After a very successful first year, Global Noncommutative Geometry Seminar (Americas) starts again this Friday at 3 PM (Toronto time), 9 PM (Paris time) with a talk by Alain Connes. Title: On the Notion of Space.

Here is the Zoom link: Join Zoom Meeting

https://wustl.zoom.us/j/95154904208?pwd=ajA2azAxK1ZwMlJUeXBEWlh5UG5WQT09

Meeting ID: 951 5490 4208

Passcode: 446996

Added Sept 7: Talk can be watched here

For abstracts and details of other forthcoming talks in Global Noncommutative Geometry Seminar please check the seminar website: Global NCG Seminar

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The video of the talk is now available at the website of the seminar, or more directly on Utube at

https://youtu.be/m20KxUB5lMU.

In the book "conversations on Quantum Gravity" which I mention at some point in my talk, the first page of my interview has

been garbled by the publisher CUP (and not at all by Jay Armas who did a fantastic job at collecting these interviews) so better the first page should read as follows

\Q{From your point of view, what are the main problems in theoretical physics at the moment?}\pp

\A{I do not have the pretension of answering this question as if I was a true physicist.

I'm a mathematician, not a physicist, but I have been, for all my life, fascinated by some problems in physics.

In particular, I have been fascinated by three main problems. The first problem is the problem of understanding

what time is and the role of time at the quantum level.

The second problem, which I have spent a

considerable amount of time on, is the problem of understanding renormalisation in a mathematical way.

Physicists have found and developed renormalisation, which is an amazing technique, and have

applied it successfully in many cases. However, the mathematical meaning of this technique has always been rather obscure.

It took a lot of time and work but now I think that, thanks to my collaboration with Dirk Kreimer, we finally understand renormalisation in a precise mathematical way.

The third problem that has fascinated me deeply is the subtleness of reality exhibited at the quantum level.

Heisenberg discovered that you cannot naively manipulate observables in microscopic systems, instead you need, for example,

to take care about the order of observables in a given product. The consequence of this discovery is the realisation that

our mathematical ideas about geometry, space and time in particular, are very naive, in the sense that they are based on sets, and that

the quantum reality is much more subtle.

These are three ``leitmotiv" underlying my reflections about parts of human thought that can be

relevant for physics but, of course, being a mathematician, I am more interested in trying to

understand the mathematical meaning of something rather than the impact that this understanding can have on making

actual measurements. The latter, you know, is what physicists actually do (laughs). My motivation is of a rather different nature.}

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