A comparative review of recent researches in geometry 1 - UCR 2025

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Geometry 1.What is Geometry? 2. Euclidean Geometry 3. Non-Euclidean Geometry 4. Plane Geometry 5. Solid Geometry4 more rows
What are the different geometries ? Euclidean geometry: This is the traditional geometry that is taught in schools. Non-Euclidean geometry: Unlike Euclidean geometry, non-Euclidean geometry does not obey the rules of Euclids geometry. Analytic geometry: This type of geometry combines algebra and geometry.
Algebraic geometry: classical approach Hypersurface. Quadric (algebraic geometry) Dimension of an algebraic variety. Hilberts Nullstellensatz. Complete variety. Elimination theory. Grbner basis. Projective variety.
The current research interests of the algebraic geometry group include homological algebra, complex geometry, arithmetic geometry, geometric representation theory, stability conditions, derived categories, moduli theory and birational geometry.
Algebraic geometry plays a significant role in different aspects of Robotics and Computer Vision such as Robotics Motion Planning, Robotics Kinematics and Dynamics, Computer Vision Calibration and Robotics and Computer Vision Integration.
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People also ask

Differential geometry is a wide and active research field in mathematics that has recently received increasing interest from statistics and machine learning. Information geometry, manifold learning, and data manifolds are examples of successful differential geometry uses.
The mainstream of algebraic geometry is devoted to the study of the complex points of the algebraic varieties and more generally to the points with coordinates in an algebraically closed field. Real algebraic geometry is the study of the real algebraic varieties.
Today, algebraic geometry is an area with geometry with connections to other areas such as commutative algebra, complex analysis, topology and number theory in mathematics, cryptography in informatics and string theory in physics.

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