The talk sits at the interface of algebraic topology and geometry. In algebraic geometry, the smooth schemes A^n\{0} form important examples of algebraic spheres (for \(n>0\)). We define a smooth scheme to be an exotic sphere if it has the \(A^1\)-homotopy type as A^n\{0} without being isomorphic as a variety. Do such exotic candidates exist? After building the necessary foundation, we will delve deeply into answering this question. This problem was carried out as a part of my Ph.D. research and can be found in my homepage (https://krishmv.github.io/)
