Learn More About This
Directory
This directory sponsored by SIQL, a Spider Makers company...
1. Algebraic Geometry
- www.math.tamu.edu
- Algebraic Geometry .
- What is Algebraic Geometry?.
- Algebraic Geometry is a subject with historical roots in analytic geometry. ... Today it is a powerful synthesis of those algebraic, geometric, and analytic techniques. ... It subsumes most of commutative algebra and much of algebraic number theory, and overlaps with differential geometry, modern "analytic geometry" (complex manifolds), Lie groups, representation theory, theoretical physics, and to a lesser extent the theory of partial differential equations. In addition to being one of the central disciplines of pure mathematics, algebraic geometry has developed an applied side which is linked to problems in computational complexity and the theory of algorithms, symbolic computation, robotics, control theory, computational geometry, geometric modeling, image recognition, computer vision, and scientific visualization. ...
2. Short CV: J.F. Jardine
- www.math.uwo.ca
- Algebraic K-theory, Algebraic Topology, Algebraic Geometry, Category Theory .
- Simplicial sheaves and presheaves, Cohomology of algebraic groups, Motivic homotopy theory .
- Rick Jardine's research is primarily in algebraic K-theory and homotopy theory. ...
- Algebraic topology is the study of algebraic approximations of space, and has been one of the driving forces in twentieth century Mathematics, beginning with the work of Poincaré in the late 1890s. ... At the same time, the Grothendieck school in Paris began a grand project to apply the wealth of homotopy theoretic calculational methods to algebraic geometry and number theory. This enterprise continues to this day, and has always been a central theme of research in algebraic K-theory. ...
- The modern period for this branch of homotopy theory began in the mid 1980s with the discovery of closed model structures for wide classes of simplicial objects in algebraic geometry by Jardine and Joyal, and has culminated in recent years with the introduction of motivic homotopy theory by Morel and Voevodsky in connection with Voevodsky's celebrated proof of the Milnor Conjecture. ...
- Jardine is the cofounder, with Dan Grayson (Urbana-Champaign), of the Algebraic K-theory Preprint Archive at the University of Illinois at Urbana-Champaign. ...
3. Algebraic Areas of Mathematics
- www.math.niu.edu
- Algebraic Areas of Mathematics.
- The algebraic areas of mathematics developed from abstracting key observations about our counting, arithmetic, algebraic manipulations, and symmetry. ...
- Besides elementary topics involving congruences, divisibility, primes, and so on, number theory now includes highly algebraic studies of rings and fields of numbers; analytical methods applied to asymptotic estimates and special functions; and geometric topics (e. ...
- They have algebraic structure, of course, and yet are also subsets of space, and so have a geometry; moreover, portions of them look just like Euclidean space, making it possible to do analysis on them (e. ...
- Of particular interest are several classes of rings of interest in number theory, field theory, algebraic geometry, and related areas; however, other classes of rings arise, and a rich structure theory arises to analyze commutative rings in general, using the concepts of ideals, localizations, and homological algebra. ...
- 08: General algebraic systems include those structures with a very simple axiom structure, as well as those structures not easily included with groups, rings, fields, or the other algebraic systems. ...
- 14: Algebraic geometry combines the algebraic with the geometric for the benefit of both. ... Conversely, the geometry of sets defined by equations is studied using quite sophisticated algebraic machinery. ...
- In practice this includes a very wide portion of mathematics! Thus linear algebra includes axiomatic treatments, computational matters, algebraic structures, and even parts of geometry; moreover, it provides tools used for analyzing differential equations, statistical processes, and even physical phenomena. ...
- While the general theory and certain types of categories have attracted considerable interest, the area of homological algebra has proved most fruitful in areas of ring theory, group theory, and algebraic topology. ...
- Originally defined for (vector bundles over) topological spaces it is now also defined for (modules over) rings, giving extra algebraic information about those objects. ...
- Various special types of lattices have particularly nice structure and have applications in group theory and algebraic topology, for example. ...
- Other fairly algebraic areas include 55: Algebraic Topology and 94: Information and Communication. ...
4. Open problems in algebraic topology
- claude.math.wesleyan.edu
- Mark Hovey's Algebraic Topology Problem List.
- This list of problems is designed as a resource for algebraic topologists. ...
- Before proceeding onto the problems, I want to make a few polemical remarks about algebraic topology. ... This is completely ridiculous, since the methods and ideas of algebraic topology have broad application to other areas of mathematics--witness Voevosdky's recent Fields Medal caliber work. We as algebraic topologists must bear part of the responsibility for this marginalization, and we must attempt to improve the situation. ... The most obvious method is to work on problems that arise externally to algebraic topology but for which the methods of algebraic topology may be helpful. ... Much of the action in mathematics in the last 10 years has come from interactions with physics, and algebraic topology can probably say more than it has. ...
- However, even if the problems we work on are internal to algebraic topology, we must strive to express ourselves better. ...
5. VBAC
- www.mi.uni-erlangen.de
- Vector Bundles on Algebraic Curves .
- This is an international research group affiliated to the European algebraic geometry research training network EAGER through the EAGER Warwick node and to EDGE (European Differential Geometry Endeavour). ...
- vector bundles (and associated structures) on algebraic curves, construction of their moduli spaces and interpretation in terms of differential equations .
6. Algebraic Geometry
- www.math.byu.edu
- Algebraic Geometry.
- Algebraic geometry seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics. ...
- European Algebraic Geometry: AGE and EUROPROJ .
- Algebraic Curves .
- Overview of Algebraic Plane Curves (Geometry Center) .
- Algebraic Surfaces.
- Algebraic Geometers and the Like.
- Weibel's algebraic K-theory book .
7. What is Algebraic Topology?
- www.math.rochester.edu
- WHAT IS ALGEBRAIC TOPOLOGY?.
- THE BEGINNINGS OF ALGEBRAIC TOPOLOGY.
- Algebraic topology is a twentieth century field of mathematics that can trace its origins and connections back to the ancient beginnings of mathematics. ...
- One of the strengths of algebraic topology has always been its wide degree of applicability to other fields. Nowadays that includes fields like physics, differential geometry, algebraic geometry, and number theory. ...
- The winding number of a curve illustrates two important principles of algebraic topology. ...
- Modern algebraic topology is the study of the global properties of spaces by means of algebra. ...
- To get an idea of what algebraic topology is about, think about the fact that we live on the surface of a sphere but locally this is difficult to distinguish from living on a flat plane. ... Algebraic topology is concerned with the whole surface and points to the obvious fact that the surface of a sphere is a finite area with no boundary and the flat plane does not have this property. ... Algebraic topology includes but is not confined to the study of spaces of dimensions only two or three. ...
- If we regard homotopic functions are being equivalent, we can make them into the algebraic object called a group, more precisely a homotopy group and, in the case we mentioned above, it is called the k-th homotopy group of the n-dimensional sphere. ...
8. ABC-KLM
- www.cf.ac.uk
- Network in Algebraic Geometry, Boundary Conformal Field Theory and Noncommutative Geometry.
- The objective of this network is to bring together groups in the UK having a common goal in pursuing the deep connections between mathematics and physics—primarily algebraic geometry, operator algebras and quantum groups in pure mathematics and conformal field theory, string theory and statistical mechanics in mathematical and theoretical physics. ...
- The three threads of algebraic geometry, noncommutative geometry and conformal field theory are interwoven. Algebraic geometry and noncommutative instantons on the one hand, and operator algebras and CFT on the other, are related by the common use of NCG to understand singular spaces. Thus moduli spaces in algebraic geometry appear as orbifolds, while orbifolds associated to the noncommutative torus and subfactors play a key role in operator algebras and CFT. Algebraic geometry is a crucial ingredient of the attempt to relate operator algebras and CFT as in the mysterious parallel between ADE classifications of quotient singularities in algebraic geometry, subfactors in operator algebras and modular invariant partition functions in CFT. ...
9. Projections of Complex Algebraic Curves to Real 3-space
- www.math.byu.edu
- Projections of Complex Algebraic Curves to Real 3-space.
10. RTN Network: K-Theory and Algebraic Groups
- www.mathematik.uni-bielefeld.de
- RTN Network HPRN-CT-2002-00287: Algebraic K-Theory, Linear Algebraic Groups and Related Structures.
- June 27--July 1, 2005 "Algebraic K- and L-theory of Infinite Groups", Workshop at Edinburgh http://www. ...
- 2005 Nottingham: Workshop on linear algebraic groups and related structures .
- Jun 25-Jul 1 2006: Oberwolfach: Quadratic forms and linear algebraic groups .
- 2006 Bielefeld: Final Postdoc Conference on K-Theory, algebraic groups and related structures (1 week) .
- February 1 -- 5, 2004, Eilat: Workshop on Linear Algebraic Groups, Quadratic Forms and Related Topics,.
- July 5 -- 8, 2004, Dublin 2004 Workshop on K-Theory, Algebraic Groups and Related Structures, 1. ...
- July 26 -- 30, 2004, Safi, Morocco: Algebraic K-theory and its Applications, organized by Hinda Hamroui (Univ. ...
- June 30--July 4, 2003, Besancon: Workshop on "Algebraic Groups, Quadratic Forms and Related Topics" 1. ...
11. Mirror Symmetry and Algebraic Geometry
- www.cs.amherst.edu
- Mirror Symmetry and Algebraic Geometry.
- The book is written for algebraic geometers and graduate students who want to learn about mirror symmetry. ...
- A list of typographical errors is available for the first printing of Mirror Symmetry and Algebraic Geometry: TeX source or postscript. ...
- To find Mirror Symmetry and Algebraic Geometry in the AMS on-line catalog, go to the AMS bookstore and enter .
12. Algebraic K-theory, groups and categories
- www.bangor.ac.uk
- TITLE: Algebraic K-theory, groups and categories .
- The origin of this project was the amalgamation in 1995 of two separate proposals for INTAS support in the areas of Algebraic K-theory from A. Bak at Bielefeld, and of Categorical Methods in Algebraic Homotopy and related topics from R. ...
- The agreed title of the joint proposal `Algebraic K-theory, groups and categories' indicates well the variety of interconnections and analogies which were envisaged. `Algebraic K-theory' is an area which has been notable from the start for its interactions and the problems it has produced. `Groups' occur as algebraic groups, classical groups, homology groups, homotopy groups, Galois groups, abstract groups, K-groups, and in many other ways. ...
- (ii) a successful British Council/ARC supported collaboration between Bangor and Bielefeld, including a number of visits both ways and several workshops on `Global actions and algebraic homotopy', which invited members from teams in the original proposals of both Bangor and Bielefeld, and had external participants, .
- (iii) a successful INTAS proposal `Algebraic homotopy, Galois theory and Descent' (Bangor, with Coimbra (Portugal) and the Georgian Academy of Sciences), .
- (iv) a successful DFG/RFBR proposal `Structure of classical-like groups over rings, nonabelian K-theory, and algebraic homotopy theory' (Bielefeld with St. ...
- This has led to new results, new calculations, new constructions and new viewpoints in algebraic topology, cohomology theory, group theory and differential topology. ...
- Porter has written a substantial survey article on proper homotopy theory for the Handbook of Algebraic Topology, ed. ...
- Pradines allows for an algebraic expression of `iteration of local procedures'. ...
- Global actions are the algebraic counterpart of topological spaces. Putting a global action structure on an algebraic object such as a group allows one to construct paths in the objects and to develop in a classical way a homotopy theory of the objects. The papers 3 , 4 , 8 , and 9 develop the foundations of the subject and 10 provides a completely algebraic construction of algebraic K-theory using global actions. ...
- Since CGT adequately extends Galois theory of commutative rings (see 6 - 9 , 30 , 32 , 33 , 41 ) and the theory of central extensions of groups and more general algebraic structures ( 30 , 36 , 42 ), those connections should help to realize our extended version of the Grothendieck program, which is supposed to provide a unified foundation not only to algebraic geometry and algebraic topology, but also to the commutator/homology theory of ``group-like" algebraic structures. ...
Other related topics:
Do you have a great site about Algebraic? Is
your Algebraic site listed here?
Would you like a prefered placement of your site in this directory?
It's easy! First place, the HTML from the box below on your page that
you would like listed in this directory.
Then use our link submission request with
your name, your contact information, and the URL of your site that has
a link to this directory. After we
verify your link to us, we'll make sure your site stays in our directory,
and we'll give it prefered placement here also.
Here is how to make a simple text link to us. Just copy the code in this
box to your website:
We can also develop a custom Guide To The Internet for your site. Please
request your own
custom Guide To The Internet.
This custom Guide To The Internet produced by
Siql. Visit us today, and find out how to get your own
custom guide to the Internet, and how to get your site
listed in our guides.
Copyright 1995-2004 by Siql. All
Rights Reserved.