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A community in Non Commutative Geometry

The address of community in Google+:


What has founded this community for?
“What is NCG? And what areas of mathematical researches it exactly covers?”
these two simple questions really make me do everything ti find the answer, and to find out, day by day, I came to this conclusion that the atmosphere of faculties and  research groups is so very serious, and maybe nobody has, even some few seconds, to answer my e-mail!!
“To receive firstly you should give”, I think. Generosity is the rule of infinite receiving! So I decided to establish this community. The aim, in simplest words, is to share everything new around NCG, even historical and philosophical discussions. So one shares one new line, even a link, in this community and instead will receive more than 100 new lines in NCG.
Generally the guideline of discussions is including as below (from Journal of Noncommutative Geometry:, but everybody can talk about and share new issues with an open point of view:

  1. Hochschild and cyclic cohomology
  2. K-theory and index theory
  3. Measure theory and topology of noncommutative spaces, operator algebras
  4. Spectral geometry of noncommutative spaces
  5. Noncommutative algebraic geometry
  6. Hopf algebras and quantum groups
  7. Foliations, groupoids, stacks, gerbes
  8. Deformations and quantization
  9. Noncommutative spaces in number theory and arithmetic geometry
  10. Noncommutative geometry in physics: QFT, renormalization, gauge theory, string theory,
  11. Gravity, mirror symmetry, solid state physics, statistical mechanics

I dedicate this community to French mathematician Alain Connes, the founder of non-commutative geometry.

xac_6809connes_1-serre_640“Alain Connes is a French mathematician, currently Professor at the Collège de France, IHÉS, The Ohio State University and Vanderbilt University. Alain Connes studies operator algebras. In his early work on von Neumann algebras in the 1970s, he succeeded in obtaining the almost complete classification of injective factors. Following this he made contributions in operator K-theory and index theory, which culminated in the Baum-Connes conjecture. He also introduced cyclic cohomology in the early 1980s as a first step in the study of noncommutative differential geometry. · Text under CC-BY-SA license
Born: Apr 01, 1947 (age 67) · Draguignan, France
Awards: Fields Medal (1982) · Crafoord Prize in Astronomy and Mathematics (2001)
Education: École Normale Supérieure
Academic advisor: Jacques Dixmier
1982: Alain Connes was awarded Fields Medal in 1982.
1985: Non-commutative differential geometry written by Alain Connes was first published in 1985.
1994: Noncommutative geometry written by Alain Connes was first published in 1994.
2001: Alain Connes was awarded Crafoord Prize in Astronomy and Mathematics in 2001.
2007: Noncommutative Geometry written by Alain Connes was first published in 2007.”

ABC conjecture solved by Japanese Mathematician Shinichi Mochizuki Claims

ABC Conjecture: Mathematician Shinichi Mochizuki Claims Proof Of Important Number Theory Problem

A Japanese mathematician claims to have the proof for the ABC conjecture, a statement about the relationship between prime numbers that has been called the most important unsolved problem in number theory. If Shinichi Mochizuki’s 500-page proof stands up to scrutiny, mathematicians say it will represent one of the most astounding achievements of mathematics of the twenty-first century. The proof will also have ramifications all over mathematics, and even in the real-world field of data encryption. …. Full story

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