Topos à l'IHES

Salle de Conférences Marilyn et James Simons (Le Bois-Marie)

Salle de Conférences Marilyn et James Simons

Le Bois-Marie

35, route de Chartres 91440 Bures-sur-Yvette

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.


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)
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.


  • Alain Connes
  • Alex Simpson
  • Alexander Gietelink Oldenziel
  • Ambroise Peugeot
  • Anatole Khelif
  • Andrea Gagna
  • Andrew Polonsky
  • André Joyal
  • Angel Israel Toledo
  • Anna Carla Russo
  • Anthony Bordg
  • Armajac Raventós i Pujol
  • Aurélien SAGNIER
  • Bruno Blind
  • Bruno Stonek
  • Bruno Vallette
  • Camell Kachour
  • Carlos Simpson
  • Carolina Rivera Arredondo
  • Caterina Consani
  • Charles ALUNNI
  • Christopher Townsend
  • Cyrus Cohier-Chevaux
  • Céline Loozen
  • Daniel Luckhardt
  • Danko Ilik
  • David Gepner
  • David Rabouin
  • David Roberts
  • Diana Catalina Ossa Orozco
  • Dimitris Scarpalezos
  • Domenico Ruoppolo
  • elisabeth vaugelade
  • Fabio Pasquali
  • Fabrizio Anella
  • Federico Zalamea
  • Francesco Meazzini
  • Frank Taipe
  • Frédéric Crozatier
  • Gabriel Catren
  • Georg Lehner
  • Guilherme Frederico Lima de Carvalho e Silva
  • henri lombardi
  • himanee arjunwadkar
  • Hugh Steele
  • Ingo Blechschmidt
  • Isar Stubbe
  • Jacqueline Zizi
  • Jean Benabou
  • Jean Petitot
  • Jean-Jacques szczeciniarz
  • Jeffrey Egger
  • Jonas Frey
  • Joost van Dijk
  • Juan-Pablo Vigneaux
  • Julien Page
  • Jun Maillard
  • Kenji Maillard
  • Laurence Honnorat
  • Laurent Lafforgue
  • Laurent Tsang
  • Luca Barbieri-Viale
  • Lucile Regourd
  • Lucius Schoenbaum
  • Luigi Lunardon
  • Marco Robalo
  • Marie Bjerrum
  • Mathieu Anel
  • Matias Data
  • Mauro Mantegazza
  • Maxim Kontsevich
  • Mehdi Zaidi
  • Michael Heather
  • Michael Lambert
  • Michael Wright
  • Michel Hilsum
  • Michel Lapidus
  • Michel Vaquié
  • Mijail Guillemard
  • Mikaël Monchicourt
  • Mike Prest
  • Ngo Quoc Hoan
  • Nicolás Canevali
  • Nicolás Ramírez Díaz
  • Ofer Gabber
  • Olivia Caramello
  • Omar Mohsen
  • Pablo Sanchez Ocal
  • Paul LESCOT
  • Paula Verdugo
  • Pierre Cagne
  • Pierre Cartier
  • Pierre Schapira
  • Pietro Polesello
  • Pol van Hoften
  • Rafaël Bocquet
  • Rehan MALAK
  • Robert Olivares
  • Samir Bouslamti
  • Sandra Mantovani
  • Serge Bouc
  • Shai Haran
  • Simon Henry
  • Snorre Harald Christiansen
  • Stefan Neuwirth
  • Stefano Guerrini
  • Stéphane Bailly
  • Stéphane Dugowson
  • Thierry Coquand
  • Urs Schreiber
  • Vincent Picouet
  • Yuri Sulyma
  • Zoran Skoda