Department of
Mathematics

Supriya Pisolkar obtained her PhD from Harish-Chandra Research Institute, Allahabad, India. She was at Tata Institute of Fundamental Research, Mumbai for her postdoctoral research. Immediately after that, she joined IISER Pune in 2014 as a Assistant professor. Dr. Supriya Pisolkar's area of research (broadly speaking) is Number theory. Following are specific topics that Dr. Pisolkar works in: Local fields, Galois groups and Galois cohomology; Ring of Witt vectors of an associative rings (based on the work of Lars Hesselholt); and Arithmetic aspects of locally symmetric spaces (based on the work of Gopal Prasad and Andrei Rapinchuk).

Research

Number theory

Dr. Supriya Pisolkar works on more than one aspect of number theory. In the theory of Witt vectors, it is very intriguing that there are various constructions of group of Witt vectors over associative rings. These constructions are all isomorphic for a commutative ring, but not much is known in the case of non-commutative rings. Dr. Pisolkar is looking at comparison of some aspects of these constructions in the non-commutative set up.

In the area of Galois cohomology, Dr. Pisolkar works on connections of Fontaine Mazur conjectures to analytic pro-p groups. The interesting part is to analyse by using Galois cohomology techniques, which pro-p groups can occur as Galois groups.

In the past, Dr. Pisolkar has worked on arithmetic aspects of locally symmetric spaces (based on the work of Gopal Prasad and Rapinchuk) , especially the commensurability type questions. This is a beautiful amalgamation of theory of Lie groups and Number theory. She has also worked on problems in arithmetic geometry, in particular computation of Chow groups of Chatelet surfaces, by using class field theory.

Selected Publications

Morphisms between two constructions of Witt vectors of associative rings. Proc. Amer. Math. Soc. 148, (2020), no. 7, 2835–2842.

On comparison of two constructions ring of Witt vectors. (With A. Hogadi) J. Algebra. 506 (2018), 379–396.

On the splitting fields of generic elements in Zariski dense subgroups. (with C. S. Rajan) J. Algebra. 457 (2016), 106–128.

On uniform lattices in real semisimple groups.(with C. Bhagwat) Proc. Amer. Math. Soc. 144, (2016), no. 7, 3151–3156.

Commensurability and representation equivalent arithmetic lattices. - (with C. Bhagwat and C. S. Rajan) Int. Math. Res. Not. (2014), no.8, 2017–2036.

Equi-characteristic analogue of Hesselholt’s conjecture on cohomology of ring of Witt vectors. (with A. Hogadi) Acta Arithmetica 158 (2013), no. 2, 165–171.

On the cohomology of Witt vectors of p-adic integers and a conjecture of Hes- selholt.(with A. Hogadi) J. Number Theory 131 (2011), no. 10, 1797–1807.

Journal de Th ́eorie des Nombres de Bordeaux 21 (2009), no.3, 733–740.

The Chow group of zero-cycles on certain Chˆatelet surfaces over local fields Indag. Math. (N.S.) 19 (2008), no. 3, 427–439.