p. 303-331.
  4. "Stark's conjecture for L-functions with first order zeroes at s = 0 ," Advances in Math. 48 (1983), p. 82-113.
  5. "Derivatives of L-functions at s = 0 ," Compositio Math. 48 (1983) p. 119-127.
  6. "On the Galois structure of algebraic integers and S-units," Inv. Math. 74 (1983), p. 321-349.
  7. "The Galois structure of S-units," Sem. Th. de Nombres de Bordeaux, annee 1982-1983, p. 40.01-40.21.
  8. "Multiplicative Galois structure," Lecture Notes in Mathematics #1068, p. 23-32.
  9. "Volumes of hyperbolic manifolds," J. Diff. Geom. 18 (1983), p. 783-789.
  10. "Salem numbers and L-functions," J. Number Theory, Vol. 18, no. 2 (1984), p. 213-214.
  11. "Multiplicative Galois module structure," J. London Math. Soc. (2) 29 (1984), p. 23-33.
  12. "On the arithmetic of two constructions of Salem numbers," Crelle's Journal 348 (1984), p. 166-179.
  13. "A small arithmetic hyperbolic three-manifold," Proc. of the AMS, Vol. 100, no. 1 (1984), p. 140-144.
  14. "Exact sequences and Galois module structure," Annals of Math. 121 (1985), p. 351-376.
  15. "Intersection theory and capacity theory on arithmetic surfaces," Proceedings of the CMS summer seminar on Number Theory, Vol. 7 (1987), p. 1-35.
  16. T. Chinburg and E. Friedman, "The smallest arithmetic hyperbolic three-orbifold," Invent. Math. 86 (1986), p. 507- 527. Erratum (1987), to appear in a sequel.
  17. "The analytic theory of multiplicative Galois structure," Memoirs of the AMS, Vol. 77, No. 395 (1989).
  18. "A quaternionic L-value congruence," J. Fac. Science of the Univ. of Tokyo, Sec. IA, Vol. 36, No. 3 (1989), p. 765-787.
  19. T. Chinburg and R. Rumely, "Well adjusted models for curves over Dedekind rings," in Arithmetic Algebraic Geometry, G. Van der Geer ed., Birkhauser (1991), p. 3-24.
  20. "Additive-Multiplicative Galois Structures," prepared in collaboration with D.J. Burns and N.P. Byott, in L-functions and Arithmetic, J. Coates and M.J. Taylor (eds.), Cambridge Univ. Press, Cambridge, p.110-123 (1991).
  21. "Capacity theory on varieties," Compositio Math. 80 (1991), p.75-84.
  22. "The capacity pairing," with R. Rumely, J. Riene Angew. Math. 434 (1993), 1-44.
  23. "Galois structure of De Rham cohomology," Sem. Th. Nombres, Bordeaux 4 (1991), 1-18.
  24. T. Chinburg and B. Erez, "Equivariant Euler-Poincar« characteristics and tameness," Asterisque 209 (1992), 179- 194.
  25. "Galois structure of De Rham cohomology of tame covers of schemes," Annals of Mathematics 139 (1994), 443-490.
  26. "Closed hyperbolic 3-manifolds whose closed geodesics are simple," with Alan Reid, J. of Diff. Geom. 38 (1993), 545- 558.
  27. "Tame actions of group schemes: Integrals and Slices," with B. Erez, G. Pappas and M. Taylor, Duke Math. J. 82:2 (1996), 269-308.
  28. "Galois structure of K-groups of rings of integers," with G. Pappas, M. Kolster and V. Snaith, C. R. Acad. Sci. Paris, t. 320, S\'erie I, (1995), 1435 - 1440.
  29. "Adams operations and integral Galois representations," with D. Burns, to appear in the Amer. J. of Math.
  30. ``$\epsilon$-constants and the Galois structure of de Rham cohomology,'' with B. Erez, G. Pappas and M. Taylor, Annals of Math.. {\bf 146} (1997), 411-473.
  31. "Riemann-Roch type theorems for arithmetic schemes with a finite group action," with B. Erez, G. Pappas and M. Taylor, J. Reine Angew. Math. 489 (1997), 151--187.
  32. "$\epsilon$-constants and the Galois structure of de Rham cohomology, II" with G. Pappas and M. Taylor, J. Reine Angew. Math. 519 (2000), 201-230.
  33. ``On the $\epsilon$-constants of a variety over a finite field,'' with B. Erez, G. Pappas and M. Taylor, Amer. J. Math. 119 (1997), no. 3, 503--522.
  34. ``Localizations of Grothendieck groups and Galois structure,'' with B. Erez, G. Pappas and M. Taylor, Recent progress in algebra (Taejon/Seoul, 1997), 47--63, Contemp. Math., 224, Amer. Math. Soc., Providence, RI, 1999.
  35. ``On the $\epsilon$-constants of arithmetic schemes,'' with B. Erez, G. Pappas and M. Taylor, Math. Ann. {\bf 311} (1998), no. 2, 377--395.
  36. "Galois structure of K-groups of rings of integers," with G. Pappas, M. Kolster and V. Snaith, $K$-Theory 14 (1998), no. 4, 319--369.
  37. "Comparison of $K$-theory Galois module structure invariants. with M. Kolster, G. Pappas and V. Snaith, Canad. J. Math. 52 (2000), no. 1, 47--91.
  38. "Quaternionic exercises in $K$-theory Galois module structure, II" with M. Kolster, G. Pappas and V. Snaith. In: Algebraic $K$-theory and its applications (Trieste, 1997), 337--369, World Sci. Publishing, River Edge, NJ, 1999
  39. `Nearly perfect complexes and Galois module structure,'' with M. Kolster, G. Pappas and V. Snaith, Compositio Math. 119 (1999), no. 2, 133--155
  40. "An embedding theorem for quaternion algebras," with E. Friedman, J. London Math. Soc. (2) 60 (1999), no. 1, 33--44.
  41. "Operations on ring structures preserved by normalized automorphisms of group rings," with F. Bleher, J. Algebra 215 (1999), no. 2, 531--542.
  42. ``Combinatorial families that are exponentially far from being listable in Gray code sequence,'' with C. D. Savage and H. S. Wilf, Trans. Amer. Math. Soc. 351 (1999), no. 1, 379--402.
  43. ``Universal deformation rings and cyclic blocks,'' with F. Bleher, to appear in Math. Annalen.  PDF 
  44. ``$\epsilon$-constants and Arakelov Euler characteristics," with G. Pappas and M. J. Taylor, Math. Res. Lett. 7 (2000), no. 4, 433--446.

B. Research articles submitted for publication.

  1. ``Locations of modules for Brauer tree algebras.'' with F. Bleher. preprint (1999).  PDF 
  2. ``Applications of universal deformations to Galois theory," with F. Bleher, preprint (2000).   PDF 
  3. ``Arithmetic classes of metrised complexes and epsilon constants,'' with G. Pappas and M. Taylor, preprint (1999).   PDF 
  4. ``Discriminants and Arakelov Euler characteristics," with G. Pappas and M. Taylor, preprint (2000).   PDF 

C. Preprints.

  1. ``Duality and Hermitian Galois module structure,'' with G. Pappas and M. Taylor, preprint (2000).   PDF 

D. Other research articles.

  1. "Mahler measures and derivatives of L-functions at non- positive integers," manuscript (1984). 9 pages.

E. Expository articles and book reviews.

  1. "An introduction to Arakelov intersection theory," in Arithmetic Geometry, G. Cornell and J.H. Silverman eds., Spring-Verlag, Berlin Heidelberg New York (1986), p. 289- 307.
  2. "Minimal models for curves over Dedekind rings," in Arithmetic Geometry, G. Cornell and J.H. Silverman eds., Spring-Verlag, Berlin Heidelberg New York (1986), p. 309- 326.
  3. Book review of "Elliptic functions and rings of integers," by M.J. Taylor and Ph. Cassou-Nogu”s, Bull. of the AMS Vol. 20. no. 1, p. 117-121 (1989).
  4. Book review of "Capacity Theory on Algebraic Curves" by R. Rumely, Bull. of the AMS Vol. 26. no. 2, p.332-336 (1992).

Last updated: 1/17/97
Send e-mail comments to: ted@math.upenn.edu