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

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

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

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

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

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

- S. Bae, Univ. of Penn. Thesis (June, 1988) "Conjectures of Lichtenbaum and Chinburg over Function Fields."
- S. Kim, Univ. of Penn. Thesis (June, 1988) "A generalization of Frohlich's Theorem to wildly ramified quaternion extensions of Q ."
- D. Solomon, Brown U. Thesis (June, 1988) "Lichtenbaum's Conjecture for Dirichlet characters."
- T. Schmidt, Univ. of Penn. Thesis (June, 1989) "Congruences for the values at s = O of quaternionic representations."
- T. Costa, Univ. of Penn. Thesis (June, 1989) "Class number congruences and modular forms."
- A. Agboola, Columbia University. Thesis (June, 1991), "Abelian varieties and Galois module structure in Global Fields."
- M. Rogers, Columbia University. Thesis (June, 1991), "On a Multiplicative-Addictive Galois Invariant."
- G. Pappas, Columbia University. Thesis (June, 1992), "The bad reductions of some Hilbert-Blumenthal moduli varieties."
- C.F. Lau, University of Pennsylvania. Thesis (June, 1993), "An arithmetic capacity on Grassmanian varieties."
- S. Kwon, University of Pennsylvania. Thesis (June 1994), "Galois module structure of tame covers".
- C. Xiao, University of Pennsylvania. Thesis (June 1997), "Galois module structure of elliptic curves".
- S. Hu, University of Pennsylvania. Thesis (Dec. 1997), "On Eisenstein Cocyles".
- M. Atria, University of Pennsylvania, Thesis (June 2002), "Improved lower bounds for the discriminants of number fields".
- D. Glass, Univerity of Pennsylvania, Thesis (June 2002), "Orthogonal epsilon constants for tame actions of finite groups on surfaces".
- M. Sabitova, University of Pennsylvania. Thesis (June 2005), ``Root numbers of abelian varieties and representations of the Weil-Deligne group".
- H. Yuan, University of Pennsylvania. Thesis (June 2005), ``Special Value Formulae of Rankin $L$-Functions".
- D. Fithian, University of Pennsylvania. Thesis (June 2008), ``Pseudomodular groups".

- T. Chinburg and M. Henriksen, "Multiplicatively Periodic Rings," Amer. Math. Monthly, Vol. 83 n. 7 (1976), p. 547- 549.
- 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.
- "`Easier' Waring problems for commutative rings," Acta Arith. 35 n. 4 (1979), p. 303-331.
- "Stark's conjecture for L-functions with first order zeroes at s = 0 ," Advances in Math. 48 (1983), p. 82-113.
- "Derivatives of L-functions at s = 0 ," Compositio Math. 48 (1983) p. 119-127.
- "On the Galois structure of algebraic integers and S-units," Inv. Math. 74 (1983), p. 321-349.
- "The Galois structure of S-units," Sem. Th. de Nombres de Bordeaux, annee 1982-1983, p. 40.01-40.21.
- "Multiplicative Galois structure," Lecture Notes in Mathematics #1068, p. 23-32.
- "Volumes of hyperbolic manifolds," J. Diff. Geom. 18 (1983), p. 783-789.
- "Salem numbers and L-functions," J. Number Theory, Vol. 18, no. 2 (1984), p. 213-214.
- "Multiplicative Galois module structure," J. London Math. Soc. (2) 29 (1984), p. 23-33.
- "On the arithmetic of two constructions of Salem numbers," Crelle's Journal 348 (1984), p. 166-179.
- "A small arithmetic hyperbolic three-manifold," Proc. of the AMS, Vol. 100, no. 1 (1984), p. 140-144.
- "Exact sequences and Galois module structure," Annals of Math. 121 (1985), p. 351-376.
- "Intersection theory and capacity theory on arithmetic surfaces," Proceedings of the CMS summer seminar on Number Theory, Vol. 7 (1987), p. 1-35.
- 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.
- "The analytic theory of multiplicative Galois structure," Memoirs of the AMS, Vol. 77, No. 395 (1989).
- "A quaternionic L-value congruence," J. Fac. Science of the Univ. of Tokyo, Sec. IA, Vol. 36, No. 3 (1989), p. 765-787.
- 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.
- "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).
- "Capacity theory on varieties," Compositio Math. 80 (1991), p.75-84.
- "The capacity pairing," with R. Rumely, J. Riene Angew. Math. 434 (1993), 1-44.
- "Galois structure of De Rham cohomology," Sem. Th. Nombres, Bordeaux 4 (1991), 1-18.
- T. Chinburg and B. Erez, "Equivariant Euler-PoincarÇ characteristics and tameness," Asterisque 209 (1992), 179- 194.
- "Galois structure of De Rham cohomology of tame covers of schemes," Annals of Mathematics 139 (1994), 443-490.
- "Closed hyperbolic 3-manifolds whose closed geodesics are simple," with Alan Reid, J. of Diff. Geom. 38 (1993), 545- 558.
- "Tame actions of group schemes: Integrals and Slices," with B. Erez, G. Pappas and M. Taylor, Duke Math. J. 82:2 (1996), 269-308.
- "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.
- "Adams operations and integral Galois representations," with D. Burns, to appear in the Amer. J. of Math.
- ``$\epsilon$-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.
- "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.
- "$\epsilon$-constants and the Galois structure of de Rham cohomology, II" with G. Pappas and M. Taylor, J. Reine Angew. Math. 519 (2000), 201-230.
- ``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.
- ``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.
- ``On the $\epsilon$-constants of arithmetic schemes,'' with B. Erez, G. Pappas and M. Taylor, Math. Ann. {\bf 311} (1998), no. 2, 377--395.
- "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.
- "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.
- "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
- `Nearly perfect complexes and Galois module structure,'' with M. Kolster, G. Pappas and V. Snaith, Compositio Math. 119 (1999), no. 2, 133--155
- "An embedding theorem for quaternion algebras," with E. Friedman, J. London Math. Soc. (2) 60 (1999), no. 1, 33--44.
- "Operations on ring structures preserved by normalized automorphisms of group rings," with F. Bleher, J. Algebra 215 (1999), no. 2, 531--542.
- ``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.
- ``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.
- ``The finite subgroups of maximal arithmetic Kleinian groups,'' with E. Friedman, Ann. Inst. Fourier (Grenoble) 50 (2000), no. 6, 1765--1798 (2001).
- ``Universal deformation rings and cyclic blocks,'' with F. Bleher, Math. Ann. 318 (2000), no. 4, 805--836.
- ``$\epsilon$-constants and Arakelov Euler characteristics," with G. Pappas and M. J. Taylor, Math. Res. Lett. 7 (2000), no. 4, 433--446.
- ``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.
- ``Locations of modules for Brauer tree algebras.'' with F. Bleher,
J. Pure and Appl. Algebra 169 (2002), no. 2 - 3, 109 - 135.

- ``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.
- ``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
- ``Embedding Problems and Finite Quotients,'' with D. Glass, Pacific J. Math. 205 (2002), no. 1, 31--41.
- ``Deformations and derived categories," with F. Bleher, C. R. Math. Acad. Sci. Paris 334 (2002), no. 2, 97--100.
- ``Surreal Dimensions," with A. Ovetsky, Adv. in Appl. Math. 29 (2002), no. 4, 604--619.
- ``Capacity Theory and Intersection Theory," with R. Rumely and C. F. Lau, Duke Math. J. 117 (2003), no. 2, 229--285.
- ``Duality and Hermitian Galois module structure,'' with G. Pappas and M. Taylor, Proc. London Mathematical Society, Volume 87, (2003), no. 1, 54--108.
- ``Applications of universal deformations to Galois theory," with F. Bleher, Comment. Math. Helv. 78 (2003), no. 1, 45--64.
- "Deformations with respect to an algebraic group," with F. Bleher, Illinois J. Math. 47 (2003), no. 3, 899--919.
- "Deformations and derived categories," with F. Bleher, Ann. Institut Fourier (Grenoble) 55 (2005), 2285-2359. PDF
- "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.
- "Pfaffians, the G-Signature Theorem and Galois Hodge discriminants," with G. Pappas and M. Taylor. Compositio Math. 143 (2007), no. 5, 1213--1254. PDF
- "Galois structure of homogeneous coordinate rings," with F. Bleher. To appear in the Transactions of the A. M. S.. PDF
- "Universal deformation rings need not be complete intersections," with F. Bleher, C. R. Math. Acad. Sci. Paris 342 (2006), 229-232.
- "Universal deformation rings need not be complete intersections," with F. Bleher. Math. Ann. 337 (2007), 739-767. PDF
- "Topological properties of Eschenburg spaces and 3-Sasakian manifolds," with C. Escher and W. Ziller. Math. Ann. 339 (2007), no. 1, 3--20. PDF
- ``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
- "Galois structure of homogeneous coordinate rings," with F. Bleher, to appear in the Trans. Amer. Math. Soc., 2006. ArXiv math.GR/0504281
- "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
- "Pullback moduli spaces," with F. Bleher. To appear in Communications in Algebra. PDF
- ``Cubic structures, equivariant Euler characteristics and lattices of modular forms," with G. Pappas and M. Taylor. PDF to appear in the Annals of Mlathematics.
- ``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.
- ``Oort groups and lifting problems," with R. Guralnick and D. Harbater, to appear in Compositio Mathematica. PDF

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

- "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.
- "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.
- 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).
- 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