Dinesh Kumar Keshari

Submitted by dinesh on 5 January, 2017 - 10:25

Designation:

Reader-F

Research Area:

Functional Analysis

Education:

Ph.D., Indian Institute of Science (IISc), Bangalore, India
M.Sc., Banaras Hindu University (BHU), Varanasi, India
B.Sc., Banaras Hindu University (BHU), Varanasi, India

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.

Preprints:

1. Geometric Similarity invariants of Cowen-Douglas Operators (jointly with Kui Ji and Chunlan Jiang) [https://arxiv.org/abs/1901.03993]

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

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- )
Member, PGCS, SMS NISER (01.01.2021- )
Member of Doctoral Committee for Amit Kumar
Member of Doctoral Committee for Rajeeb Ranjan Mohanta
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).

School of Mathematical Sciences

Faculty