http://hdl.handle.net/123456789/1325 Dissertation submitted by MP -2017 batch as part of their course. Mon, 15 May 2023 07:53:43 GMT 2023-05-15T07:53:43Z http://hdl.handle.net/123456789/1702 Title: Geometric Measure Theory Authors: Ashok, Satpute Ganesh; Sahu, Lingaraj Abstract: The aim of this thesis is to study the Geometric measure theory. First part of this thesis mainly focuses on the Hausdorff measure and Hausdorff dimensions. In sub- sequent chapters Haar measure, covering theorems and the Area-Corea formulas and applications are discussed. Wed, 28 Jul 2021 00:00:00 GMT http://hdl.handle.net/123456789/1702 2021-07-28T00:00:00Z http://hdl.handle.net/123456789/1429 Title: Theory of Elliptic Curves and the Mordell-Weil Group Authors: Sharma, Shreya; Balwe, Chetan T. Abstract: Abstract not available Thu, 30 Apr 2020 00:00:00 GMT http://hdl.handle.net/123456789/1429 2020-04-30T00:00:00Z http://hdl.handle.net/123456789/1428 Title: Resolution of Curves and Surfaces Authors: Bhutani, Shikha; Vaish, Vaibhav Abstract: The resolution of singularity exists for varieties of all dimensions over an algebraically closed field of characteristic zero. However, for positive characteristic, it is an open problem for dimensions ≥ 4. In this document, we show that embedded resolution exists for curves and surfaces over fields of arbitrary characteristics. We also talk about other techniques involved in the resolution of singularities and their limitations. Sat, 25 Apr 2020 00:00:00 GMT http://hdl.handle.net/123456789/1428 2020-04-25T00:00:00Z http://hdl.handle.net/123456789/1427 Title: Hyperbolic Structures on Manifolds and CAT (k) Geometry Authors: Shaji, George; Gongopadhyay, Krishnendu Abstract: This thesis is largely split into two parts. The first introduces the readers to certain manifolds that may be endowed with a hyperbolic structure. The most notable of these are the compact, closed surfaces and the fighure-eight knot. The second part deals with the geometry of CAT (k) spaces. The CAT (k) condition is a generalization of sectional curvature in a Riemannian manifold to geodesic spaces. Following the general study of such spaces, we shall then restrict ourselves to CAT (0) spaces and study various interesting theorems that give us deeper insight about the geometric structure of these spaces. Wed, 22 Apr 2020 00:00:00 GMT http://hdl.handle.net/123456789/1427 2020-04-22T00:00:00Z