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, deformation theory, group actions on varieties, Arakelov theory,
                         capacity theory

HONORS AND GRANTS

NSF grants 1982-1989, 1992-2011
G. de B. Robinson research Award, Canadian Mathematical Society, 2002
NSA grant, 1990 - 1992
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

Editor, Proceedings of the A. M. S., 2006 - present
Editor, J. Theorie de Nombres de Bordeaux, 2006 - present
Editor, Compositio Mathematica, 2002 - 2005
Visitor, I.H.E.S., Summer 2002, 1996, 1988, 1981, 1980
Visitor, Universite de Bordeaux, Summer 2008, 2006, 2001, 1994, 1992, 1983
Visitor, University of Meunster, Summer 1995
Visitor, University of Manchester, Summer 2006, 1993
Visitor, University of Amsterdam, Summer 1991
Member, MSRI, 1986 - 1987
Visitor, Cambridge University, 1983
Member, Institute for Advanced Study, 1982 - 1983

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".
  13. M. Atria, University of Pennsylvania, Thesis (June 2002), "Improved lower bounds for the discriminants of number fields".
  14. D. Glass, Univerity of Pennsylvania, Thesis (June 2002), "Orthogonal epsilon constants for tame actions of finite groups on surfaces".
  15. M. Sabitova, University of Pennsylvania. Thesis (June 2005), ``Root numbers of abelian varieties and representations of the Weil-Deligne group".
  16. H. Yuan, University of Pennsylvania. Thesis (June 2005), ``Special Value Formulae of Rankin $L$-Functions".
  17. D. Fithian, University of Pennsylvania. Thesis (June 2008), ``Pseudomodular groups".

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-PoincarÇ 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. ``Hilbert symbols, class groups and quaternion algebras,'' with E. Friedman, Colloque International de Thorie des Nombres (Talence, 1999). J. Th. Nombres Bordeaux 12 (2000), no. 2, 367--377.
  44. ``The finite subgroups of maximal arithmetic Kleinian groups,'' with E. Friedman, Ann. Inst. Fourier (Grenoble) 50 (2000), no. 6, 1765--1798 (2001).
  45. ``Universal deformation rings and cyclic blocks,'' with F. Bleher, Math. Ann. 318 (2000), no. 4, 805--836.
  46. ``$\epsilon$-constants and Arakelov Euler characteristics," with G. Pappas and M. J. Taylor, Math. Res. Lett. 7 (2000), no. 4, 433--446.
  47. ``The arithmetic hyperbolic 3-manifold of smallest volume,'' with E. Friedman, K. N. Jones and A. W. Reid, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 30 (2001), no. 1, 1--40.
  48. ``Locations of modules for Brauer tree algebras.'' with F. Bleher, J. Pure and Appl. Algebra 169 (2002), no. 2 - 3, 109 - 135.
  49. ``Epsilon constants and equivariant Arakelov Euler characteristics,'' with G. Pappas and M. Taylor, Annales de l'Ecole Normale Superieure, Volume 35, Issue 3 (2002), 307--352.
  50. ``Discriminants and Arakelov Euler characteristics," with G. Pappas and M. Taylor. Number theory for the millennium, I (Urbana, IL, 2000), 229--255, A K Peters, Natick, MA, 2002.   PDF 
  51. ``Embedding Problems and Finite Quotients,'' with D. Glass, Pacific J. Math. 205 (2002), no. 1, 31--41.
  52. ``Deformations and derived categories," with F. Bleher, C. R. Math. Acad. Sci. Paris 334 (2002), no. 2, 97--100.
  53. ``Surreal Dimensions," with A. Ovetsky, Adv. in Appl. Math. 29 (2002), no. 4, 604--619.
  54. ``Capacity Theory and Intersection Theory," with R. Rumely and C. F. Lau, Duke Math. J. 117 (2003), no. 2, 229--285.
  55. ``Duality and Hermitian Galois module structure,'' with G. Pappas and M. Taylor, Proc. London Mathematical Society, Volume 87, (2003), no. 1, 54--108.
  56. ``Applications of universal deformations to Galois theory," with F. Bleher, Comment. Math. Helv. 78 (2003), no. 1, 45--64.
  57. "Deformations with respect to an algebraic group," with F. Bleher, Illinois J. Math. 47 (2003), no. 3, 899--919.
  58. "Deformations and derived categories," with F. Bleher, Ann. Institut Fourier (Grenoble) 55 (2005), 2285-2359.   PDF 
  59. "Can deformation rings of group representations not be local complete intersections?" in: Problems from the workshop on Automorphisms of Curves (Leiden, 2004), Gunther Cornelissen and Frans Oort, eds.
  60. "Pfaffians, the G-Signature Theorem and Galois Hodge discriminants," with G. Pappas and M. Taylor. Compositio Math. 143 (2007), no. 5, 1213--1254.   PDF 
  61. "Galois structure of homogeneous coordinate rings," with F. Bleher. To appear in the Transactions of the A. M. S..   PDF 
  62. "Universal deformation rings need not be complete intersections," with F. Bleher, C. R. Math. Acad. Sci. Paris 342 (2006), 229-232.
  63. "Universal deformation rings need not be complete intersections," with F. Bleher. Math. Ann. 337 (2007), 739-767.  PDF 
  64. "Topological properties of Eschenburg spaces and 3-Sasakian manifolds," with C. Escher and W. Ziller. Math. Ann. 339 (2007), no. 1, 3--20.  PDF 
  65. ``Cusps of minimal non-compact arithmetic hyperbolic 3-orbifolds" with D. Long and A. Reid. To appear in the Pure and Applied Math Quarterly   PDF 
  66. "Galois structure of homogeneous coordinate rings," with F. Bleher, to appear in the Trans. Amer. Math. Soc., 2006. ArXiv math.GR/0504281
  67. "Capping groups and some cases of the Fontaine-Mazur Conjecture," with F. Bleher and J. Froelich. To appear in the Proceedings of the A. M. S..  PDF 
  68. "Pullback moduli spaces," with F. Bleher. To appear in Communications in Algebra.  PDF 
  69. ``Cubic structures, equivariant Euler characteristics and lattices of modular forms," with G. Pappas and M. Taylor.   PDF  to appear in the Annals of Mlathematics.
  70. ``Geodesics and commensurability classes of arithmetic hyperbolic $3$-manifolds," with E. Hamilton, D. Long and A. Reid.   PDF  to appear in the Duke Mathematical Journal.
  71. ``Oort groups and lifting problems," with R. Guralnick and D. Harbater, to appear in Compositio Mathematica.  PDF 

B. Other research articles.

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

C. 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-Noguäs, 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: 2/10/07
Send e-mail comments to: ted@math.upenn.edu