Timothy Hodges

Timothy J Hodges

Professor

French Hall

4504

A&S Mathematical Sciences - 0025

Education

PhD, University of Leeds Leeds, England, 1981 (Mathematics)

BSc, University of Leeds Leeds, England, 1977 (Mathematics)

Positions and Work Experience

2015 -2018 Program Director, Algebra and Number Theory, Secure and Trustworthy Cyberspace, National Science Foundation, Alexandria, Virginia

2011 -2015 Graduate Program Director, Department of Mathematical Sciences, University of Cincinnati,

2001 -2010 Head, Department of Mathematical Sciences, 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 and Practice Interests

Abstract algebra: cryptography, quantum groups, Poisson groups, Lie algebras, Lie bialgebras, noncommutative algebra, noetherian rings, K-theory

Research Support

2011 C. P. Taft Research Center Summer Research Fellowship Role:PI Type:Fellowship Level:College

Grant: #MDA904-01-1-0084 07-13-2001 -07-12-2003 National Security Agency Degeneration of R-Matrices and Structure of Nonstandard Quantum Groups Role:PI $36,565.00

Grant: #MDA 904-01-1-0084 2001 -2003 National Security Agency Degeneration of R-Matrices and Structure of Non-Standard Quantum Groups Role:PI $36,565

Grant: #MDA 904-99-1-0026 1999 -2001 National Security Agency Algebraic Structure of Nonstandard Quantum Groups Role:PI $31,481

Grant: #MDA9049910026/P00002 11-25-1998 -02-24-2001 National Security Agency Algebraic Structure of Non-Standard Quantum Groups Role:PI $31,481.00

Grant: #DMS 9501484 1995 -1998 National Science Foundation Algebraic Structure of Quantum Groups Role:PI $50,000

Grant: #MDA 904-93-3042 1993 -1995 Algebraic Structure of Quantum Groups Role:PI $24,000

1993 Taft Foundation, University of Cincinnati Summer Faculty Research Grant Role:PI Type:Grant

Grant: #MDA 904-91-H0045 1991 -1993 National Security Agency Quantum and Classical Enveloping Algebras of Semisimple Lie Algebras Role:PI $58,459

Grant: #MDA 904-89-H2046 1989 -1991 National Security Agency and National Science Foundation Noncommutative Algebras Role:PI $41,811

1988 Taft Foundation, University of Cincinnati Summer Faculty Research Grant Role:PI Type:Grant

Grant: #DMS 8602291 1986 -1988 National Science Foundation Structure and K-Theory of Group Rings and Rings of Differential Operators Role:PI $40,329

1985 University Research Council, University of Cincinnati Summer Faculty Research Scholarship Role:PI Type:Grant

Abbreviated Publications

Peer Reviewed Publications

Timothy J Hodges, Sergio Molina and Jacob Schlather, On the existence of homogeneous semi-regular sequences, Journal of Algebra, 476 (2017) 519-547

Hodges, Timothy J., Petit, Christophe and Schlather, Jacob, First Fall Degree and Weil Descent, Finite Fields and their Applications, 30 (2014), 155-177

Ding J, Hodges T, Kruglov V, Schmidt D & Tohaneanu S. Growth of the ideal generated by a quadratic multivariate function over GF(3). Journal of Algebra & its Applications, 12 (2013), 1250219 (23 pages)

Hodges Timothy J. and Schlather, Jacob, The degree of regularity of a quadratic polynomial, Journal of Pure and Applied Algebra, 217 (2013) 207-217

R. Huang, R. A. G. D. Silva, W. G. Jerome, A. Kontush, M.J. Chapman, L. K. Curtiss, T.J. Hodges and W. S. Davidson, (2011) Apolipoprotein A-I structural organization in high density lipoproteins isolated from human plasma, Nature Structural and Molecular Biology 18, 416-422

Ding, Jintai & Hodges, Timothy J., (2011)  Inverting HFE is Quasi-Polynomial for all Fields. In: Advances in Cryptology -- CRYPTO 2011, Rogaway, Phillip (Ed.) Lecture Notes in Computer Science, vol. 6841 pp. 724-742

Ding, J, Hodges Timothy J & and Kruglov V, (2010) Growth of the ideal generated by a quadratic Boolean function, PQCrypto 2010, Lecture Notes in Computer Science 6061, Springer, 13-27

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.

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.

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., & 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. (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., & 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. (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.

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.

Work in Progress

Hodges, Timothy J and Molina, Sergio, Koszul complexes and bounded regularity, in preparation

Book

P. Argyres, T. Hodges, F. Mansouri, J. Scanio, P. Suranyi, & R. Wijewardhana (eds) (2004). Quantum Theory and Symmetries, Proceedings of the Third International Symposium. World Scientific.

Review

(1997). A guide to quantum groups. Bull. London Math. Soc., 506-508.

(1989). Torsion Theories. Bull. Amer. Math. Soc., 148-151.

Presentations

Invited Presentations

(08-2015. ) Existence of Semi-Regular Sequences .SIAM Conference on Applied Algebraic Geometry (AG15), National Institute for Mathematical Sciences, Daejeon, South Korea.

(07-2015. ) The operational degree of Gr¨obner basis algorithms for systems of equations over finite fields .The 12th International Conference on Finite Fields and Their Applications, Skidmore College, NY.

(01-2015. ) Mathematical problems in multivariate cryptography .DIMACS Workshop on the Mathemtics of Post Quantum cryptgraphy, Rutgers University.

(10-2013. ) Semi-Regular Sequences over F2 .AMS Special Session on Algebraic Cryptography, University of Louisville.

(08-2013. ) Degree of Regularity of Generalized HFE Cryptosystems .SIAM Conference on Applied Algebraic Geometry, Fort Collins, Colorado.

(10-2012. ) First Fall Degree and Weil Descent .Universite Catholique de Louvain, Louvain-la-Neuve, Belgium.

(09-2012. ) First Fall and Degree and Weil Descent .YACC 2012, Porquerolles, France.

(08-2011. ) Inverting HFE Systems is Quasi-polynomial for all Fields .CRYPTO 2011, Santa Barbara, CA, USA. Conference. . Level:International

(05-2010. ) Growth of ideals in the algebra of Boolean functions .PQ Crypto 2010, Darmstadt, Germany.

(01-2010. ) Growth of ideals in Boolean Algebras .Special session on algebraic cryptography, AMS annual meeting, San Francisco.

(10-2004. ) Fermat's Conjecture .Undergraduate Colloquium talk, Loyola University, Chicago.

(07-2004. ) Algebraic structure of triangular quantum groups .International Conference on Quantum Groups, Technion, Haifa, Israel.

(06-2003. ) Degeneration of R-matrices .12-th International Colloquium on Quantum Groups and Integrable Systems, Prague, Czech Republic.

(05-2001. ) Symplectic foliations of Poisson groups .Midwest Conference on Lie Algebras and Related Topics, University of Wisconsin-Milwaukee.

(01-2001. ) Symplectic foliations of triangular Poisson groups .Workshop on quantum and semi-classical structures, Fields Institute, Toronto.

(04-2000. ) Recent developments in quantum groups .IU/UC Algebra Day, Indiana University.

(03-2000. ) Generalized Jordanian R-matrices of Cremmer-Gervais type .Workshop on Quantum Groups, Morelia, Mexico.

(02-2000. ) Degeneration of R-matrices .Workshop on Interactions between noncommutative algebra and geometry, Mathematical Sciences Research Institute, Berkeley, CA.

(07-1999. ) R-matrices on rational function fields .LMS Symposium on Quantum Groups, Durham University, England.

(10-1998. ) Algebraic structure of the quantum Lorentz group .Special session on noncommutative algebra, AMS meeting, Wake Forest University.

(03-1998. ) Quantization of Belavin-Drinfeld triples .Special session on quantum groups, AMS meeting, Kansas State University.

(10-1997. ) The Cremmer-Gervais solution of the Yang-Baxter equation .Special session on enveloping algebras and quantum groups, AMS meeting, Milwaukee.

(08-1997. ) Nonstandard quantum groups .Ring theory and Representation Theory, Oberwolfach, Germany.

(05-1997. ) Nonstandard quantum groups .Special session on Noncommutative Ring Theory, Wayne State University,Detroit.

(03-1997. ) Quantum groups - symmetry for the 21st century .Colloquium talk, University of Louisville.

(06-1996. ) Non-standard quantum groups associated to belavin-Drinfeld triples .Joint Summer Research Conference on Quantization, Mount Holyoke College.

(03-1995. ) The algebraic structure of Cremmer-Gervais quantum groups .Seminaire d'algebre, Universite de Paris VII.

(03-1995. ) Seminar talk, Universite de Poitiers, France.

(01-1995. ) Algebraic structure of Cremmer Gervais quantum groups .Special Session on noncommutative algebra, AMS meeting, San Francisco.

(08-1993. ) Ring theory and Representation Theory .Oberwolfach, Germany.

(07-1993. ) Workshop on Ring Theory, University of Washington.

(01-1993. ) Primitive Spectra of Quantum Groups .Special session on Quantum Groups, AMS meeting, San Antonio, Texas.

(09-1991. ) Primitive ideals of C[SLq(3)] and symplectic leaves of SL(3) .Mid-Atlantic Algebra Conference, Develoments in Algebra related to Quantum Groups, Wake Forest University.

(02-1991. ) A Bernstein-Beilinson theorem for Uq(sl(2)) .Seminar talk, 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. ) Analog of the Bernstein-Beilinson theorem for Uq(sl(2)) .Joint Summer Research Conference: Deformation and quantization of algebras, University of Massachusetts, Amherst.

(02-1990. ) A Bernstein-Beilinson theorem for Uq(sl(2)) .Special session on quantum groups, AMS Meeting, Penn State.

(12-1989. ) D-module methods for quantum groups .IU/UC Algebra Day, University of Cincinnati.

(10-1989. ) Morita equivalence of primitive factors of the enveloping algebra U(sl(2)) .Special session on Noncommutative algebra, AMS meeting , Muncie, IN.

(09-1989. ) Quantum D-modules .Midwest Noncommutative Ring Theory Conference, Ohio University.

(09-1989. ) Colloquium talk .Miami University.

(07-1989. ) K-theory of D-modules .Microprogram on Noncommutative Rings, Mathematical Sciences Research Institute, Berkeley.

(06-1989. ) Quantum Kleinian singularities .Ringe und Moduln, Oberwolfach, Germany.

(05-1989. ) Quantum Kleinian singularities .Special session on Noncommutative Ring Theory, AMS Meeting , Chicago.

(05-1988. ) Noncommutative Ring Theory .N. Illinois U.,

(06-1987. ) Fixed rings of Weyl algebras .Special session on Ring Theory and Invariant Theory, AMS meeting, Salt Lake City.

(06-1987. ) K-theory of Noetherian rings .Seminaire d'algebre,, University of Paris VII.

(07-1986. ) Seminar talk, University of Warwick, England.

(07-1986. ) Equivariant K-theory of Noetherian rings and schemes .Ring Theory Symposium, Leeds, England.

(04-1986. ) Equivariant K-theory of Noetherian rings .Midwest Ring Theory Conference, Milwaukee.

(04-1984. ) Sheaves of twisted differential operators .Colloquium talk, University of Milwuakee.

(08-1983. ) Differential operators on projective space .NATO Advanced Study Institute, Antwerp, Belgium.

(04-1983. ) Global dimension of simple factors of the enveloping algebra of semi-simple Lie algebras .Special session on Noncommutative Ring Theory, AMS Meeting , Salt Lake City.

(03-1983. ) Sheaves of differential operators on projective space .Special session on Noncommutative Ring Theory, AMS Meeting , Norman, Oklahoma.

(09-1982. ) Seminar talk, University of Southern California.

(06-1981. ) Seminar talk, University of Leeds.

(05-1981. ) Primitive polynomial rings .Seminar talk, University of Southern California.

(04-1980. ) Krull dimension of skew-Laurent polynomial rings .British Mathematical Colloquium,

Service

(A&S Faculty Senate ) Vice President Type:University/College Service Level:College

(Faculty Senate Budget and Priorities ) Committee Member Type:University/College Service Level:University

(Graduate Affairs Committee ) Committee Member Type:Departmental Service Level:Department

(Graduate Student Evaluation Committee ) Committee Chair Type:Departmental Service Level:Department

(A&S Graduate Council ) Committee Member Type:University/College Service Level:College

(A&S Graduate Council Executive Committee ) Committee Member Type:University/College Service Level:College

(A&S RPT Committee ) Committee Chair Type:University/College Service Level:College

Proceedings of the London Mathematical Society Reviewer Type:Editorial Service Level:International

(Graduate Program Director ) Type:Departmental Service Level:Department

(UC Hepcats ) Faculty Coordinator Type:Service to Student Groups Level:University

(Algebra Prelim ) Committee Member Type:Departmental Service Level:Department

Keywords

Algebra

Faculty Development Activities

06-13-2011 -06-17-2011 Instructional Technology Workshop University of Cincinnati Type:Workshop