The address of community in Google+: https://plus.google.com/communities/107070668912728728463

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: http://www.ems-ph.org/journals/journal.php?jrn=jncg), but everybody can talk about and share new issues with an open point of view:

- Hochschild and cyclic cohomology
- K-theory and index theory
- Measure theory and topology of noncommutative spaces, operator algebras
- Spectral geometry of noncommutative spaces
- Noncommutative algebraic geometry
- Hopf algebras and quantum groups
- Foliations, groupoids, stacks, gerbes
- Deformations and quantization
- Noncommutative spaces in number theory and arithmetic geometry
- Noncommutative geometry in physics: QFT, renormalization, gauge theory, string theory,
- Gravity, mirror symmetry, solid state physics, statistical mechanics
- …

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

“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.

en.wikipedia.org · 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

Timeline

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.”