PhD thesis title: Iwasawa algebras for p-adic Lie groups and Galois groups.

Institution:    Département de Mathématiques de Orsay, Université Paris-Sud 11, Université Paris-Saclay (ComUE), France.

Defense date : 02 July 2018

Advisors: Prof. Laurent Clozel and Prof. Ariane Mézard 

                   Jury:   

• • • • 1. Prof. Laurent Clozel (Université Paris-Sud), Director

        2. Prof. Ariane Mézard (Sorbonne Université), Co-directrice

        3. Prof. Christophe Breuil (Université Paris-Sud), Examiner

        4. Prof. Gabriel Dospinescu (Ecole Normale Supérieure de Lyon), Examiner

        5. Prof. Christine Huyghe (Université de Strasbourg), Examiner

        6. Prof. Peter Schneider (Universität Münster), Reporter

                    Referees:      

              7. Prof. Ralph Greenberg (University of Washington, Seattle)

              8. Prof. Peter Schneider (Universität Münster)            

Web-link to download thesis:  You can download my PhD thesis here                           

Summary: Algebraic number fields are number systems which arose in this context, generalizing the familiar rational numbers, and Galois cohomology is a tool for studying them. Recent developments in the p-adic Langlands program allow us to revisit classical conjecture of Greenberg concerning "p-rational fields", which are algebraic number fields whose Galois cohomology is particularly simple and which are interesting because they offer ways of constructing Galois representations with big open images. A key tool in the study of algebraic number fields are Iwasawa algebras, originally constructed by Iwasawa in the 1960s to study the "class groups" of those fields, but since appearing in varied settings such as a Lazard’s work on p-adic Lie groups and Fontaine’s work on local Galois representations. In my PhD, I combine results from arithmetic geometry, Iwasawa Theory, and the theory of Galois representations to construct new families of p-rational fields. I give explicit constructions of Iwasawa algebras and propose a new computer algorithm for certifying a useful property of an algebraic number field when it holds, and also conduct numerical experiments using a computer algebra system (SAGE) which give heuristic support to Greenberg’s conjecture. I use this to go beyond Greenberg’s work and construct novel Galois representations with big open images in reductive groups.

Master degree:

(Sept 2013 – Aug 2015)                 ALGANT  master [double degree], I spent my first year (2013-2014) at Universita degli studi di Padova, Italy, and my second year (2014-2015) at Université Paris-Sud 11, Université Paris-Saclay (ComUE), Orsay, France. 

Master thesis:

Topic: On the Growth of Cohomology of Arithmetic Quotients of Symmetric Spaces. 

Advisor: Prof. Laurent Clozel (Département de Mathématiques de Orsay)

Weblink:  You can download my master's thesis here.

Bachelor degree:

(July 2010 – June 2013)         Bachelor in Math [Honours], Statistics and Mathematics Unit, Indian Statistical Institute, Bangalore, India. Mention: First Division with Distinction.

Secondary and Higher Secondary education

(July 2008 – June 2010) Higher  Secondary Examination 2010 [(10+2)th Standard]. Nava Nalanda, West Bengal Council of Higher Secondary Education, India.

(May 2006 – April 2008) Madhyamik Pariksha (Secondary Examination) 2008 [10th Standard]. Nava Nalanda, West Bengal Board of Secondary Education, India.