Here is a collection of some expository articles/presentation slides that I wrote/made for various reasons. If you find any errors they are entirely due to me.
Expository Articles
- Homework exercises for the course MA310:Algebraic Geometry at IISc Bangalore. (Winter 2023) (pdf)
- "Pontryagin Duality" for the course MA220: Representation Theory of Finite groups at IISc Bangalore. (Fall 2022) (pdf)
- "Homological Dimension" for the course MTH613: Rings and Modules at IIT Kanpur. (Winter 2022) (pdf)
- "Heegner Points and Kolyvagin's Theorem" for the Master's project at IIT Kanpur. (Winter 2022) (pdf)
- "Elliptic Curves with Complex Multiplication and Heegner Points" for the Master's project at IIT Kanpur. (Fall 2021) (pdf)
- "Main Theorem of Elimination Theory" for the VSRP project at TIFR, Mumbai. (Summer 2021) (pdf)
- "Milnor's K-theory" for the course MTH724: Algebraic K-theory at IIT Kanpur. (Winter 2021) (pdf)
- "Mordell-Weil Theorem" for the course MTH393: Undergraduate Project III at IIT Kanpur. (Winter 2021) (pdf)
Presentation Slides
- Given a talk on "Modular curves over Z" in the reading seminar on Mazur's Eisenstein Ideal paper. (13th March 2024)
- Given a talk on "Group Schemes" in the reading seminar on Mazur's Eisenstein Ideal paper. (24th January 2024)
- Final presentation on "Congruences of Modular Forms" for the course MA354: Galois Representations at IISc Bangalore. (12th December 2023) (slides)
- Given a talk on "Automorphic representations and Cusp forms" in the reading seminar on Automorphic Representations. (30th October 2023)
- Given an expository talk on "The Congruent Number Problem" in the Prime Time Seminar Series at IISc. (26th September 2023)
- Given two lectures on "Neron Models" and two lectures on "Abelian Varieties" to Ph.D. students at IISc for preparation of the ICTS
workshop "Rational Points on Modular Curves". (August 2023)
- Final presentation on "Mordell-Weil theorem for function fields" for the course MA353: Elliptic Curves at IISc Bangalore. (24th April 2023) (slides)
- Final presentation on "Divisors on Schemes" for the course MA310: Algebraic Geometry. (18th April 2023)
- Final presentation on "Homological Dimension" for the course MTH613: Rings and Modules at IIT Kanpur. (21st April 2022) (slides)
- Master's project presentation on "Heegner Points and Kolyvagin's Theorem" at IIT Kanpur. (12th April 2022) (slides)
- End-term presentation on "Modular Forms" for the course MTH688: A course in Arithmetic at IIT Kanpur. (21st Nov 2021)
- Mid-term presentation on "Quadratic forms over Z" for the course MTH688: A course in Arithmetic at IIT Kanpur. (14th Nov 2021)
- Two lectures in Monsoon Math Camp on "pi using Number Theory". (3rd July 2021)
- Final presentation on "Main theorem of Elimination Theory" for the VSRP project at TIFR, Mumbai. (14th June 2021) (slides)
- Final presentation on "Classical applications of Homology groups" for the course MTH759: Algebraic Topology II at IIT Kanpur. (1st May 2021) (slides)
- Final presentation on "Milnor K-theory" for the course MTH724: Algebraic K-theory at IIT Kanpur. (23rd April 2021) (slides)
- End-term presentation on "Integer points on Cubic Curves" for the course MTH671: Introduction to Arithmetic Geometry at IIT Kanpur. (7th Dec 2020) (slides)
- Final presentation on "Hecke operators" for the course MTH392: Undergraudate project II. (3rd Dec 2020) (slides)
- Mid-term presentation on "Real and Complex Points on Cubic Curves" for the course MTH671: Introduction to Arithmetic Geometry at IIT Kanpur. (27th Oct 2020) (slides)