# Projects

You can also see this list on my CV.

##### List of projects and reports

- Quantum covariant bit threads (Oct 2023-Present)
- Sparse Double-Scaled SYK (Oct 2023-Present)
- Holographic description of M-theory (Nov-Dec 2023)
- AdS/CFT correspondence and the information paradox (Aug-Nov 2022)
- Quantum Raychaudhuri Equation and its applications to cosmology (May-July 2022)
- Black hole information paradox (June-November 2021)
- Higgs mechanism (April 2022)
- Category theory applications in physics (October-November 2020)
- One-dimensional photonic bound states in the continuum (March-April 2021)
- Covid-19:analysis of a modified SEIR model (October-November 2020)

##### Quantum covariant bit threads (Oct 2023-Present)

*Supervisor: Prof. Matthew Headrick, Dept. of Physics, Brandeis University*

- Studied several papers about the bit thread formulation of holographic entanglement entropy, especially ”Quantum bit threads” (2105.08072) and ”Covariant bit threads” (2208.10507)
- Proposed a definition for ”Quantum covariant bit threads” that unifies the quantum static version 2105.08072 with the classical covariant version 2208.10507 and showed that it has the expected properties.
- Currently trying to prove that this definition is equivalent to the Quantum Extremal Surface (QES) prescription.

##### Sparse Double-Scaled SYK (Oct 2023-Present)

*Supervisor: Prof. Brian Swingle, Dept. of Physics, Brandeis University*

- Studied the chord diagram technique that can be used to solve Double Scaled SYK at all energy scales and $\lambda$.
- Studied the sparse version of SYK.
- Currently working on sparsifying the Double Scaled SYK. We are developing hyperchord diagram technique for calculating next-order corrections to sparse DSSYK, and I am also working on sparsifying ${\mathcal N} = 1$ and ${\mathcal N} = 2$ supersymmetric DSSYK.

##### Holographic description of M-theory (Nov-Dec 2023)

*Supervisor: Prof. Daniel Jafferis, Dept. of Physics, Harvard University*

- Studied the duality between $AdS_{4}\times S^{7}/\mathbb{Z}_{k}$ M-theory and the $\mathcal N = 6$ $U(N)_k \times U(N)_{-k}$ super Chern–Simons theory (ABJM CFT).
- Gave a presentation focusing on the M2-brane construction and obtaining the gravity dual.

##### AdS/CFT correspondence and the information paradox (Aug-Nov 2022)

*Supervisor: Prof. Pichai Ramadevi, Dept. of Physics, IIT Bombay*

- Studied the AdS/CFT correspondence (with a focus on black hole thermodynamics) from a textbook by Năstase.
- Studied several review articles related to the holographic entanglement entropy.
- Read recent papers on the resolution of the information paradox using the Island prescription.
- After reading recent papers on islands in de Sitter spacetimes, started working on a related research problem.
##### Quantum Raychaudhuri Equation and its applications to cosmology (May-July 2022)

*Supervisor: Prof. Saurya Das, Dept. of Physics and Astronomy, University of Lethbridge, Canada*

- Studied a semi-classical gravity theory obtained by replacing classical geodesics in the Raychaudhuri equation with Bohmian trajectories.
- Studied a cosmological model within this theory where both dark matter and dark energy are unified into a dark Bose-Einstein condensate.
- Implemented a special case of this theory in CLASS and estimated the cosmological parameters by doing Monte Carlo sampling in Cobaya using Planck 2018 data.

##### Black hole information paradox (June-November 2021)

*Supervisor: Prof. Vikram Rentala, Dept. of Physics, IIT Bombay*

- Studied quantum scalar field theory in curved spacetime and how it compares with QFT in ﬂat spacetime.
- Reviewed the four laws of black hole mechanics and their similarity with thermodynamics and Penrose process in a Kerr black hole.
- Studied
**Unruh effect**which explains that the vacuum state of a Minkowski observer will be a thermal state as observed by a Rindler observer and how entanglement between the left and right Rindler wedges prevents a firewall at the Rindler horizon. - Studied
**Hawking radiation**and the conditions under which a black hole can be in stable or unstable equilibrium. - Assuming that the evaporation is unitary, studied the characteristics of
**Page curve**using the**Page theorem**.

View PDF

##### Higgs mechanism (April 2022)

*Supervisor: Prof. Urjit Yajnik, Dept. of Physics, IIT Bombay*

- Studied how abelian and non-abelian gauge bosons can become massive using spontaneous symmetry breaking.
- Studied how the theory is renormalizable even after gauge bosons acquire mass through Higgs mechanism using $R_\xi$ gauges.

##### Category theory applications in physics (October-November 2020)

*Supervisor: Prof. Vikram Rentala, Dept. of Physics, IIT Bombay*

- Studied basic concepts of category theory like Functors, Natural transformations, Monoidal categories.
- Studied axiomatization of physical systems using strict monoidal categories. \item Investigated
**FdHilb**category and studied**no-cloning, no-deleting theorems**in categorical quantum mechanics.

View PDF

##### One-dimensional photonic bound states in the continuum (March-April 2021)

*Supervisor: Prof. Anshuman Kumar, Dept. of Physics, IIT Bombay*

- Studied bound states in the continuum (BICs) which emerge due to precise destructive interference of waves for an electron in a one-dimensional quantum well under an external magnetic field.
- Using the correspondence between the spin states of the above electron model and the polarisation states of an one dimensional photonic system made up of an anisotropic layer conjugated with a 1D photonic crystals consisting of alternating layers, found BICs for the photonic system.
- Calculated numerical values and generated graphs of several quantities such as transmittance, reflectance, Q factor, wave function using python for both the electron model and the photonic model.

GitHub

##### Covid-19:analysis of a modified SEIR model (October-November 2020)

*Supervisor: Prof. Amitabha Nandi, Dept. of Physics, IIT Bombay*

- Studied the normal Susceptible-Exposed-Infected-Recovered (SEIR) model. Later used a modified model to incorporates the fact that asymptomatic or mildly symptomatic individuals play a significant role in the transmission of Covid-19.
- Generated different projections for India under different intervention parameters.
- By varying intervention parameters in the modified model we concluded that testing-quarantining is more efficient in controlling the pandemic than lockdowns.

GitHub