Dr. Pranab Sardar
Associate Professor, Mathematical  Sciences

Research Focus

Gromov initiated a study of finitely generated infinite group as geometric objects in early 1980's. Out of many different, and deep aspects of this philosophy he has written an about two hundred page note on (Gromov) hyperbolic groups. My current area of interest is in hyperbolic groups and properties of subgroups of hyperbolic groups.

My PhD thesis was on a combination theorem of hyperbolic groups where we generalize earlier work of Mladen Bestvina and Mark Feighn. Bestvina and Feighn worked with a graph of hyperbolic groups and they provide sufficient conditions under which the fundamental group of the same is hyperbolic. I have generalized this result in a joint work with Mahan Mj to a complex of hyperbolic groups in some special cases. Recently, a joint work with M. Kapovich resulted in a new and more geometric proof of the theorem of Bestvina-Feighn.

On the other hand, based on some earlier work of Mahan Mitra among others and inspired by some questions of Chris Hruska and Dani Wise I got interested in bounded packing properties of subgroups of finitely generated groups.

*Algebraic groups and Invariant theory*: Before my Ph D, I did some work on algebraic groups and invariant theory jointly with S. Kannan and S. Pattanayak.

• Packing Subgroups in Solvable Groups. Pranab Sardar Int. J. Algebra Comput., Vol 25, No. 05, July 2015, p 917-926.

• A combination theorem for metric bundles. Pranab Sardar, Mahan Mj, Geometric and Functional Analysis, Dec 2012, Vol 22, Issue 6, pp 1636-1707.

• Projective normality of finite group quotients. Pranab Sardar, S. Kannan and S. Pattanayak, Proc. Amer. Math. Soc., Vol 137, No 3, March 2009, pp. 863-867

• Torus quotients of homogeneous spaces of the general linear group and the standard representation of certain symmetric groups. Pranab Sardar and S. Kannan, Proc. Indian Acad. Sci. (Math. Sci.) Vol 119, No 1, February 2009, pp. 81-100