Rabeya Basu obtained her PhD (Mathematics) in 2007 from Tata Institute of Fundamental Research (TIFR), Mumbai, India on the topic of Classical K-theory. She was a postdoctoral fellow at Harish Chandra Research Institute, Allahabad and a National Board for Higher Mathematics posdoctoral fellow at the Indian Statistical Institute, Kolkata before joining IISER Pune in 2010.
Dr. Raneya Basu's work is based on problems in classical K-theory which are related to Serre’s problem on projective modules. This famous theorem says that finitely generated projective modules over a polynomial ring over field are free. This involves problems in lower K-theory, in particular study of the Whitehead group K_1 due to Hyman Bass, which generalizes the group of units of a ring. Initially, these problems were studied for the general linear groups. Then people started generalizing those results for other classical groups and also for the relative cases.
At present, Dr. Basu is working on analog problems for the general quadratic groups over graded structures.
A. Bak, R. Basu & Ravi A. Rao; Local-Global Principle for Transvection Groups. Proceedings of the American Mathematical Society. Vol. 138 (2010), 1191--1204.
R. Basu, Ravi A. Rao; Injective Stability for K_1 of Regular Rings. Journal of Algebra. Vol. 323 (2010) 367--377.
R. Basu; Absence of torsion for NK_1(R) over Associative Rings; Journal of Algebra and Its Applications. Vol. 10, No. 4 (2011) 793--799.
R. Basu; Local-Global Principle for the General Quadratic and the General Hermitian Groups and the Nilpotence of KH}_1. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 452 (2016), Voprosy Teorii Predstavleniĭ Algebr i Grupp. 30, 5--31; English translation in J. Math. Sci. (N.Y.) 232 (2018), no. 5, 591--609.
R. Basu; On Transvection Subgroups of General Quadratic Modules. Journal of Algebra and Its Application. Vol. 17, No. 11, 1850217 (2018).
R. Basu, Manish Kumar Singh; On Quillen--Suslin Theory for Classical Groups; Revisited over Graded Rings.Contemp. Math. Amer. Math. Soc., Vol. 751, 2020, 5-18.