Sets Within Geometry, An International Symposium Nancy, France 27-30 July 2011, Archives Henri Poincare Maison Sciences De L’Homme First Announcement and Call for Submitted Papers The Theory of Sets, founded in the last quarter of the 19th Century by Georg Cantor, underwent rapid development at the hands of many contributors. Within that develoment, several distinct lines can be traced, and these have connected in contrasting ways with the subsequent overall development of mathematical knowledge. The aim of this Symposium is to study and compare these, with particular focus on the question how far set theory might be re-conceived as a fragment of Geometry For a more extended discussion of the manner in which this question naturally arises from the study of these various lines of development, see the website of this Meeting at http://www.archmathsciphil.com/conferences-and-workshops/symposium-sets-with... . The confirmed Speakers so far are: Professor FW Lawvere.(Buffalo) Professor Yuri I. Manin (Bonn and IHES) Professor Anders Kock (Aarhus) Professor Christian Houzel (Paris) Professor Colin McLarty (CWRU Cleveland) Professor Jean-Pierre Marquis (Montreal) Professor Alberto Peruzzi (Florence) By way of orientation, the organisers of the Symposium offer the following statement of aims —oOo— Those 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. —oOo— Details of Registration and Titles and Abstracts of the Invited Speakers and other information about the venue and arrangements for the Symposium will be available shortly on http://www.archmathsciphil.com/conferences-and-workshops/symposium-sets-with... . —oOo— The Topics of the Symposium fall under three broad headings : Mathematics – Conceptual Analysis – History 1. Mathematics Examination of Mathematical Developments yielding a deeper understanding of the place of sets in mathematics. 2. Conceptual Analysis The connection between these Mathematical developments and broader analysis of the epistemological sources of mathematical ideas. One illustration of such analysis is the investigation of the meaning of Extensionality and Choice principles in the setting of Topos Theory 3. History Related Historical investigations such as a re-examination of the work of Cantor and Dedekind and other figures and discussion of different approaches to the Continuum Hypothesis. —oOo— CONTRIBUTED TALKS and POSTER SESSIONS Proposals for Talks relevant to the Themes of the Meeting are welcome and Titles and Abstracts of such proposed talks should be sent no later than May 1st to the Secretary of the Organising Committee Michael Wright, Archive of Mathematical Sciences: mike.wright@archmathsci.org Abstracts should be no more than 400 words but can be shorter. Anyone submitting a proposed talk is asked first to study the extended announcement on the website for guidance as to whether their proposed talk may be relevant to the themes of the Symposium. In order to accommodate as many Speakers as possible, Contributed Talks (Talks by other than the Invited Speakers ) will be of 30 minutes, including discussion time. There will be no parallel sessions. A Second Announcement will be made by May 1st 2011. The site will be regularly updated with Titles and Abstracts of Invited Talks and other Information. Those submitting proposals for Contributed Talks will be advised no later than May 30th 2011 if their talks have been accepted for inclusion in the Program. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]