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Official Website of Rajiv Gandhi Institute of Petroleum Technology, Jais, Amethi, India. / Algebraic Geometry

Algebraic Geometry

Algebraic geometry is classically the study of common zeros of multivariate polynomials. In modern algebraic geometry, the geometric problems of these zeros are solved using abstract algebraic techniques, mainly from commutative algebra. Most of the classical plane algebraic curves like circles, parabolas, hyperbolas, cubic curves, etc. are examples of varieties that are the fundamental objects of study in algebraic geometry. Algebraic geometry is one of the most important subjects in modern mathematics and has multiple conceptual connections with various other fields like algebra, topology, complex analysis and number theory. It has now applications in various fields of mathematics and physics including control theory, string theory, game theory, robotics, statistics and more.

The research work done in the algebraic geometry group in the Department of Mathematics is related to the analytic aspects of the problems in the theory of moduli spaces that occur in algebraic geometry. Searching for complex analytic properties, mainly the Kähler geometric properties, and differential geometry of the moduli spaces is one of the main research interests of this group. Finding different algebraic invariants like Chow groups, Brauer groups, spaces of algebraic functions, Chen-Ruan cohomologies etc of different moduli spaces of vector bundles and sheaves are other research interests of this group.