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Topos à l'IHES

de au (Europe/Paris)
à Le Bois-Marie ( Salle de Conférences Marilyn et James Simons )
35, route de Chartres 91440 Bures-sur-Yvette
Description

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 topos as 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 with topos theory.

Scientific committee : O. CARAMELLO*, P. CARTIER, A. CONNES, S. DUGOWSON, A. KHELIF

23-24 November : Tutorials by: Olivia CARAMELLO and André JOYAL

25-27 November : Invited speakers :

Mathieu ANEL (University Paris-Diderot)
Luca BARBIERI-VIALE (Università degli Studi di Milano)
Jean BÉNABOU (University Paris 13)
Caterina CONSANI (Johns Hopkins University, Baltimore)
Thierry COQUAND (University of Göteborg)
Simon HENRY (Radboud University, Nijmegen)
André JOYAL (Université du Quebec, Montréal)
Mike PREST (University of Manchester)
Urs SCHREIBER (Eduard Čech Institute for Algebra, Geometry and Physics, Prague)
Carlos SIMPSON (University of Nice-Sophia-Antipolis) 
Michel VAQUIÉ (University Paul Sabatier, Toulouse)

25 & 27 November: Short Communications Speakers

Ingo BLECHSCHMIDT (University of Augsburg)
Matias DATA (Universidad de Buenos Aires)
Jonas FREY (Copenhagen University)
Camell KACHOUR
Guilherme Frederico LIMA de CARVALHO e SILVA (University of Cambridge)
Pietro POLESELLO (Universita di Padova)
David ROBERTS (University of Adelaide)
Anna Carla RUSSO (University of Salerno & Université Paris-Diderot)
Alex SIMPSON (University of Ljubljana)
Zoran  SKODA (University of Hradec Kralové)
Christopher TOWNSEND (Royal Bank of Canada)

* holder of a fellowship "L'Oréal-Unesco for Women in Science" which supports the conference
 


The non-official website of the conference  ­(maintained by S. Dugowson)
contains further materials provided by the speakers
­in connection with their talks and edited versions of the videos of the tutorials.


logos

Documents:
Contact Email: topos@ihes.fr Telephone: 0160926604
Go to day
  • lundi 23 novembre 2015
    • 08:30 - 17:00 Lundi 23 novembre
      • 08:30 Accueil des participants 30'
      • 09:00 Ouverture de la conférence par Olivia CARAMELLO 5'
      • 09:05 Pierre CARTIER 1h10'
        Conférence inaugurale
        Documents: Abstract pdf file
      • 10:15 André JOYAL 1h15'
        A crash course in topos theory : the big picture (I) 
        Documents: Programme pdf file
      • 11:30 Pause-café 15'
      • 11:45 André JOYAL 45'
        A crash course in topos theory : the big picture (II) 
      • 12:30 Lunch 1h30'
      • 14:00 Olivia CARAMELLO 1h15'
        Introduction to categorical logic, classifying toposes and the « bridge » technique  
        (I)  
        
        Documents: Programme pdf file
      • 15:15 Pause café 30'
      • 15:45 Olivia CARAMELLO 1h15'
        Introduction to categorical logic, classifying toposes and the « bridge » technique 
        (II)  
        
  • mardi 24 novembre 2015
    • 09:00 - 17:00 tuesday
      • 09:00 Café d'accueil 30'
      • 09:30 André JOYAL 1h15'
        A crash course in topos theory : the big picture (III) 
      • 10:45 Pause café 30'
      • 11:15 André JOYAL 1h15'
        A crash course in topos theory : the big picture (IV)
      • 12:30 Lunch 1h30'
      • 14:00 Olivia CARAMELLO 1h15'
        Introduction to categorical logic, classifying toposes and the « bridge » technique 
        (III) 
        
      • 15:15 Pause café 30'
      • 15:45 Olivia CARAMELLO 1h15'
        Introduction to categorical logic, classifying toposes and the « bridge » technique 
        (IV) 
  • mercredi 25 novembre 2015
    • 09:30 - 16:30 wednesday
      • 09:30 Welcome coffee 30'
      • 10:00 Michel VAQUIÉ 1h0'
        Théorie spectrale en géométrie relative
        Documents: Résumé pdf file
      • 11:00 Coffee break 15'
      • 11:15 Caterina CONSANI 1h15'
        On the geometry of the adele class space of Q
        Documents: Abstract pdf file
      • 12:30 Lunch 1h30'
      • 14:00 Mathieu ANEL 1h15'
        Toposes are commutative rings
        Documents: Abstract pdf file
      • 15:15 Simon HENRY 1h0'
        Operator algebras from toposes
        Documents: Abstract pdf file
      • 16:15 Pause café 15'
    • 16:30 - 18:00 Courtes Présentations - Amphi Motchane: test sub
      Courtes communications (30') en 2 sessions parallèles :  Amphithéâtre Léon Motchane
      • 16:30 Pietro POLESELLO 30' ( Amphithéâtre Léon Motchane )
        Proper stacks and costacks
        Documents: Abstract pdf file
      • 17:00 Jonas FREY 30' ( Amphithéâtre Léon Motchane )
        Realizability toposes as homotopy categories
        Documents: Abstract pdf file
      • 17:30 Zoran SKODA 30' ( Amphithéâtre Léon Motchane )
        Localizations and semiquantals
        Documents: Abstract pdf file
    • 16:30 - 18:00 Courtes Communications - CCMJS: test subtitle
      Courtes communications (30') en 2 sessions parallèles: Centre de conférences Marilyn et James Simons
      • 16:30 Guilherme-Frederico LIMA DE CARVALHO E SILVA 30'
        From Essential Inclusions to Local Geometric Morphisms
        Documents: Abstract pdf file
      • 17:00 Anna Carla RUSSO 30'
        Morita-equivalences for MV-algebras
        Documents: Abstract pdf file
      • 17:30 Christopher F. TOWNSEND 30'
        There are categories of ‘spaces' that are not categories of locales
        Documents: Abstract pdf file
  • jeudi 26 novembre 2015
    • 09:30 - 16:15 thursday
      • 09:30 Welcome coffee 30'
      • 10:00 Carlos SIMPSON 1h0'
        Pre-buildings as sheaves on the site of enclosures
        Documents: Abstract pdf file
      • 11:00 Coffee break 15'
      • 11:15 Mike PREST 1h15'
        Model-theoretic imaginaries and localisation for additive categories
        Documents: Abstract pdf file
      • 12:30 Lunch 1h30'
      • 14:00 André JOYAL 1h15'
        New variations on the notion of topos
        Documents: Abstract pdf file
      • 15:15 Luca BARBIERI-VIALE 1h0'
        T-Motives
        Documents: Abstract pdf file
  • vendredi 27 novembre 2015
    • 09:30 - 16:30 friday
      • 09:30 Welcome coffee 30'
      • 10:00 Thierry COQUAND 1h0'
        Logic and topology
        Documents: Abstract pdf file
      • 11:00 Coffee break 15'
      • 11:15 Urs SCHREIBER 1h0'
        Synthetic prequantum field theory in a cohesive homotopy topos
        Documents: Abstract pdf file
      • 12:30 Lunch 1h30'
      • 14:00 Jean BÉNABOU 1h0'
        Very, almost, and so on, ... (when fragments of the language find their way into Topos Theory)
      • 15:15 General discussion 1h0'
      • 16:15 Coffee break 15'
    • 16:30 - 18:00 Courtes Communications - CCMJS: Courtes communications : CCMJS
      Courtes communications (30') en 2 sessions parallèles: Centre de conférences Marilyn et James Simons
      • 16:30 Ingo BLECHSCHMIDT 30'
        Using the internal language of toposes in algebraic geometry
        Documents: Abstract pdf file
      • 17:00 David Michael ROBERTS 30'
        Class forcing and topos theory
        Documents: Abstract pdf file
      • 17:30 Alex SIMPSON 30'
        Probability sheaves
        Documents: Abstract pdf file
    • 16:30 - 18:00 Courtes Présentations - Amphi Motchane: Courtes communications : Amphithéâtre Motchane
      Courtes communications (30') en 2 sessions parallèles :  Amphithéâtre Léon Motchane
      • 16:30 Matias I. DATA 30' ( Amphithéâtre Léon Motchane )
        A construction of 2-filtered bicolimits of categories with 2-fibrations
        
        Documents: Abstract pdf file
      • 17:00 Camell KACHOUR 30' ( Amphithéâtre Léon Motchane )
        Globular perspective for Grothendieck ∞-topos and Grothendieck (∞,n)-topos
        Documents: Abstract pdf file