Designation
Reader-F
Research Area
Functional Analysis
Education
- Ph.D., Indian Institute of Science (IISc), Bangalore, India, 2012.
- M.Sc., Banaras Hindu University (BHU), Varanasi, India, 2006.
- B.Sc., Banaras Hindu University (BHU), Varanasi, India, 2004.
Professional Experiences:
- Reader-F (Since July, 2019), National Institute of Science Education and Research (NISER), Bhubaneswar, India.
- Assistant Professor (December, 2016--June, 2019), National Institute of Science Education and Research (NISER), Bhubaneswar, India.
- Inspire Faculty (April, 2015--December, 2016), Indian Statistical Institute, Bangalore, India.
- Visiting Scientist (June, 2014--March, 2015), Indian Statistical Institute, Bangalore, India.
- Visiting Scholar (September, 2013--May, 2014), Texas A&M University, College Station, Texas, United States of America (USA).
- Research Associate (December, 2012-- August, 2013), Indian Institute of Science, Bangalore, India.
Research Interest
Cowen-Douglas Class of operators, Hilbert modules over function algebra and Dilation theory.
Awards
- Inspire faculty award by Department of Science and Technology (DST), 2014 (Session-II).
- National Board for Higher Mathematics (NBHM) Post Doctoral Fellowship, 2014.
- Indo-US The Virtual Institute for Mathematical and Statistical Sciences (VI- MSS) Research Fellowship during September 2013 to February 2014 .
- Council of Scientific and Industrial Research (CSIR) Junior Research Fellowship, 2007.
- National Board for Higher Mathematics (NBHM) Ph.D Scholarship, 2007.
- Indian Statistical Institute Research Fellowship, 2007.
- Placed 84th (All India Rank) in Graduate Aptitude Test in Engineering (GATE) in Mathematics, 2007.
- R.B Munsi Shiva Prasad Medal for standing first in Mathematics at the B.A. and B.Sc (Hons.) pt.III, 2004.
Publications
- Infinitely divisible metrics and curvature inequalities for operators in the Cowen-Douglas class, (jointly with Shibananda Biswas and Gadadhar Misra), J. Lond. Math. Soc. (2) 88 (2013), no. 3, 941–956.
- Trace Formulae for Curvature of Jet Bundles over Planar Domains, Complex Analysis and Operator Theory, Volume 8, No. 2, 2014, 1723-1740.
- Flag structure for operators in the CowenDouglas class, (jointly with Kui Ji, Chunlan Jiang and Gadadhar Misra), Comptes Rendus Mathematique, Volume 352, Issue 6, June 2014, Pages 511–514.
- Generalized bundle shift with application to Multiplication operator on the Bergman space (Jointly with Ron Douglas, Anjian Xu), J. Operator Theory 75 (2016), no. 1, 3–19.
- Rigidity of the flag structure for operators in the Cowen-Douglas Class, (jointly with Kui Ji, Chunlan Jiang and Gadadhar Misra), J. Func. Anal., 272 (2017), no. 7, 2899–2932.
- Dilations, wandering subspaces, and inner functions, (jointly with Monojit Bhattacharjee, Jörg Eschmeier and Jaydeb Sarkar), Linear Algebra Appl. 523 (2017), 263–280.
- q-Commuting dilation, (jointly with Nirupama Mallick), Proc. Amer. Math. Soc. 147 (2019), no. 2, 655–669.
Teaching
- M308- Complex Analysis (Even Semester-2017), NISER.
- M451- Advanced Complex Analysis (Odd Semester- 2017), NISER.
- M308- Complex Analysis (Even Semester-2018), NISER.
- M306- Calculus of Several Variable (Odd Semester-2018), NISER.
- M659- Topology and Complex Analysis (Ph.D., Odd Semester-2018), NISER ( Taught jointly with Panchugopal Bikram).
- M310- Geometry of Curves and Surfaces (Even Semester-2019), NISER .
- M306- Calculus of Several Variable (Odd Semester-2019), NISER.
- M607- Complex Analysis (Ph.D., Even Semester-2020), NISER.
- M466-Measure Theory (Odd Semester-2020), NISER.
- M310- Geometry of Curves and Surfaces (Even Semester-2021), NISER
- M607- Complex Analysis (Ph.D., Odd Semester-2021), NISER.
- M603- Analysis I (Ph.D., Even Semester-2022), NISER (Going to teach).
Preprints
1. Geometric Similarity invariants of Cowen-Douglas Operators (jointly with Kui Ji and Chunlan Jiang) [https://arxiv.org/abs/1901.03993]
Responsibility
- Organizer: Stat-Math, Symposium by Doctoral and Post-doctoral Fellows, Indian Statistical Institute, Bangalore, August 06-07, 2015.
- Organizer (jointly with Soumen Dey): Stat-Math, Symposium by Doctoral and Post-doctoral Fellows, Indian Statistical Institute, Bangalore, August 04-05, 2016.
- Member of phd interview committee, SMS NISER ( May 17-18, 2017)
- Member of phd interview committee, SMS NISER (December, 2017)
- Member of phd interview committee, SMS NISER (May 23-24, 2018)
- Member, UGCS, SMS NISER(24.09.2018- 31.12.2020)
- Member of phd interview committee, SMS NISER ( May 27-29, 2019)
- PDF Convener, SMS NISER (August, 2019- September 2021)
- Member, PGCS, SMS NISER (01.01.2021- )
- Member of Doctoral Committee for Amit Kumar
- Member of Doctoral Committee for Atibur Rahaman
- Member of Doctoral Committee for Rajeeb Ranjan Mohanta
- Member of Doctoral Committee for Diptesh Kumar Saha
- Member of Doctoral Committee for Suman Mukherjee
Academic Presentations
- Relation between real and complex differentiable functions, Department of Mathematics, Science & Technology, Mahatma Gandhi Kashi Vidyapith, Varanasi, January 28, 2021.
- Similarity invariants of Cowen-Douglas class of operators, National Institute of Science Education and Research (NISER), P.O. Jatni, Khurda , Odisha, India, January 10, 2020.
- Similarity invariants of a subclass of Cowen-Douglas class of operators, Hilbert Modules in Analytic Function Space Workshop, TSIM, Sanya, China, December 31 , 2019.
- Unitary and Similarity invariants of a subclass of Cowen-Douglas class of operators, Symposium on Operator Theory, IISc Bangalore, India, February 20, 2019.
- A series of lectures on Complex Analysis in The Summer Outreach Program in Mathematics (SOPM 2018), at NISER, Bhubaneswar , India, June 25-30, 2018.
- Rigidity of the flag structure for a class of Cowen-Douglas operators, Multivariable Operator Theory, Technion – Israel Institute of Technology, Haifa, Israel, June 22, 2017.
- Rigidity flag structure for operators in the Cowen-Douglas Class, Hilbert Modules in Analytic Function Space Workshop, TSIM, Sanya, China, 25 May, 2017.
- A Subclass of the Cowen-Douglas class of operators with a complete computable set of invariants Stat- Math, Symposium by Doctoral and Post-doctoral Fellows, Indian Statistical Institute, Bangalore, India, 04 August , 2016.
- On the Wandering Subspace Property of a C·,0 contraction operator, Stat-Math, Symposium by Doctoral and Post-doctoral Fellows, Indian Statistical Institute, Bangalore, India, 06 August , 2015.
- Rigidity of the flag structure for operators in the Cowen-Douglas class, Stat-Math, Symposium by Doctoral and Post-doctoral Fellows, Indian Statistical Institute, Bangalore, India, 17 July , 2014.
- Flag structure for operators in the Cowen-Douglas Class, Analysis Seminar, Department of Mathematics, University of Houston , Houston, USA, 07 March 2014.
- Jet Bundles over an open subset of complex plane, In-House symposium of the Department of Mathematics, Indian Institute of Science, Bangalore, India, 09 February 2012.
Academic Visits
Conferences/Schools/Workshops Attende
- Conference on Noncommutative geometry and its applications, National Institute of Science Education and Research (NISER), P.O. Jatni, Khurda 752050, Odisha, India, January 06-10, 2020.
- Hilber Modules in Analytic Functions Space Workshop, Tsinghua Sanya International Mathematics Forum (TSIM), No. 100 Tsinghua Road, Tianya District, Sanya, Hainan, China, December 30, 2019 to January 3, 2020.
- Symposium on Operator Theory, IISc Bangalore, India, February 20-22, 2019.
- Conference on Quantum Groups and Noncommutative Geometry, National Institute of Science Education and Research (NISER), P.O. Jatni, Khurda 752050, Odisha, India, January 15-19, 2018.
- Multivariable Operator Theory Workshop, Technion – Israel Institute of Technology, Haifa, Israel, June 18-22, 2017.
- Hilber Modules in Analytic Functions Space Workshop, Tsinghua Sanya International Mathematics Forum (TSIM), No. 100 Tsinghua Road, Tianya District, Sanya, Hainan, China, May 22-26, 2017.
- Recent Advances in Operator Theory and Operator Algebras, Indian Statistical Institute, Bangalore, India, December 13, 2016 - December 22, 2016.
- TSSRK Fest, Indian Statistical Institute, Bangalore, India, September 22, 2016 - September 24, 2016.
- Complex Geometry and Operator Theory, Indian Statistical Institute, Bangalore, India, December 01, 2015 - December 03, 2015.
- Recent advances in Operator Theory and Operator Algebras, Indian Statistical Institute, Bangalore, India, December 09, 2014 - December 19, 2014.
- Noncommutative Geometry Festival, Texas A&M University, College station, Texas, USA, April 30, 2014 - May 03, 2014.
- Almora Mathematical Surveys, Kumaun University, Almora (Uttarakhand), India, October 03, 2012 - October 06, 2012.
- Workshop on the functional of quantum Information Theory, The institute of mathematical Sciences, Chennai, India, December 26, 2011 - January 06, 2012.
- International Congress of Mathematicians, Hyderabad, India, August 19, 2010 - August 27, 2010.
- Satellite Conference on Functional Analysis and Operator Theory, Indian Statical Institute, Bangalore, India, August 08, 2010 - August 11, 2010.
- ATM Workshop on Several Complex Variables and Complex Dynamics, IISc, Bangalore, India, March 01, 2010 - March 13, 2010.
- Advanced Instructional School on Operator Theory, Institute of Mathematics and Applications Bhubaneswar, India, December 07, 2009 - December 12, 2009.
- Conference in Analysis and its Applications, IISc, Bangalore, India, May 27, 2009 - May 30, 2009.
- Workshop in Analysis and its Applications, IISc, Bangalore, India, May 14, 2009 - May 23, 2009.
- The IISc Centenary Conference, IIsc, Bangalore, India, December 13, 2008 - December 16, 2008.
- Workshop in Harmonic Analysis and PDE, IISc, Bangalore, India, December 05, 2008 - December 13, 2008.
- Advanced Instructional School on complex Analysis, Bhaskaracharya Pratishthana, Pune, India, June 05, 2008 - July 02, 2008.
- Visiting Student Research Programme (VSRP), TIFR, Mumbai, India, June 15, 2006 - July 14, 2006.
- Visiting Student Summer Programme (VSSP), HRI, Allahabad, India, June 07, 2005 - June 28, 2005.
Institutes Visited
- Indian Institute of Technology Bhilai, India ( February 28, 2020 to March 08, 2020).
- Indian Institute of Science, Bangalore, India (February 18, 2019 to March 3, 2019) .
- Hebei Normal University, Shijiazhuang, Hebei, China (December 8, 2018 to January 6, 2019).
- Indian Institute of Science Education and Research Kolkata, India (December 18-25, 2017).
Sponsored Projects
- Unitary, similarity invariants and curvature inequalities for operators in the Cowen-Douglas class (MTR/2019/000319), Funding Agency: Department of Science and Technology, Govt. of India, Duration: February 19, 2020- February 18, 2023.