### Symposium: Sets Within Geometry

#### Posted by David Corfield

There is to be a Symposium – Sets Within Geometry – held in Nancy, France on 26-29 July, 2011. Confirmed speakers are: FW Lawvere (Buffalo), Yuri I. Manin (Bonn and IHES), Anders Kock (Aarhus), Christian Houzel (Paris), Colin McLarty (CWRU Cleveland), Martha Bunge (Montreal), Jean-Pierre Marquis (Montreal) and Alberto Peruzzi (Florence).

Statement of aims:

Posted at March 7, 2011 10:22 AM UTCThose who have come together to organise this Symposium believe that the ultimate aim of foundational efforts is to provide clarifying guidance to teaching and research in mathematics, by concentrating the essential aspects of past such endeavors. By mathematics we mean the investigation of the Relations between Space and Quantity, of the reflected relations between quantity and quantity and between space and space, and the development of our knowledge of these in other words Geometry.

Using tools developed by Cantor and his contemporaries, much more explicit forms of the relation between space and quantity were developed in the 1930s in the field of functional analysis by Stone and Gelfand, partly through the notion of Spectrum (a space corresponding to a given system of quantities). In the 1950s Grothendieck applied those same tools, around the notion of Spectrum, to algebraic geometry by using and developing the further powerful tool of category theory . Further developments have strongly suggested that it is now possible to incorporate the whole set-theoretic “foundation” of Geometry, explicitly as part of that space-quantity dialectic, in other words as a chapter in an extended Algebraic Geometry.

## Re: Symposium: Sets Within Geometry

Thanks, David. I had meant to forward this announcement to the blog, too, but didn’t get around to it.

I’d be interested in seeing the titles and topics of the invited talks, to see how participants intend to try to fill with life what – if I am not mistaken – is Bill Lawvere’s formulation of his grand vision of topos theory and geometry, for instance when it says: