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. **