# Ajaykumar K

### Areas of Interest & Expertise

- Lie Algebra and Lie Group Bundles
- Generalisations of Lie Groups
- Mathematics Teacher Education

### Biography

Prior to joining the University, Ajaykumar taught for three years (2019 – 2022) at Chinmaya Vishwa Vidyapeeth, a deemed-to-be university at Ernakulam, Kerala. He is passionate about teaching undergraduates, especially the ones training to become teachers.

He obtained his doctoral degree in mathematics from the University of Mysore, Mysuru. During that period, he worked on geometric and algebraic properties of Lie algebra bundles and Lie group bundles and generalisation of Lie group bundles.

Currently, he is interested in problems concerning the book embedding of graphs. Apart from research in mathematics, he is also interested in the pedagogy of mathematics at both the school and university levels.

He is passionate about filmmaking, and during his free time, he writes for films. He loves playing cricket, volleyball, and table tennis.

### Courses

#### Explorations in Mathematics I

Taught through inquiry-based learning, this course, is an exploration of geometry and algebra motivated by questions of congruence of triangles, along with the nature and language of mathematics.

#### Differential Equations

Modelling systems described by functions and their derivatives

#### Calculus 2: Real Analysis

The second of three courses of calculus for your Mathematics Major.

#### Introduction to Mathematical Thinking 2

Two of a two-part introduction that introduces you to the foundations of mathematical thinking.

#### Publications

- Madhu, B., Kiranagi, B.S., Rangarajan, R., & Ajaykumar, K. (2021). Engel’s and Lie’s theorems for Lie algebra bundles.
*Advanced Studies in Contemporary Mathematics*,*31*(1), 99 – 106. https://jangjeonopen.or.kr/public/upload/1611956112-ascm31‑1 – 9.pdf - Ajaykumar, K., Kiranagi, B.S., & Rangarajan, R. (2020). Pullback of Lie algebra and Lie group bundles, and their homotopy invariance.
*Journal of Algebra and Related Topics*,*8*(1), 15 – 26. https://dx.doi.org/10.22124/jart.2020.13988.1156 - Ajaykumar, K., & Kiranagi, B.S. (2019). Connections on smooth Lie algebra bundles.
*Indian Journal of Pure and Applied Mathematics*,*50*(4), 891 – 901. https://doi.org/10.1007/s13226-019‑0362‑3 - Ajaykumar, K., & Kiranagi, B. S. (2019). Lie algebra bundles and a generalization of Lie group bundles.
*Proceedings of the Jangjeon Mathematical Society*,*22*(4), 529– 542. https://jangjeonopen.or.kr/public/upload/1573600828-pjms22‑4 – 3‑fin.pdf - Prasad, V. S. Bagewadi, C. S., & Ajaykumar, K. (2017). On submanifolds of codimension two and one of Kenmotsu manifolds.
*Indian Journal of Mathematics*,*59*(3), 409 – 423.