Topos à l'IHES

23 nov. 2015, 08:30 → 27 nov. 2015, 19:30 Europe/Paris

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

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
 

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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.

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Poster poster-TOPOS_anglais.pdf

lundi 23 novembre

Lundi 23 novembre

1 Accueil des participants

2 Ouverture de la conférence par Olivia CARAMELLO

3 Pierre CARTIER

Conférence inaugurale

Abstract CARTIER.pdf

4 André JOYAL

A crash course in topos theory : the big picture (I)

Programme introductionJoyal.pdf

11:30 Pause-café

5 André JOYAL

A crash course in topos theory : the big picture (II)

12:30 Lunch

6 Olivia CARAMELLO

Introduction to categorical logic, classifying toposes and the « bridge » technique (I)

Programme IntroductionCaramello.pdf

15:15 Pause café

7 Olivia CARAMELLO

Introduction to categorical logic, classifying toposes and the « bridge » technique (II)

mardi 24 novembre

tuesday

09:00 Café d'accueil

8 André JOYAL

A crash course in topos theory : the big picture (III)

10:45 Pause café

9 André JOYAL

A crash course in topos theory : the big picture (IV)

12:30 Lunch

10 Olivia CARAMELLO

Introduction to categorical logic, classifying toposes and the « bridge » technique (III)

15:15 Pause café

11 Olivia CARAMELLO

Introduction to categorical logic, classifying toposes and the « bridge » technique (IV)

mercredi 25 novembre

wednesday

09:30 Welcome coffee

12 Michel VAQUIÉ

Théorie spectrale en géométrie relative

Résumé VAQUIE.pdf

11:00 Coffee break

13 Caterina CONSANI

On the geometry of the adele class space of Q

Abstract CONSANI.pdf

12:30 Lunch

14 Mathieu ANEL

Toposes are commutative rings

Abstract ANEL.pdf

15 Simon HENRY

Operator algebras from toposes

Abstract HENRY.pdf

16:15 Pause café

Courtes Communications - CCMJS: test subtitle

Courtes communications (30') en 2 sessions parallèles: Centre de conférences Marilyn et James Simons

16 Guilherme-Frederico LIMA DE CARVALHO E SILVA

From Essential Inclusions to Local Geometric Morphisms

Abstract LimaDeCarvalho.pdf

17 Anna Carla RUSSO

Morita-equivalences for MV-algebras

Abstract Russo.pdf

18 Christopher F. TOWNSEND

There are categories of ‘spaces' that are not categories of locales

Abstract Townsend.pdf

Courtes Présentations - Amphi Motchane: test sub

Courtes communications (30') en 2 sessions parallèles : Amphithéâtre Léon Motchane

19 Pietro POLESELLO

Proper stacks and costacks

Abstract Polesello.pdf

20 Jonas FREY

Realizability toposes as homotopy categories

Abstract Frey.pdf

21 Zoran SKODA

Localizations and semiquantals

Abstract Skoda.pdf

jeudi 26 novembre

thursday

09:30 Welcome coffee

22 Carlos SIMPSON

Pre-buildings as sheaves on the site of enclosures

Abstract C.simpson.pdf

11:00 Coffee break

23 Mike PREST

Model-theoretic imaginaries and localisation for additive categories

Abstract Pest.pdf

12:30 Lunch

24 André JOYAL

New variations on the notion of topos

Abstract JOYAL.pdf

25 Luca BARBIERI-VIALE

T-Motives

Abstract BARBIERI.pdf

vendredi 27 novembre

friday

09:30 Welcome coffee

26 Thierry COQUAND

Logic and topology

Abstract COQUAND.pdf

11:00 Coffee break

27 Urs SCHREIBER

Synthetic prequantum field theory in a cohesive homotopy topos

Abstract SCHREIBER.pdf

12:30 Lunch

28 Jean BÉNABOU

Very, almost, and so on, ... (when fragments of the language find their way into Topos Theory)

29 General discussion

16:15 Coffee break

Courtes Communications - CCMJS: Courtes communications : CCMJS

Courtes communications (30') en 2 sessions parallèles: Centre de conférences Marilyn et James Simons

30 Ingo BLECHSCHMIDT

Using the internal language of toposes in algebraic geometry

Abstract Blechschmidt.pdf

31 David Michael ROBERTS

Class forcing and topos theory

Abstract Roberts_abstract.pdf

32 Alex SIMPSON

Probability sheaves

Abstract SimpsonAlex.pdf

Courtes Présentations - Amphi Motchane: Courtes communications : Amphithéâtre Motchane

Courtes communications (30') en 2 sessions parallèles : Amphithéâtre Léon Motchane

33 Matias I. DATA

A construction of 2-filtered bicolimits of categories with 2-fibrations

Abstract Data.pdf

34 Camell KACHOUR

Globular perspective for Grothendieck ∞-topos and Grothendieck (∞,n)-topos

Abstract Kachour2.pdf