Education

• Ph.D. (University of Hyderabad)
• M.Phil. (University of Hyderabad)
• M.Sc. (University of Kerala)

Experience

Taught two semesters at Department of Mathematics, University of Hyderabad and Thirteen years at the Department of Mathematics, University of Calicut for the M.Sc and M.Phil courses.

Research Experience:

• Worked in a DAE project on Geometry of Complex Tori at University of Hyderabad. Visited TIFR Mumbai.
• Research Associate (UGC) at University of Hyderabad.
• Guided Three M.Phil dissertations and two Ph D thesis.

Research Work / Area

Differential Geometry and Applications.

 
Journal Publications

• (with M Sitaramayya) Picard bundles as Subbundles - Journal of Indian Mathematical Society vol.62, no.1, 1995.
• (with M Sitaramayya) Flat GL(2,C)-bundles over compact Kaehler manifolds - Journal of the Ramanujan Mathematical Society  vol.11, no.2, Dec 1996.
• (with M Sitaramayya) Differential Geometric Uniformization Theorems for Complex Manifolds – The Aligarh Bulletin of Mathematics, vol 20 No.1 (2001) 21-94.
• (with Fazeela K) Division Property of the Momentum Map - An. St. Univ. Ovidus Constants, Vol 15(2), 29-34, 2007.
• (with Fazeela K) Momentum maps on symplectic manifolds-I–Proc. of A.P. Akad. of Sciences, volume14,  part2, 47-68, 2012. (Special issue on the eve of National Mathematics Year. Guest Editor: Prof. V. Kannan, University of Hyderabad)
• (with Harsha K V) F-geometry and Amari’s α-geometry on a Statistical Manifold. Entropy, 16(5): 2472-2487, 2014.
• (with Harsha K V) Dually Flat Geometries of the Deformed Exponential Family. Physica A: Statistical Mechanics and its Applications, 433: 136-147, 2015.
• (with Harsha K V) A dually Flat Geometry of the Manifold of F-escort Probability Distributions,  Journal of Combinatorics, Information and System Sciences, 40, 1-12, 2015.
• (with Fazeela K) Momentum maps on symplectic manifolds-II – Bulletin of Allahabad Mathematical Society, vol 30, part I, 1-28, 2015.
• (with Harsha K V) Hessian Structures and (F,G)-geometry on a Deformed Exponential Family, Lecture Note in Computer Science (LNCS), 9389, 213-221, 2015, Springer.
• (with M. Sitaramayya and Harsha K V) Generalized Geometric Structures on Statistical manifolds”, Ganita, 65, 19-44, 2016.
• (with M. Sitaramayya and N.  Hasan) Differential Analytic aspects of statistical models, Ganita, 67(1), 1-31, 2017.
• (with Nandakumar M) Rank one critical points of the momentum maps of Integrable Hamiltonian systems with two degrees of freedom, Bulletin of Kerala Mathematics Association, vol.15, No. 2,2018.
• (with M. Sitaramayya)Geometry of an infinite dimensional Lie group and applications, Ganita, 68(3), 5-32,  2018
• (with Mahesh T V)Submanifolds of Exponential Families - Global Journal of Advanced Research on Classical and Modern Geometries ISSN: 2284-5569, Vol.9, (2019), Issue 1, pp.18-25.
• (with Mahesh T V)Minimal statistical immersions of statistical manifolds- accepted in Ganita.

Conference Papers

• Subvarieties of Jacobi and Picard varieties - Presented in the 60th Indian Mathematical Society conference held in Dec 1994. 
• Some applications of implicit function theorem - Proc. of the National seminar on analysis and applications, March99, UC College, Kerala, India.
• Universality of Mathematics – Proc. of the Annual meeting of Kerala Mathematical association, Jan 2000.
• On Harmonic maps of Riemann Surfaces - Presented at the International Conference on Geometry, Analysis and Applications, August 21-24, 2000, BHU, Varanasi, India.
• On Tangent Vectors, Proc. of the UGC sponsored National Seminar on Recent Developments in Mathematical Applications, Feb 2002, Sri. G V G V College.
• Lagrangian Submanifolds of Cn – Presented at the National conference at Govt. Victoria College, Palakkad, Kerala, India 12-02-2005.
• Hamiltonian Mechanics and Geometry – Proc. of the National Conference at Sree Kerala Varma College, Thrissur, 2006.
• On Existence of Standard Momentum maps – presented at the International conference of FIM, IIT Madras, 2007.  
• Levi-Civita Connection and Energy Functional –Proceedings of the “International Conference on PDE, Geometry and Number theory”, University of Calicut, August 2010.
• The Four Vertex Theorem, Proc. of the UGC sponsored National Seminar on Analysis and Its Applications, Dec 2011, M G University.
• The Jordan Curve Theorem- Geometric Approach, Proc. of the UGC sponsored National Seminar on Topology and Geometry, Jan 2012, NAM College.
• Information Geometry and its Applications, presented in the Indian Women and Mathematics held at IISER, Pune during July 26th-28th, 2013.
• Methods of Least Squares and its Geometry, In Proceedings of the International Conference on Mathematics Education and Mathematics in Engineering and Technology (ICMET’13), MCET Trivandrum, 91-95, 2013.
• Geometry of F-likelihood Estimators and F-Max-Ent Theorem, In AIP Conference Proceedings on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, 1641, 263-270, 2015.
• Estimation in a deformed exponential family, Information geometry and its applications IV, Liblice, Czech Republic, June 12-16, 2016.
• Mismatched Estimation in an Exponential Family, Information geometry and its applications IV, Liblice, Czech Republic, June 12-16, 2016.
• Information Geometry - Geometry of Exponential Family, International Conference on Differential Geometry, Algebra and Analysis, JMI (Central University), New Delhi, Nov 15-17, 2016.
• Minimal statistical immersions of statistical manifolds,67th Annual Conference of Bharat Ganita Parishad Conference on Modern Analysis & Applications – An International Meet, Babu Banarasi Das University, Lucknow, 16-17 November, 2019.