I work on problems in the calculus of variations and nonlinear PDEs. In simple words, the calculus of variations is a subfield of analysis concerned with extremising functionals over infinite-dimensional spaces. With my advisor, Tim Healey, I have been working on energy minimisation problems for nonlinearly elastic surfaces (with curvature and membrane elasticity). My work has a strong geometric flavour and usually involves techniques from the theory of harmonic maps and more recently, minimal surfaces.
In the past I have also been involved in projects related to statistical mechanics and nonlinear dynamics. One of these projects was on the dynamics of coupled oscillators (with applications to the power grid) and another was on fission-fusion behaviour of animal herds.
- Healey, T.J. & Nair, G.G. (2022). Energy Minimizing Configurations for Highly Deformable Single-Director Elastic Surfaces. Journal of Elasticity [Journal][arXiv]
- Nagpal, S. V., Nair, G. G., Parise, F., & Anderson, C. L. (2022). Designing for Robustness in Electric Grids via a General Effective Resistance Measure. IEEE Transcations on Control of Network Systems [Journal][arXiv]
- Lipton, M. & Nair, G.G. (2022). Stationary curves under the Möbius-Plateau energy. arXiv preprint [arXiv]
- Nair, G. G., Senthilnathan, A., Iyer, S. K., & Guttal, V. (2019). Fission-fusion dynamics and group-size-dependent composition in heterogeneous populations. Physical Review E. [Journal][arXiv]