Some Notes by Me
“One should never try to prove anything that is not almost obvious.”
― Alexander Grothendieck
Algebraic Geometry
Intersection homology - [pdf] This pdf contains the materials of my two talks of Intersection homology seminar at ISI, Bangalore.
Riemann Roch and Serre duality - [pdf] Here I have discussed about Riemann Roch theorem and it's application on Riemann surfaces including Moduli spaces. It was the contents for my talks of seminar on Riemann surfaces.
Algebraic Topology
Applications of Cohomology operation in Homotopy theory - [pdf, html] This is my lecture notes of the talk delivered in the "What is...?" seminar organized by Mathclub, ISI Bangalore.
Cohomology and Poincaré Duality - [pdf]
Some Fixed point theorems - [pdf]
Acyclic Model theorem and equivalence of homology theories - [pdf] This is part of my VSRP 2023 report.
Künneth formula and Universal coefficient theorem - [pdf]
Analysis
Hahn Banach Separation and Riesz representation theorem - [pdf] This is not pure Analysis but convex Geometry. These were used in the functional analysis course (5th semester 2023, fall).
The spaces of Lebesgue integrable functions L1(X) and L2(X) - [pdf]
Notes on Complex analysis - [pdf]
Notes on analysis of several variables - [pdf]
General
(These notes were written during my first year at ISI. These notes may contain some typos.)
One point compactification with examples - [pdf]
Ordinal numbers and Cardinal numbers - [pdf]