Professor
Department of Mathematical Sciences
📍 AB2 1F7
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Research Area
Algebra : central simple algebras and related structures, word maps on groups
Research Interests
My research interests include central simple algebras, quadratic forms, linear algebraic groups, and word maps on groups.
I have worked on the problem of R-equivalence in adjoint classical groups over fields of virtual cohomological dimension of 2. I have investigated power maps on reductive groups over finite fields. My work on central simple algebras includes study of the weak isotropy of involutions, using the concept of gauges. I have also explored differential central simple algebras and their splitting fields.
Recently, my research has expanded to encompass various aspects of word maps on groups, with a particular focus on the problems concerning the sizes of their images and fibers.
Since 2021 : Member, Board of Studies for Five Year Integrated Program, Punjabi University, Patiala.
Since 2022 : Member of the Vision Group, Pushpa Gujral Science City, Kapurthala.
2007 - 2008 : Visiting Scientist, Indian Statistical Institute, Bangalore/Delhi
2005 - 2007 : Postdoctoral fellow, University catholique de Louvain, Belgium
1999 - 2005 : PhD, Tata Institute of Fundamental Research, Mumbai
Best Teacher Award 2014 as a recognition for the outstanding teaching contributions at IISER Mohali.
TIFR Alumni Association Fellowship during 2002-05.
President's Medal for securing highest marks in the university in all undergraduate classes, and Director’s Medal for securing first rank in undergraduate mathematics honours class.
Amit Kulshrestha and Kanika Singla. Finite splittings of differential matrix algebras. Journal of Algebra 634:74–96, 2023. Amit Kulshrestha and Varadharaj R Srinivasan. Quaternion algebras with derivations. Journal of Pure and Applied Algebra 226(2):106805, 2022. Alexey Galt, Amit Kulshrestha, Anupam Singh and Evgeny Vdovin. On Shalev's conjecture for type $A_n$ and $^2A_n$. Journal of Group Theory 22(4):713–728, 2019. Dilpreet Kaur and Amit Kulshrestha. Strongly real special 2-groups. Communications in Algebra 43(3):1176–1193, 2015. Amit Kulshrestha. Strongly anisotropic involutions on central simple algebras. Communications in Algebra 39(5):1686–1704, 2011. Amit Kulshrestha and R Parimala. R-equivalence in adjoint classical groups over fields of virtual cohomological dimension 2. Transactions of the American Mathematical Society 360(3):1193–1221, 2008.