Geometry - Contemporary Geometry - Algebraic Geometry

Algebraic Geometry

The field of algebraic geometry is the modern incarnation of the Cartesian geometry of co-ordinates. From late 1950s through mid-1970s it had undergone major foundational development, largely due to work of Jean-Pierre Serre and Alexander Grothendieck. This led to the introduction of schemes and greater emphasis on topological methods, including various cohomology theories. One of seven Millennium Prize problems, the Hodge conjecture, is a question in algebraic geometry.

The study of low dimensional algebraic varieties, algebraic curves, algebraic surfaces and algebraic varieties of dimension 3 ("algebraic threefolds"), has been far advanced. Gröbner basis theory and real algebraic geometry are among more applied subfields of modern algebraic geometry. Arithmetic geometry is an active field combining algebraic geometry and number theory. Other directions of research involve moduli spaces and complex geometry. Algebro-geometric methods are commonly applied in string and brane theory.

Read more about this topic:  Geometry, Contemporary Geometry

Other articles related to "geometry, algebraic geometry, algebraic":

List Of Incomplete Proofs - Examples
... set of (second order) axioms for Euclidean geometry, called Hilbert's axioms, and between 1926 and 1959 Tarski gave some complete sets of first order axioms ... Italian school of algebraic geometry ... A major exception to this is the Italian school of algebraic geometry in the first half of the 20th century, where lower standards of rigor gradually became acceptable ...
Motivic Integration
... Motivic integration is a branch of algebraic geometry which was invented by Maxim Kontsevich in 1995 and was developed by Jan Denef and François Loeser ... introduction it has proved to be quite useful in various branches of algebraic geometry, most notably birational geometry and singularity theory ... Roughly speaking, motivic integration assigns to subsets of the arc space of an algebraic geometry a volume living in the Grothendieck ring of algebraic varieties ...
Martin Kreuzer
... fellowship at Queen's University in Kingston, Ontario, Canada, from 1989 to 1991, working in algebraic geometry with Professor Anthony Geramita ... After substituting for the chair of algebraic geometry at the University of Bayreuth in 2000-2001 and for the chair of algebra at Technical University of Dortmund from 2002 to 2007, he moved to ... computer algebra, cryptography, computational commutative algebra, algebraic geometry, and their industrial applications ...
The Story Of Maths - "To Infinity and Beyond" - Algebraic Geometry
... The final section briefly covers algebraic geometry ... Weil's work connected number theory, algebra, topology and geometry ...
Algebraic Geometry - Applications
... Algebraic geometry now finds application in statistics, control theory, robotics, error-correcting codes, phylogenetics and geometric modelling ...

Famous quotes containing the words geometry and/or algebraic:

    ... geometry became a symbol for human relations, except that it was better, because in geometry things never go bad. If certain things occur, if certain lines meet, an angle is born. You cannot fail. It’s not going to fail; it is eternal. I found in rules of mathematics a peace and a trust that I could not place in human beings. This sublimation was total and remained total. Thus, I’m able to avoid or manipulate or process pain.
    Louise Bourgeois (b. 1911)

    I have no scheme about it,—no designs on men at all; and, if I had, my mode would be to tempt them with the fruit, and not with the manure. To what end do I lead a simple life at all, pray? That I may teach others to simplify their lives?—and so all our lives be simplified merely, like an algebraic formula? Or not, rather, that I may make use of the ground I have cleared, to live more worthily and profitably?
    Henry David Thoreau (1817–1862)