KOCHI:
Dr. A.A. Ambily , Asst. Professor, Department of Mathematics, Cochin University of Science and Technology has bagged the Kerala State Young Scientist Award 2020, for her valuable contribution to ‘classical algebraic K-theory’ in study of the structure of orthogonal groups and its subgroup, known as the Dickson-Siegel-Eichler-Roy(DSER) elementary orthogonal group.
To study the DSER group structure, she developed the commutator calculus, which is crucial for any classical groups. In joint work with Ravi A Rao, she proved the quadratic version of the Bass-Quillen conjecture under some conditions on the hyperbolic rank of the quadratic space. Moreover, they obtained the analogue of Quillen’s local-global principle.She studied the normal subgroup structure of the orthogonal group.
Under the conditions on the hyperbolic rank of the quadratic space, she proved normality and stability results for the DSER elementary orthogonal group. In joint work with Ravi A Rao, she proved that the DSER elementary orthogonal group is a normal subgroup of the orthogonal group.She compared the DSER elementary orthogonal group with the existing generalizations of the classical groups and found a unified approach to study these groups.Her work promises to unify the study of various orthogonal groups due to Anthony Bak, Guoping Tang, Viktor Petrov and Amit Roy’s DSER groups.
Dr. Ambily has also made contributions in the emerging area ‘Leavitt path Algebras’. These structures are related to the combinatorial object ‘Graph’. This subject has applications in symbolic dynamics.
