I work on problems in the calculus of variations and nonlinear elasticity. 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 finite membrane elasticity). My work has a strong geometric flavour and usually involves techniques from the theory of harmonic maps and more recently, minimal surfaces.
I have also been involved in projects on coupled oscillations and synchronisation on networks. With my collaborators we use techniques from analysis and optimisation to prove synchronisation and robustness results for systems of coupled oscillators. In the past (as an undergraduate), I also worked on problems related to collective dynamics and active matter.
- Healey, T.J. & Nair, G.G. (2022). Energy Minimizing Configurations for Highly Deformable Single-Director Elastic Surfaces. Journal of Elasticity [Journal][arXiv]
- Healey, T.J. & Nair, G.G. (2023). Nonlinearly Elastic Maps: Energy Minimizing Configurations of Membranes on Prescribed Surfaces. arXiv preprint [arXiv]
- Lipton, M. & Nair, G.G. (2022). Stationary curves under the Möbius-Plateau energy. arXiv preprint [arXiv]
- Nagpal, S. V., Nair, G. G., & Parise, F. (2023). Dynamics and Synchronization in Random Networks of Coupled Phase-Oscillators: A Graphon Approach. (working manuscript)
- 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]
- 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]