My main field of studies is Algebra, in particular the Theory of Rings and Modules. I am interested in analyzing modules over (usually) non-commutative rings, modules endowed with certain properties - for example, injectivity/projectivity, noetherianity/artinianity are the most known ones; more "esoteric" such as C1/C2/C3 conditions. As a matter of custom, one can still study a ring as well, since a ring can be viewed as a module over itself.
I studied quite extensively a category of modules called CS (or extending) modules. At the moment I'm devoting my time to Baer and quasi-Baer modules, a concept I helped create and study (a number of papers have been published, and gave several presentations - seemingly well-received - at International conferences).
I am quite interested in other fields of algebra (and not only!), and I'm always trying to find connections with what I am very familiar with. For instance, I believe there is a connection between the above mentioned Baer modules and Algebraic Geometry (I get a topology which is very similar to Zarisky's topology). Cryptography or coding theory - also, there are certain connections via ring theory, and I like to play with these as well.
I also like to solve olympiad-style problems, or Putnam competition-style problems ... at OSU we have the Rasor-Gordon-Bareis competition, that has some neat problems involved as well. Here is a bunch of Putnam problems, with solutions (some ...)
You can check my math lineage (follow the links through the ages; click on "Advisor"), and if you have access to MathSciNet, find my articles. My Erdos number is 5 (for the moment ...).
S. T. Rizvi, Cosmin Roman. 2004. Baer and Quasi-Baer Modules. Communications in Algebra. Vol. 32, no. 1: 103-123.
S. T. Rizvi, Cosmin Roman. 2005. Baer Property of Modules and Applications. Advances in Ring Theory: 225-241.
S. T. Rizvi, Cosmin Roman. 2007. On K-Nonsingular Modules and Applications. Communications in Algebra. Vol. 35, no. 9: 2960-2982.
S. T. Rizvi, Cosmin Roman. 2009. On Direct Sums of Baer Modules. Journal of Algebra. Vol. 321, no. 2: 682-696.
G. Lee, S. T. Rizvi, Cosmin Roman. 2009. Rickart Modules. Journal of Algebra. (First submission)
Conferences (invited talks)
2002. Baer and Quasi-Baer Modules. Presented at the 26th Ohio State-Denison Mathematics Conference. Granville, OH. (May 17 - 19)
2004. Idempotents and Annihilators in Endomorphism Rings. Presented at Sixth International Joint Meeting of the AMS and the Sociedad Matematica Mexicanan (SMM). Houston, TX. (May 13 - 15)
2004. Type Theory for Nonsingular CS Modules. Presented at the 27th Ohio State-Denison Mathematics Conference. Columbus, OH. (June 11 - 13)
2005. Type Decompositions for Nonsingular Extending Modules. Presented at International Conference on Rings and Applications. Athens, OH. (March 22 - 26)
2006. On K-Nonsingularity and Continuous Modules. Presented at the 28th Ohio State-Denison Mathematics Conference. Columbus, OH. (May 19 - 21)
2007. On Sigma -Baer Modules. Presented at International Conference on Rings and Things. Ohio University, Zanesville, OH. (June 15 - 17)
2007. On Baer and Quasi-Baer Properties for Modules. Presented at 6-th Congress of Romanian Mathematicians. University of Bucharest. Bucharest, Romania. (June 28 - July 4)
2007. On Direct Sums of Baer and Extending Modules. Presented at 5th China-Japan-Korea International Conference. Tokyo, Japan. (September 10 - 15)
2008. A Generalized Relative Injectivity for Extending Modules. Presented at International Conference on Modules and Representation Theory. Babes Bolyai University. Cluj-Napoca, Romania. (July 7 - 12)