PROF. SETHURAMAN'S Biography

Prof. Sethuraman's biography and research interests

Research Interests
Finite-dimensional division algebras.

Matrix varieties: applications of algebraic geometry to problems in matrix theory.

Application of division algebras to space-time coding (wireless communication).

Biography

Ph.D 1991, University of California, San Diego, Mathematics.

B.Tech 1980, Indian Institute of Technology (IIT) Chennai, Mechanical Engineering.

Positions held

Professor, California State University Northridge (1999 to Present)
Associate Professor, California State University Northridge (1994 to 1999).
Visiting Professor, University of California at Santa Barbara, Spring 2000.
Visiting Associate Professor, University of Southern California, Spring 1998.
Visiting Associate Professor, New Mexico State University, Spring 1996.
Assistant Professor, California State University Northridge (1991 to 1994)
Instructor, University of San Diego, 1990--91.
Software Engineer, Calma, San Diego, 1984--1988.
Engineer Trainee, Eicher, New Delhi, 1980--1981.

Grants

National Science Foundation, Division of Mathematical Sciences, 2007-2010, $121,031.
National Science Foundation, International Research, 2002--2005, $27,178
K.B. Chandrashekhar Family Foundation Award, 2000-2001, $113,865.
National Science Foundation, Division of Mathematical Sciences, 1994--97, $59,850.
Miscellaneous internal CSU Northridge Research Awards, 1991--Present.

Publications

Research Publications

Perfect space-time codes for any number of antennas (with Petros Elia and P. Vijaykumar), IEEE Transactions on Information Theory, 53, 3853--3868, November 2007.
Moving Zeros Among Matrices (appendix with Tomaz Kosir to a paper by John Holbrook and Jean-Pierre Schoch), Linear Algebra and Applications, Special Issue Honoring Roger Horn, 424, 83--95, 2007.
Information-lossless space-time block codes from crossed product algebras (with B.Sundar Rajan and V.Shashidhar) IEEE Transactions on Information Theory, 52, 3913--3935, September 2006 .
Valuation on tensor powers of a division algebra (with Pat Morandi), Journal of Algebra, 293, 385--394, 2005.
A note on the special unitary group of a division algebra (with B. Sury), Proc. Amer. Math. Soc, 134, 351--354, 2005.
A Groebner basis for the 2X2 determinantal ideal mod t^2 (with Tomaz Kosir), Journal of Algebra, 292, 138--153, 2005.
Division algebras with an anti-automorphism but no involution (with Pat Morandi and Jean-Pierre Tignol), Advances in Geometry, 5, 485--495, 2005.
Determinantal varieties over truncated polynomial rings (with Tomaz Kosir), Journal of Pure and Applied Algebra, 195, 75--95, 2005 .
Full-diversity, high-rate space-time block codes from division algebras (with B. Sundar Rajan and V. Shashidhar), IEEE Transactions on Information Theory, Oct 2003, Special Issue on Space-Time Coding.
Decomposition of involutions on inertially split division algebras, (with Pat Morandi), Math. Zeitschrift , 235 , 195--212, 2000.
Generalized cocycles with values in one-units of henselian division algebras, (with Pat Morandi), Journal of Algebra , 224 , 123--129, 2000.
Commuting pairs and triples of matrices, and related varieties, (with Robert Guralnick), Linear Algebra and Applications , 310 , 139--148, 2000.
Commuting pairs in the centralizers of 2-regular matrices, (with Michael Neubauer) Journal of Algebra 214 (1999) 174--181.
Divisors on division algebras and error correcting codes, (with Pat Morandi) Communications in Algebra 26 (1998), 3211--3221.
Degrees of high-dimensional subvarieties of determinantal varieties, Proc. Amer. Math. Soc. 126 (1998) 9--14.
Indecomposable division algebras with a Baer ordering, (with Pat Morandi) Communications in Algebra, 22 (1994), 5401--5418.
Noncrossed product division algebras with a Baer ordering, (with Pat Morandi) Proc. Amer. Math. Soc. 123 (1995), 1995--2003.
Kummer subfields of tame division algebras, (with Pat Morandi) Journal of Algebra, 172 (1995), 554--583.
Division algebras whose p^ith powers have arbitrary indices, Journal of Algebra, 165 (1994), 476--482.
Dec groups of arbitrarily high exponent, Pacific J. Math., 162 (1994), 373--391.
Indecomposable division algebras, Proc. Amer. Math. Soc., 114 (1992), 661-665.

Textbooks

Rings, Fields, and Vector Spaces, published in Springer-Verlag's Undergraduate Texts in Mathematics series, 1997, ISBN 0-387-94848-1.
Abstract Algebra: A One-Semester Introduction, in preparation.

Refereed Engineering Conference Proceedings

Construction of Orthonormal Lattices and Quaternion Division Algebras for Totally Real Number Fields (with Frederique Oggier), Proceedings of Applied Algebra and Error Correcting Codes 17 (Lecture Notes in Computer Science), Bangalore, December 2007.
Codes Achieving The DMD Tradeoff Of The MIMO-ARQ Channel} (with Petros Elia, K. Raj Kumar, P. Vijay Kumar, and Sameer A. Pawar), Proceedings of IEEE International Symposium on Information Theory (ISIT 2005).
Perfect Space-Time Codes with Minimum and Non-Minimum Delay for Any Number of Antennas} (with Petros Elia and P. Vijay Kumar), WirelessCom 2005, International Conference on Wireless Networks, Communications, and Mobile Computing, June 2005
Information -Lossless STBCs from Crossed-Product Algebras} (with B. Sundar Rajan and V. Shashidhar), Proceedings of IEEE International Symposium on
Information Theory (ISIT 2004), Chicago, 2004.
STBCs using capacity achieving designs from crossed-product division algebras} (with B. Sundar Rajan and V. Shashidhar), Proceedings of IEEE International Conference on Communications (ICC 2004), Paris, France, 2004.
Information-Lossless Space-Time Block Codes from Division Algebras} (with B. Sundar Rajan and V. Shashidhar),Oberwolfach Meeting on Kodierungstheorie held at Mathematisches Forschungsinstitut Oberwolfach, Germany, 2003.
STBCs using Capacity Achieving Designs from Cyclic Division Algebras (with B. Sundar Rajan and V. Shashidhar), IEEE Globecomm, San Francisco, 2003.
High-Rate Full-Diversity STBCs from Field Extensions (with B. Sundar Rajan et al), IEEE ISIT conference, Yokohama, Japan 2003.

An Algebraic Description of Orthogonal Designs and the Uniqueness of the Alamouti Code (with B. Sundar Rajan), IEEE Globecomm, Taipei, Taiwan 2002.
Full-Rank, Full-Rate STBCs from Division Algebras (with B. Sundar Rajan), IEEE Information Theory Workshop, Bangalore, India 2002.
STBC from field extensions of the rational field (with B. Sundar Rajan). IEEE ISIT conference, Lausanne, Switzerland 2002.

Optimal STBC from PSK signal sets from cyclotomic field extensions (with B. Sundar Rajan). IEEE ICC conference, New York, 2002.

Research Work in Progress

Valued division algebras (with Pat Morandi)
Varieties of commuting pairs and triples of matrices, (with Tomaz Kosir).
Applications of fields and division algebras to space-time codes (with B. Sundar Rajan, P. Vijay Kumar, Petros Elia, Frederique Oggier, et. al.).

Collaborations with Students and Postdocs

Boyan Jonov: Masters student in pure mathematics at CSU Northridge. Currently writing a masters thesis with me. Has done independent research and is currently writing up his results for publication. His paper is titled "Shellability of a complex associated to the first order jet scheme of a determinantal variety.”
Mario Garcia Armes: An undergraduate student at the Universidad de La Habana, Cuba. We collaborated on the paper "The Hankel Matrices of the Central Binomial Coefficients and the Trace Form in Cyclotomic Fields" to which he contributed very substantially.
Frederique Oggier: A former postdoc at Caltech. We collaborated on the paper "Construction of Orthonormal Lattices and Quaternion Division Algebras for Totally Real Number Fields".
Petros Elia: A former Ph.D student at USC. We collaborated on the paper "Perfect space time codes for any number of antennas".
V. Shashidhar: A former Ph.D student at Indian Institute of Science. We collaborated on two papers: "Information lossless spacetime block codes from crossed product algebras" and "Full-diversity, high-rate space-time block codes from division algebras".