Topos à l'IHES
23-27 novembre 2015
The concept of topos was introduced by A. Grothendieck during his Séminaire de Géométrie Algébrique du Bois-Marie, which took place at the IHES in the early sixties. The original motivation was that of defining a general notion of space on which one could define cohomological invariants in the algebro-geometric setting needed for proving the Weil's conjectures. In spite of this quite specific technical motivation, the notion of topos appeared at the very beginning as defining a new conception of space, capable of unifying the continuous and the discrete in an harmonious marriage: in the words of Grothendieck, "Un lit si vaste en effet (telle une vaste et paisible rivière très profonde...), que “tous les chevaux du roi y pourraient boire ensemble...” ".
In the following years, new perspectives on the notion on topos emerged. According to Lawvere and Tierney, a topos can be considered not only as a generalized space but as a mathematical universe within which one can carry out most familiar set-theoretic constructions, but which also, thanks to the inherent ‘flexibility' of the notion of topos, can be profitably exploited to construct `new mathematical worlds' having particular properties. On the other hand, the theory of classifying toposes allows to regard a Grothendieck toposas a suitable kind of first-order theory modulo Morita-equivalence. Toposes have also been proved effective in studying dualities and establishing ‘bridges’ across different mathematical theories with a related semantic content.
The conference aims to illustrate the fruitfulness and wide-ranging impact of the notion of topos, by featuring presentations on new theoretical advances in the subject (including the theory of higher toposes) as well as on applications of toposes in different fields such as number theory, algebraic geometry, logic, functional analysis, topology, mathematical physics and computer science. The conference is preceded by a two-day introductory mini-course for the benefit of students and mathematicians who are not already familiar withtopos theory.
The schedule will not be tight in order to allow ample time for exchanges and informal discussions between the participants. There is still room for a few short communications; if you want to submit a one-page abstract for a short talk at the conference, please do it before the 30th of September by sending it at the address .... You will be notified about the result of your submission by the 30st of October.
Olivia Caramello
Liste des interventions
(Stars indicate videos availability from now on this website)
* Mathieu Anel : "Toposes are commutative rings"
* Luca Barbieri-Viale : "T-Motives"
* Ingo Blechschmidt : Using the internal language of toposes in algebraic geometry
* Anna Carla-Russo : Morita-equivalences for MV-algebras (with O. C.)
* Pierre Cartier : Conférence Inaugurale
* Caterina Consani : "On the geometry of the adele class space of Q"
* Thierry Coquand : "logic and topology"
Matias I. Data : A construction of 2-filtered bicolimits of categories with 2-fibrations
Jonas Frey : Realizability toposes as homotopy categories
*Simon Henry : "Operator algebras from toposes"
* André Joyal : "New variations on the notion of topos" + * (tutorials :) "A crash course in topos theory: the big picture"
* Camell Kachour :Globular perspective for Grothendieck ∞-topos and Grothendieck (∞,n)-topos
Pietro Polesello : Proper stacks and costacks
* Mike Prest : "Model-theoretic imaginaries and localisation for additive categories"
* David Michael Roberts : Class forcing and topos theory
* Urs Schreiber : "Synthetic prequantum field theory in a cohesive homotopy topos"
* Alex Simpson : Probability sheaves
* Carlos Simpson : "Pre-buildings as sheaves on the site of enclosures"
Zoran Skoda : Localizations and semiquantals
* Christopher F. Townsend : There are categories of `spaces' that are not categories of locales
General discussion
O. Caramello, A. Connes, A. Joyal, L. Lafforgue
and also J. Benabou, M. Kontsevitch, Urs Schreiber...
Alexandre Grothendieck
28 mars 1928 (Berlin) - 13 novembre 2014 (Saint-Girons)
Comité d'Organisation du colloque : Olivia Caramello, Pierre Cartier, Alain Connes, Stéphane Dugowson et Anatole Khélif
Par les transports en commun RATP depuis Paris : http://goo.gl/ELtlsw