"Noncommutative geometry, as developed by Connes starting in the early ’80s ..., extends the tools of ordinary geometry to treat spaces that are quotients, for which the usual “ring of functions”, defined as functions invariant with respect to the equivalence relation, is too small to capture the information on the “inner structure” of points in the quotient space. Typically, for such spaces functions on the quotients are just constants, while a nontrivial ring of functions, which remembers the structure of the equivalence relation, can be defined using a noncommutative algebra of coordinates, analogous to the non- commuting variables of quantum mechanics."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Science authorsPhysicists from ItalyWomen academics from ItalyMathematicians from ItalyNon-fiction authors from Italy
Original Language: English
Available Languages (1)
Sources
(quote from p. 5)
https://en.wikiquote.org/wiki/Matilde_Marcolli
Revision History
No revisions have been submitted for this quote.
Categories
Matilde Marcolli
Matilde Marcolli is an Italian mathematical physicist. She was an Invited Speaker at the International Congress of Mathematicians held in 2010 in Hyderabad.
6 quotes on TrueQuotesView all quotes by Matilde Marcolli →
Related Quotes
"The physicists' approach to the equivalence of Seiberg-Witten and Donaldson theory is based on Witten's interpretatio…"
"It turns out that noncommutative geometry is a very good framework for theories of (modified) gravity coupled to matt…"
"Violence, bullying, and intimidation exist and are practiced on a daily basis within the mathematical community, and …"
"The general discourse of scientists about science is marred by beliefs of the Ancient Greeks in the kalos kai agathos…"
"Matilde Marcolli describes how she came to mathematics influenced by her parents’ involvement in Italian contemporary…"
"Interviewer: Are you looking for God? Gianotti: No. I don’t think physics will ever be able to answer that question. …"
"Si, io credo in Dio. Non ci sono contraddizioni tra scienza e fede, l’importante è lasciare i due piani separati: ess…"
"The rose colours of madder have justly been considered as supplying a desideratum, and as the most valuable acquisiti…"
"Green...contrasts more agreeably with all colours than any other individual colour. It has accordingly been adopted w…"
"The general powers of green, as a colour, associate it with the ideas of vigour and freshness; and it is hence symbol…"