Amit Kulshrestha

PIC

Subject Area: Central Simple Algebras and related structures

Background and Research Interests

My research interests lie in the theory of Central Simple Algebras and related structures such as Quadratic Forms and Algebraic Groups. Currently I am engaged in investing the connections between strong reality and total orthogonality of groups using quadratic forms over fields of characteristic 2.

After joining IISER Mohali I became interested in understanding the simple components and involutions arising from group algebra of real groups with canonical involution. In this direction using quadratic forms over characteristic 2 fields, we have studied strongly real special 2-groups. We have produced a large class of groups which are strongly real and not totally orthogonal, and vice versa. In literature, these are the only known examples of such groups.

Recently in collaboration with Varadharaj Srinivasan I have started working on Differential Central Simple Algebras. The plan is to explore the field extensions which split Differential Crossed Product Algebras.

I am also interested in the pedagogy of mathematics and developing mathematical demonstrations for school children.

Select Publications

  1. (with D. Kaur), Strongly real special 2-groups, Comm. Algebra (to appear).
  2. (with A. Singh), Real elements and Schur indices of a group, Math. Student 80 (2011) pp73-84.
  3. Strongly anisotropic involutions on central simple algebras, Comm. Algebra 39 (2011) pp1686-1704.
  4. (with R. Parimala), R-equivalence in adjoint classical groups over fields of virtual cohomological dimension 2, Trans. Amer. Math. Soc. 360 (2008) pp 1193-1221.