Non-commutitative geometry

  • Thread starter Megus
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In summary, the conversation is about a request for useful links on non-commutative geometry. The links provided include information from Wikipedia, AMS Notices, arXiv, and personal research collections. Some recommended sources include "Non commutative geometry for outsiders" by Daniela Bigatti, "Noncommutative Geometry Year 2000" by Alain Connes, "Noncommutative Geometry for Pedestrians" by J. Madore, and "An Introduction to Noncommutative Geometry" by Joseph C. Varilly. The conversation ends with a friendly offer for assistance in collecting bibliographies.
  • #1
Megus
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I'm asking for some useful links about non-commutitative geometry: some basics, related materials, anything. Something to start the subject with. Any explanations welcome as well.
 
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  • #2
From Googling,

http://en.wikipedia.org/wiki/Noncommutative_geometry

http://www.ams.org/notices/199707/lesniewski.pdf
http://www.ams.org/notices/199707/jones.pdf


"Non commutative geometry for outsiders; an elementary introduction to motivations and tools" (Daniela Bigatti)
http://xxx.lanl.gov/abs/hep-th/9802129

"Noncommutative Geometry Year 2000" (Alain Connes)
http://xxx.lanl.gov/abs/math.QA/0011193

"Noncommutative Geometry for Pedestrians" (J. Madore)
http://arxiv.org/abs/gr-qc/9906059

"An Introduction to Noncommutative Geometry" (Joseph C. Varilly)
http://arxiv.org/abs/physics/9709045

http://www.math.washington.edu/~smith/Research/research.html
 
  • #3
Thanks a lot - this is what I needed
 
  • #4
for the first ten years, I collected a bibliography table here.
http://dftuz.unizar.es/~rivero/research/ncactors.html [Broken]

(By the way, it someone from the perimeter institute needs a bit of help collecting this kind of bibliography, just email me [to @unizar.es] :-)
 
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1. What is non-commutative geometry?

Non-commutative geometry is a branch of mathematics that studies spaces and structures that do not follow the usual rules of multiplication. In traditional geometry, the order of multiplication of two elements does not matter, but in non-commutative geometry, this is not the case. Non-commutative geometry has applications in both mathematics and theoretical physics.

2. How is non-commutative geometry different from traditional geometry?

Non-commutative geometry is different from traditional geometry in that it allows for the multiplication of elements to not be commutative, meaning the order of multiplication matters. This allows for the study of non-commutative spaces, which are not able to be described by traditional geometry. Non-commutative geometry also uses tools from abstract algebra and functional analysis, making it a more abstract and complex field of study.

3. What are some real-world applications of non-commutative geometry?

Non-commutative geometry has applications in many fields, including theoretical physics, coding theory, and cryptography. It has been used to study non-commutative spaces in quantum mechanics and string theory, as well as in the development of error-correcting codes for data transmission. Non-commutative geometry has also been applied to cryptography, specifically in the development of quantum-resistant cryptographic algorithms.

4. Who are some notable figures in the field of non-commutative geometry?

Some notable figures in the field of non-commutative geometry include Alain Connes, who developed the concept of non-commutative geometry in the 1980s, as well as mathematicians Maxim Kontsevich and Nigel Higson. Non-commutative geometry has also been influenced by the work of physicists such as Edward Witten and Stephen Hawking.

5. What are some current research topics in non-commutative geometry?

Current research topics in non-commutative geometry include the development of new methods for studying non-commutative spaces, such as the use of spectral triples and noncommutative integration. There is also ongoing research into the applications of non-commutative geometry in areas such as quantum gravity and topological insulators. Additionally, there is a growing interest in the connections between non-commutative geometry and other areas of mathematics, such as number theory and algebraic geometry.

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