IAI

Research and Education

My research interests primarily include (non-) associative algebras, Rota-Baxter operators, Yang-Baxter equations, deformation theory, and Homotopy algebras. I am also interested in quantum groups, tensor categories, and the theory of operads.

I completed my M.Sc. (Mathematics) and Ph.D. from the Indian Institute of Technology Kanpur. I defended my thesis (‘Hom-Lie-Rinehart algebras’) on 2nd May 2019 under the supervision of Prof Ashis Mandal, Associate Professor, Dept of Mathematics and Statistics. 

After my Ph.D., I worked as a visiting scientist (one year) and NBHM Postdoc (one year and nine months) in the Stat-Math Unit, Indian Statistical Institute Bangalore Centre. During my Ph.D. and Postdoc, I have visited Jilin University, China and Malardalen University, Sweden, for research collaborations. 

Teaching Experience

• Tutor, Linear algebra, ISI Bangalore, 2021
• Tutor, Complex Analysis, IIT Kanpur, Summer 2018
• Tutor, MTH-102A: Mathematics-II, IIT Kanpur, Summer 2018
• Tutor, Algebra, Annual Foundation School – I, IIT Kanpur, 2018
• Teaching Assistant, MTH-102: Mathematics-II, IIT Kanpur, 2015, 2017
• Teaching Assistant, MTH-204: Algebra-I, IIT Kanpur, 2016
  
  

Publications

The following is the list of my publications:

1. A. Das, S. K. Mishra, and A. Naolekar: Noncommutative Differential Calculus Structure on Secondary Hochschild (co)homology,  To appear in Communications in Algebra.
   
   
2. S. K. Mishra, G. Mukherjee, and A. Naolekar: Cohomology and deformation of Filippov algebroids, Proceedings of the Indian Academy of Sciences – Mathematical Sciences, 132(2), 2022.   [Link]
   
   
3. A. Mandal and S. K. Mishra: Universal central extensions and non-abelian tensor product of Hom-Lie-Rinehart algebras, Colloquium Mathematicum, 166, 23–52, 2021.
   
   
4. S.K. Mishra and A. Naolekar: O-operators on Hom-Lie algebras, Journal of Mathematical Physics, 61, 121701 (19 pages), 2020.
   
   
5. J. Jiang, S.K. Mishra, and Y. Sheng: Hom-Lie algebras and Hom-Lie groups, integration and differentiation, Symmetry, Integrability, and Geometry: Methods and Applications, SIGMA 16, 137 (22 pages), 2020. 
   
   
6. A. Mandal and S. K. Mishra: Deformations of Courant Pairs and Poisson algebras, Journal of Algebra and Its Applications, In Press, DOI: 10.1142/S0219498821502297.
   
   
7. A. Madal and S. K. Mishra: Deformation of Hom-Lie-Rinehart algebras, Communications in Algebra, 48(4), 1653–1670, 2020. 
   
   
8. A. Mandal and S. K. Mishra: On Hom-Gerstenhaber algebras, and Hom-Lie algebroids, Journal of Geometry and Physics, 133, 287–302, 2018.
   
   
9. A. Mandal and S. K. Mishra: Hom-Lie-Rinehart algebras, Communications in Algebra, 46(9), 3722–3744, 2018.