Research
My research interests are in the calculus of variations and elasticity theory. In simple words, the calculus of variations is a subfield of analysis concerned with minimising (or maximising) functionals over infinite-dimensional spaces.
My PhD work, under the supervision of Tim Healey, focused on energy minimisation problems for nonlinearly elastic surfaces. Unlike linear elasticity, where deformations are ``small'', nonlinear elasticity deals with problems where deformations can be ``large'', and thus, more sophisticated tools from analysis and geometry are required to solve them. I am strongly motivated by this interplay of physics, analysis and geometry. To varying degrees, I use techniques from the direct method of the calculus of variations (i.e., issues of convexity and lower semicontinuity), geometric measure theory, degree theory and rigorous asymptotics (Γ-convergence) in my research.
Over the last few years, I have been fortunate to be involved in a number of projects outside of my thesis work. One of these in particular concerns the synchronisation of coupled nonlinear oscillators on large networks. With my collaborators we use techniques from analysis, probability 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.
Publications
- 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. Quarterly of Applied Mathematics[Journal] [arXiv]
- Lipton, M. & Nair, G.G. (2022). Stationary curves under the Möbius-Plateau energy. arXiv preprint [arXiv]
- Nagpal, S. V., Nair, G. G., Strogatz, S. H. & 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]