Before mathematical physics, my undergraduate and Master's years at IIT Kanpur (B.Tech + M.Tech, Materials Science and Engineering, with minors in Quantum Mechanics, Statistical Physics, and Cognitive Science) were spent on a wide range of projects. Here are some of the ones I enjoyed most — click through to read the actual reports, surveys, and slides.
Materials Science
Spiral Eutectic Microstructures in Zn–Mg Alloys
Synthesized a Zn–Mg alloy at eutectic composition and imaged the self-organising spiral eutectic microstructure with optical and scanning electron microscopy, then used EDX to work out why and how the spirals formed.
Crystallographic Texture and Fatigue in Titanium
Used electron backscatter diffraction and fractography to study how crystallographic texture from cold working affects dwell-fatigue behaviour in commercially pure titanium.
Transparent Flexible Electrodes via the Crackle Technique
Fabricated a micron-thin metallic mesh network using the crackle technique, and proposed an Ag–Adenine 1D-polymer nanowire matrix as an electrode or hole-transport layer for large-area flexible electronics.
A Refractory High-Entropy Alloy for Spacecraft Applications
Characterised the phase structure and high-temperature mechanical properties of a novel MoNbTaWV refractory alloy made by vacuum hot pressing of ball-milled powders — a candidate for replacing ceramics in high-stress, high-temperature spacecraft components.
A Survey of Chip Manufacturing for Wearable Healthcare Devices
A term paper surveying fabrication techniques for smart wearable healthcare devices, written for a course on materials processing.
Biomaterials: Bacterial Adhesion on Implant Surfaces
A survey of how the adhesion force of Staphylococcus aureus varies across different biomaterial surfaces, written for a course on biomaterials.
Physics
Reproducing the Hofstadter Butterfly in Twisted Bilayer Graphene
Used the Bistritzer–Macdonald continuum model to find the zero modes of twisted bilayer graphene, and reproduced the Hofstadter butterfly pattern in its Landau-level spectrum under a magnetic field.
Correlation Energy of the 2D Electron Gas
Computed correlation energy for many-electron systems using Density Functional Theory, comparing analytic and numerical techniques against semi-analytic wavefunctions for the two-dimensional electron gas.
A Numerical Schrödinger Equation Solver
A small C and Python codebase for numerically solving the Schrödinger equation.
Mathematics
Gauge Theory and Knots
A semester-long seminar on the mathematical foundations of gauge theory in the theory of principal bundles with connection, and Witten's paper linking Chern–Simons theory to knot invariants.
CFT and Elliptic Cohomology
A talk for the course Introduction to Conformal Field Theory, looking for a physical explanation of Topological Modular Forms via boundary CFT.
Super-Symmetric QFT and Integral Modular Functions
A talk given to Jürgen Jost's research group at the Max Planck Institute for Mathematics in the Sciences, Leipzig, on why the partition function of a 2D minimally supersymmetric QFT is an integral modular function.
Functorial Properties of Discrete Morse Theory
A write-up on simplicial complexes and discrete Morse theory, examining how Morse-theoretic constructions behave functorially.
Constructing a 3,2-TQFT with Defects from a 3,2,1-TQFT
A write-up constructing, from a 3-2-1 TQFT, the vector spaces and linear maps of a 3-2 TQFT with defects on marked surfaces and embedded ribbon graphs.
Cognitive Science
Drift Diffusion Modelling of Social Decision-Making
Applied the Drift Diffusion Model to decision-making in a social context, exploring how social information shapes the speed and accuracy of individual choices.
Debate: Will Voltage-Sensitive Dyes Replace Electrophysiology?
Argued the case for voltage-sensitive dye imaging over traditional electrophysiology in neuroscience research, as part of a structured debate for the Neurobiology course.
The Neural Underpinnings of Mental Effort
A literature survey and research proposal on the quantitative and neural basis of mental effort.
Inductive Reasoning: A Survey
A survey of the cognitive science literature on inductive reasoning, written for a foundations of cognitive science course.
Reconsolidation of Memories
A literature review on memory reconsolidation — how retrieved memories become temporarily labile and can be updated before being re-stored.
How Peer Pressure Shapes Decision-Making in Adolescents
An experiment and literature review on how peer pressure and social perception influence decision-making in young adults.
Philosophical Investigations: Mathematical Approaches to Cognitive Science
An essay comparing different formal approaches to theorising cognition, written between physics courses.