Cosmology and Dark Matter
Summer of Science, Maths and Physics Club, IITB
I studied special relativity, with emphasis on its tensorial analysis, the mathematical foundations of general relativity, Einstein tensors, Bianchi identities and the field equations from A First Course in General Relativity by Bernard Schutz. In addition, I studied applications of general relativity such as the production and detection of gravitational waves, Schwarzschild and Kerr Blackholes and the metric around relativistic stars.
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The report is here
Algebraic Topology
Summer of Science, Maths and Physics Club, IITB
I studied Abstract Algebra by Dummit & Foote for an introduction to groups, subgroups, quotient groups and group actions. I then applied the group-theoretic structure to the study of topological spaces, specifically to understand Fundamental Groups, Separation theorems and Seifert-van Kampen theorem from Topology by Munkres.
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The report can be found here
Simultaing Kirkwood Gaps
Krittika Summer Projects, Astronomy Club, IITB
I facilitated the implementation of a Monte Carlo simulation to evolve large distributions of asteroids over millions of years around the sun. I also simulated the emergence of Kirkwood gaps in the asteroid belt along with features like the Jupiter Trojans. I also studied the general n-body problem and its numerical solutions using exactly conservative integrators.
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Our report (in progress) is here
Star Hopping Guide
Krittika Summer Projects, Astronomy Club, IITB
I facilitated a group of 7 students ranging from UG freshmen to PhD to develop a portal to aid DSO observation, and created a star hopping mechanism for 104 Messier Objects to aid the process of finding them in the sky. I also coordinated with 4 subgroups working on databases, data plotting, user and editor interfaces and hopping mechanisms, and helped them integrate their work into one finalized portal.
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Our report (in progress) is here
HR Diagrams
Krittika Winter Projects, Astronomy Club, IITB
I studied the details of stellar evolution and interiors of stars from an Introduction to Modern Astrophysics by Carroll and Ostlie. I then plotted the relevant HR Diagrams for multiple globular clusters such as NGC-0104, NGC-2808 and NGC-5272 using Numpy, and Matplotlib. I also implemented manual Isochrone Fitting and Main Sequence Matching to find the ages and relative distances to these globular clusters.