Here is a list of ideas for projects I have in mind currently.
Quantum Information and Computation with applications to condensed matter
Differential Geometry and applications in holography
Quantum Information in Quantum Gravity
Connections between various notions of Quantum Computational Complexity
Quantum Mechanical Bootstrap
Non-hermitian quantum mechanics and holography
Arunima Das (NISER, Jatni) : Krylov Complexity in Heisenberg and Schrodinger Picture. It was reading project done during summer of 2023. (Presently a graduate student at Arizona State University, USA with Maulik Parikh).
Himanshu Sahu (IISc Bangalore) : Operator Growth in Open Quantum Systems. It started as a summer project and then we kept on working on the ideas we began thinking about, and published a few papers. (Presently a PhD student at the Perimeter Institute with Sisi Zhou).
Aneek Jana (IISc Bangalore) : Complexity for Scattering amplitudes. Started as a summer project. We are continuing our work on studying chaotic scattering amplitudes.
Maitri Ganguly (IISc Bangalore) : Krylov complexity for quench and con-mat