Visiting Researcher, University of Copenhagen, Denmark, December 01, 2020 to March 31, 2021.
Postdoctoral Fellow, University of Copenhagen, Denmark, October 1, 2019 to November 30, 2020.
Postdoctoral Fellow, Hebrew University of Jerusalem, Israel, July 15, 2018 to September 30, 2019.
Visiting Faculty, Chennai Mathematical Institute, Chennai, India, December 06, 2015 - July 12, 2018.
Visiting Scientist, Weizmann Institute of Science, Israel, May - June, 2017.
Visiting Fellow, Ecole Normale Suprieure de Lyon and University of Lyon 1, Lyon, France, April 21 - June 30, 2018.
Visiting scholar, Humboldt University, Berlin, Germany, September 2011 - May 2012.
SHORT-TERM ACADEMIC VISIT
University of Duisburg-Essen, Germany, June 16-30, 2019.
MSRI, Berkely, USA, April 08-12, 2019.
Tata Institute of Fundamental Reseach, Mumbai, September 11-14, 2015.
Harish-Chandra Reseach Institute, Allahabad, Nov 1-30, 2015.
TEACHING EXPERIENCES (AS AN INSTRUCTOR)
August - November, 2016, p-adic Analysis, Chennai Mathematical Institute (CMI), Chennai, India.
August - November, 2017, Arithmetic Geometry, CMI.
January - April, 2018, Algebraic Number Theory, CMI.
Research Interests
Converse Problem in the Galois side: In the automorphic side of Langlands program, there are converse theorems. But in the Galois side, we do not have any such theorems. Currently, I have been trying to give a converse theorem for local Galois representations.
Geometric Analog of epsilon factors: By work of Robert Langlands and P. Deligne we can attach a unique complex number (which we call epsilon factor) for a given complex Galois representation. We also can attach a similar constant for a given elliptic curve over number field. But the relationship between epsilon factors of Galois representations and elliptic curves are not yet known. An explicit connection between these epsilon factors are very much important in arithmetic geometry. I am trying to find a result which connect them.
Galois representations and Analytic torsion: I also have been trying to construct Galois representations by using analytic torsions for some Riemannian manifolds.
Awards & Fellowships
Postdoctoral Fellowship from the University of Copenhagen, Denmark, 2019.
Postdoctoral Fellowship from the Israel Science Foundation (grant no: 1676/17) at the Hebrew University of Jerusalem, Israel, 2018.
Postdoctoral Fellowship from the Chennai Mathematical Institute and the Infosys Foundation, India, 2015.
IMU-Berlin Einstein Foundation Fellowship for nine months in Berlin, Germany, 2011.
Received National Scholarship for the period: 2001-2006, Govt. of India.
Qualified in NET Examination held in December, 2007 and June, 2008 with CSIR Fellowship, Govt. of India.
Qualified in GATE, 2008, Govt. of India.
Postdoctoral Fellowship at Harish-Chandra Research Institute, Allahabad, India, 2016 (did not avail).
Postdoctoral Fellowship at Indian Statistical Institute, Bangalore, India, 2016 (did not avail).
International travel grant from DST and NBHM for attending workshop and conference in Italy, 2011.
Travel grant from the Ecole Normale Suprieure de Lyon, France, 2018.
700 USD nancial support from the MSRI, Berkeley, USA, 2019.
Travel grant from the University of Duisburg-Essen, Germany, 2019.
Travel support from the Berlin Mathematical School, Berlin, Germany, 2011.
