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Course Information
Timothy J Hodges
Professor and Department Head
839C Old Chemistry Building
513-556-4052
timothy.hodges@uc.edu
http://math.uc.edu/~hodgestj
Education
PhD, University of Leeds, Leeds, England, 1981 (Mathematics).
BSc, University of Leeds, Leeds, England, 1977 (Mathematics).
Positions & Work Experience
2001 to Present, Head, University of Cincinnati, Cincinnati, Ohio.
03-1995-04-1995, Visiting Research Professor, University of Poitiers, Poitiers, France.
1993 to Present, Professor, University of Cincnnati, Cincinnati, Ohio.
1990-1991, Visiting Associate Professor, Universite de Bretagne Occidentale, Brest, France.
1987-1993, Associate Professor, University of Cincinnati, Cincinnati, Ohio.
1984-1987, Assistant Professor, University of Cincinnati, Cincinnati, Ohio.
1981-1984, Instructor, University of Utah, Salt Lake City, Utah.
1980-1981, Teaching Associate, University of California at Santa Barbara, Santa Barbara, California.
Research Interests
Abstract algebra: quantum groups, Poisson groups, Lie algebras, Lie bialgebras, noncommutative algebra, noetherian rings, K-theory, cryptography
Research Support
(PI) Degeneration of R-Matrices and Structure of Non-Standard Quantum Groups, National Security Agency. (MDA 904-01-1-0084); $36,565. Funded 2001 to 2003.
(PI) Algebraic Structure of Nonstandard Quantum Groups, National Security Agency. (MDA 904-99-1-0026); $31,481. Funded 1999 to 2001.
(PI) Algebraic Structure of Quantum Groups, National Science Foundation. (DMS 9501484); $50,000. Funded 1995 to 1998.
(PI) Algebraic Structure of Quantum Groups, (MDA 904-93-3042); $24,000. Funded 1993 to 1995.
(PI) Summer Faculty Research Grant, Taft Foundation, University of Cincinnati. Funded 1993
(PI) Quantum and Classical Enveloping Algebras of Semisimple Lie Algebras, National Security Agency. (MDA 904-91-H0045); $58,459. Funded 1991 to 1993.
(PI) Noncommutative Algebras, National Security Agency and National Science Foundation. (MDA 904-89-H2046); $41,811. Funded 1989 to 1991.
(PI) Summer Faculty Research Grant, Taft Foundation, University of Cincinnati. Funded 1988
(PI) Structure and K-Theory of Group Rings and Rings of Differential Operators, National Science Foundation. (DMS 8602291); $40,329. Funded 1986 to 1988.
(PI) Summer Faculty Research Scholarship, University Research Council, University of Cincinnati. Funded 1985
Peer Reviewed Publications
Hodges, Timothy J., & Yakimov, Milen (2005). Triangular Poisson structures on Lie groups and symplectic reduction. Contemporary Mathematics, 391, 123.
Endelman, Robin, & Hodges, Timothy J. (2004). Degenerations and representations of twisted Shibukawa-Ueno R-operators. Lett. Math. Phys., 68(3), 151.
Ding, Jintai, & Hodges, Timothy J. (2004). Cryptanalysis of an implementation scheme of the tamed transformation method cryptosystem. J. Algebra & Appl., 3(3), 273.
Hodges, Timothy J., & Yakimov, Milen (2001). The double and dual of a quasitriangular Lie bialgebra. Math. Res. Lett., 8(1), 91, 105.
Hodges, Timothy J. (2001). Generating functions for Cremmer-Gervais quantum groups. J. Pure Appl. Algebra, 157(1), 69.
Endelman, R., & Hodges, Timothy J. (2000). Generalized Jordanian R-matrices of Cremmer-Gervais type. Lett. Math. Phys., 52(3), 225-237.
Hodges, Timothy J. (1999). The Cremmer-Gervais solution of the Yang-Baxter equation. Proc. Amer. Math. Soc., 127(6), 1819 - 1826.
Hodges, Timothy J. (1998). Non-standard quantum groups associated to Belavin-Drinfeld triples. Contemporary Mathematics, 214, 63 - 70.
Giaquinto, Anthony, & Hodges, Timothy J. (1998). Nonstandard solutions of the Yang-Baxter equation. Lett. Math. Phys., 44(1), 67 - 75.
Hodges, Timothy J. (1997). Double quantum groups and Iwasawa decomposition. J. Algebra, 192(1), 303 - 325.
Hodges, Timothy J., Levasseur, Thierry, & Toro, Margarita (1997). Algebraic structure of multiparameter quantum groups. Adv. Math., 126(1), 52 - 92.
Hodges, Timothy J. (1995). On the Cremmer-Gervais quantizations of SL(n). Internat. Math. Res. Notices, 10, 465 - 481.
Hodges, Timothy J., & Levasseur, Thierry (1994). Primitive ideals of C_q[SL(n)]. J. Algebra, 168(2), 455 - 468.
Hodges, Timothy J., & Holland, Martin (1994). Chern characters, reduced ranks and D-modules on the flag variety. Proc. Edinburgh Math. Soc. (2), 37(3), 477 - 482.
Hodges, Timothy J. (1993). Noncommutative deformations of type-A Kleinian singularities. J. Algebra, 161(2), 271 - 290.
Hodges, Timothy J., & Levasseur, Thierry (1993). Primitive ideals of C_q[SL(3)]. Comm. Math. Phys., 156(3), 581 - 605.
Hodges, Timothy J., & Kim, Kyunghee (1991). Behaviour of Krull dimension under extension of the base field. Comm. Algebra, 19(1), 143 - 156.
Alev, Jacques, Hodges, Timothy J., & Velez, Juan-Diego (1990). Fixed rings of the Weyl algebra A_1(C). J. Algebra, 130(1), 83 - 96.
Hodges, Timothy J. (1989). Equivariant K-theory for noetherian rings. J. London Math. Soc. (2), 39(3), 414 - 426.
Hodges, Timothy J., & Tesser, Steven B. (1989). Representing Clifford algebras as crossed products. J. Algebra, 123(2), 500 - 505.
Hodges, Timothy J., & Stafford, J. Toby (1989). Noetherian rings with big indecomposable modules. Bull. London Math. Soc., 21(3), 249 - 254.
Hodges, Timothy J. (1989). K-theory of D-modules and primitive factors of enveloping algebras of semisimple Lie algebras. Bull. Sci. Math. (2), 113(1), 85-88.
Hodges, Timothy J. (1987). A noncommutative Bass-Tate sequence. Bull. Soc. Math. Belg. Ser. B, 39(3), 255-257.
Hodges, Timothy J. (1987). K-theory and right ideal class groups for HNP rings. Trans. Amer. Math. Soc., 302(2), 751-767.
Hodges, Timothy J., & Osterburg, James A. (1987). A rank two indecomposable projective module over a Noetherian domain of Krull dimension one. Bull. London Math. Soc., 19(2), 139-144.
Hodges, Timothy J. (1986). On the primitivity of polynomial rings with nonprimitive coefficient rings. Proc. Amer. Math. Soc., 98(4), 553-558.
Hodges, Timothy J., & Smith, S. Paul (1985). On the global dimension of certain primitive factors of the enveloping algebra of a semisimple Lie algebra. J. London Math. Soc. (2), 32(3), 411-418.
Hodges, Timothy J., & Smith, S. Paul (1985). Sheaves of noncommutative algebras and the Bernstein-Beilinson equivalence of categories. Proc. Amer. Math. Soc., 93(3), 379-386.
Goodearl, K. R., Hodges, T. J., & Lenagan, T. H. (1984). Krull and global dimensions of Weyl algebras over division rings. J. Algebra, 91(2), 334-359.
Hodges, Timothy J. (1984). An example of a primitive polynomial ring. J. Algebra, 90(1), 217-219.
Hodges, Timothy J. (1984). The Krull dimension of skew Laurent extensions of commutative rings. Comm. Algebra, 12(11), 1301-1310.
Hodges, Timothy J., McConnell, John C., & (1981). On Ore and skew Laurent extensions of noetherian rings. J. Algebra, 73(1), 56-64.
Books
Argyres, Hodges, Mansouri, Scanio, Suranyi, & Wijewardhana (eds) (2004). Quantum Theory and Symmetries, Proceedings of the Third International Symposium. World Scientific.
Book Chapters
A. Diene, J. Ding, J. E. Gower, T. J. Hodges, & Z. Yin (2006). Dimension of the linearization equations of the Matsumoto-Imai cryptosystems. In Oyvind Etrehus (Eds.), Coding and Cryptography (pp. 242-251). Lecture Notes in Computer Science 3969, Springer-Verlag.
Ding, Jintai, & Hodges, Timothy J. (2002). The Yang-Baxter equation for operators on function fields. In A. Pressley (Eds.), Quantum Groups and Lie theory (pp. 168, 174). Cambridge University Press.
Hodges, Timothy J. (1992). Morita equivalence of primitive factors of U(sl(2)). In Vinay Deodhar (Eds.), Kazhdan-Lusztig theory and related topics (pp. 175, 179). Providence, RI: Contemporary Mathematics 139, Amer. Math. Soc.
Hodges, Timothy J. (1990). Ring-theoretical aspects of the Bernstein-Beilinson theorem. In S. K. Jain and S. R. Lopez-Permouth (Eds.), Noncommutative ring theory (pp. 155, 163). Berlin: Lecture Notes in Math. 1448, Springer.
Hodges, Timothy J. (1989). K-Theory of Noetherian rings. In M.-P. Malliavin (Eds.), Seminaire d'Algebre Paul Dubreil et Marie-Paul Malliavin, 39eme Annee (pp. 246, 268). Berlin: Lecture Notes in Math. 1404, Springer.
Reviews
(1997). A guide to quantum groups. Bull. London Math. Soc., 506-508.
(1989). Torsion Theories. Bull. Amer. Math. Soc., 148-151.
Invited Presentations
(10-2004). Loyola University, Chicago.
(07-2004). Quantum Groups. Technion, Haifa, Israel.
(05-2001). Midwest Conference on Lie Algebras and Related Topics. University of Wisconsin-Milwaukee
(01-2001). Workshop on quantum and semi-classical structures. Fields Institute, Toronto
(04-2000). IU/UC Algebra Day. Indiana University
(03-2000). Workshop on Quantum Groups. Morelia, Mexico
(02-2000). Workshop on Interactions between noncommutative algebra and geometry. Mathematical Sciences Research Institute, Berkeley, CA.
(07-1999). Conference on Quantum Groups and Lie Theory. Durham University, England,
(10-1998). Special session on noncommutative algebra. AMS meeting, Wake Forest University.
(03-1998). Special session on quantum groups. AMS meeting, Kansas State University.
(10-1997). Special session on enveloping algebras and quantum groups. AMS meeting, Milwaukee.
(08-1997). Ring theory and Representation Theory. Oberwolfach, Germany.
(03-1997). University of Louisville
(06-1996). Joint Summer Research Conference on Quantization
(03-1995). Seminaire d'algebre. Universite de Paris VII
(03-1995). Universite de Poitiers
(01-1995). Special Session on noncommutative algebra. AMS meeting, San Antonio.
(08-1993). Ring theory and Representation Theory. Oberwolfach, Germany.
(07-1993). Workshop on Ring Theory, University of Washington.
(01-1993). Special session on Quantum Groups. AMS meeting, San Antonio, Texas.
(09-1991). Conference on Quantum Groups, Wake Forest University.
(02-1991). Universite de Strasbourg
(11-1990). Seminaire sur les algebres enveloppantes. Universite de Paris VI
(10-1990). Seminaire d'algebre. Universite de Paris VI
(06-1990). JSRC: Deformation and quantization of algebras.
(02-1990). Special session on quantum groups. AMS Meeting, Penn State.
(12-1989). IU/UC Algebra Day, University of Cincinnati.
(10-1989). Special session on Noncommutative algebra. AMS meeting , Muncie, IN.
(09-1989). Midwest Noncommutative Ring Theory Conference, Ohio University.
(09-1989). Miami University.
(07-1989). Microprogram on Noncommutative Rings. MSRI, Berkeley.
(06-1989). Ringe und Moduln, Oberwolfach, Germany.
(05-1989). Special session on Noncommutative Ring Theory. AMS Meeting , Chicago.
(05-1988). Noncommutative Ring Theory. N. Illinois U.
(06-1987). Salt Lake City.
(07-1986). University of Warwick, England.
(07-1986). Ring Theory Symposium. Leeds, England.
(04-1986). Midwest Ring Theory Conference, Milwaukee.
(08-1983). NATO Advanced Study Institute, Antwerp, Belgium.
(04-1983). Special session on Noncommutative Ring Theory. AMS Meeting , Salt Lake City.
(03-1983). Special session on Noncommutative Ring Theory. AMS Meeting , Norman, Oklahoma.
(09-1982). University of Southern California
(06-1981). University of Leeds
(05-1981). University of Southern California
(04-1980). British Mathematical Colloquium
Student Advising
Kyunghee Lee, , Dissertation ,Chair, 1986.
Ricardo Alfaro, , Dissertation ,Chair, 1989.
Sei-Qwon Oh, , Dissertation ,Chair, 1991.
Margarita Toro, , Dissertation ,Chair, 1993.
Robin Endelman, , Dissertation ,Chair, 2002.
