Research Focus
My research interests include central simple algebras, quadratic forms, linear algebraic groups, word maps on groups.
Using algebraic techniques, I have proved that classical algebraic groups over many fields, for example number fields, have trivial R-equivalence class only. This study has consequences in the study of rationality properties of varieties of algebraic groups and certain norm principles for quadratic forms.
Isotropy of involutions of central simple algebras is another difficult question to answer in general. I have contributed by giving weak isotropy criterion for a class of central simple algebras. This uses the newly developed notions of gauges. I have also studied differential central simple algebras and their splitting fields.
Recently, I have started working on various aspects of word maps on groups, specifically the problems concerning the sizes of their images and fibres.
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Selected Publications
- Amit Kulshrestha and Kanika Singla, Finite splittings of differential matrix algebras, Journal of Algebra 634 (2023), no. 15, pp. 74-96.
- Amit Kulshrestha and Varadharaj R. Srinivasan, Quaternion algebras with derivations, Journal of Pure and Applied Algebra 226 (2022), no. 2, Paper No. 106805, 14 pp.
- Alexey Galt, Amit Kulshrestha, Anupam Singh, Evgeny Vdovin, On Shalev's conjecture for type An and 2An, Journal of Group Theory 22 (2019), pp. 713-728.
- Dilpreet Kaur and Amit Kulshrestha, Strongly real special 2-groups, Communications in Algebra 43 (2015), pp. 1176-1193.
- Amit Kulshrestha, Strongly anisotropic involutions on central simple algebras, Communications in Algebra 39 (2011), pp. 1686-1704.
- Amit Kulshrestha and Raman Parimala, R-equivalence in adjoint classical groups over fields of virtual cohomological dimension 2, Transactions of the American Mathematical Society 360 (2008), pp. 1193-1221.
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