June 2011

In June 2011 the Archive plans to record the following

Monday 30th  May – Friday 3rd June 2011

Rencontres with Jean BENABOU

Followed by

Friday 3rd June – Saturday 5th June 2011

3rd-4th JUNE 2011 ENS Paris Salle Henri CARTAN

Colloquium in Honour of Jean BENABOU

Category Theory Yesterday Today (and Tomorrow?) :
A Colloquium in Honour of Jean Benabou

A Colloquium : “Category Theory : Yesterday, Today and Tomorrow” sponsored by The Archive Trust for Mathematical Sciences and Philosophy together with The Categories en Fondements Programme of The Universite Paris 7 Denis Diderot and the Institut Mathematiques de Jussieu took place in The Salle Henri Cartan at The Ecole Normale Superieure Paris on Friday 3rd and Saturday 4th June 2011.

This event was intended to honour Professor Jean Benabou as he entered his 80th Year and to be a reflection and celebration of his many contributions, in particular to the Theory of Categories, during an active and continuing research career already spanning over 50 years.

The Colloquium was  preceded by a series of Rencontres/Discussions between Professsor Benabou and a panel of his mathematical colleagues which which took place between the afternoon of Monday 30th May and the morning of Friday 3rd June. Attendance at these Rencontres was by invitation.

The Agenda for these Rencontres/Discussions will shortly be added to this page and edited Transcripts of the Discussions and extracts from the recordings will also be made available here in due course.

Important Acknowledgement : The Archive Trust and The Colloquium Organiser wish to offer particular thanks and grateful acknowledgement to The Seminaire de Logique Categorique at the Institut Mathematique Jussieu and in particular to  Dr Paul-Andre MELLIES, without whose indispensable aid and support – both financial and adminsitrative – the Colloquium would not have been possible.

THE PROGRAM of The Colloquium was as follows

VENUE : Salle Henri Cartan, Department of Mathematics, Ecole Normale Superieure 45 Rue D’Ulm, Paris 75005

Links to the recordings of the Talks below and to notesof the speakers presentations (or copies of overheads where used) will be operational on this page shortly.

Further Note : Professor Francois CHARGOIS (Universite Nancy 2, Archives Henri Poincare) and Professor Christian HOUZEL (CNRS) were prevented by illness from speaking at the Colloque. The Text of Professor CHARGOIS’s Talk entitled “BOURBAKI, GROTHENDIECK ET LA THEORIE DES CATEGORIES” was read into the Record of the Colloquium and will appear in the online record of the Proceedings below in due course.

We wish both Professor Chargois and Professor Houzel a swift and complete recovery.

FRIDAY 3rd June 2011

9:30 AM : Welcome and Introductory Remarks

9:45 – 10:45 AM :

Professor Pierre CARTIER (IHES, CNRS) :

TITLE :  GROUPOIDES HIER ET AUJOURD HUI

RESUME : Les groupoïdes ont été inventés par Brandt vers  1930 , à l’occasion d’un problème d’arithmétique : généralisation de la théorie des idéaux de Dedekind au cas non commutatif . Prequ’aussitôt , Reidemeister à utilisé cette notion pour introduire le “groupoïde fondamental (de Poincaré) d’un espace topologique” . Ehresmann a utilisé les groupoïdes de Lie dans sa construction des espaces fibrés , suivi peu de temps plus tard par Grothendieck dans sa théorie des espaces fibrés à faisceau structural . La définition usuelle d’un groupoïde comme une catégorie dans laquelle toutes les flèches sont inversibles est trop pauvre , à moins de considérer des groupoïdes enrichis dans une catégorie (notion due à Benabou) . Je décrirai les multiples développement récents , allant des feuilletages à la théorie de Galois , d’une théorie en plein développement .

Click here for link to Recording of Prof. CARTIER’s Talk

plus here for Notes of Presentation

—oOo—

10: 45 – 11:45 AM :

Professor Rene Guitart (Univ. Paris 7 Denis Diderot)

Title :  DISTRIBUTEURS ET CARRES EXACTS, AVEC APPLICATIONS A LA COHOMOLOGIE

Abstract :

La bonne gestion du calcul des fonctions a lieu au sein du calcul des relations
binaires, et le calcul de la composition des fonctions est un sous-produit de
celui des relations,
lui-même effectivement pratiqué par produits fibrés de spans représentants
lesdites relations. De même, le calcul des foncteurs est à concevoir au sien
des distributeurs et du calcul de leur composition, dans la bicatégorie ainsi
constituée. Le point clé que nous voulons mettre en relief est que la
composition effective de distributeurs se fera naturellement par produit exact
de spans, c’est-à-dire en utilisant au lieu de carrés produits fibrés des carrés exacts.

Ainsi les carrés exacts sont à comprendre comme des présentations de
compositions de distributeurs ; et, dans l’autre sens, les distributeurs
apparaissent aussi comme classe d’équivalence de spans modulos des carrés
exacts. Ensuite nous expliquerons comment les carrés exacts servent à définir
l’homologie d’une 0-suite, comment les distributeurs et les carrés exacts
servent en théorie de la forme, dans l’analyse de diverses cohomologies, pour  la définition en générale des théories de cohomologie.

Click here for link to Recording of Prof. GUITART’s Talk

plus here for Notes of Presentation

—oOo—

11:45 – 12:00 : Pause

—oOo—

12:00 – 1:00 PM  :  Professor Dominique  BOURN (Universite de Littoral, Calais)

“Protomodularité et fibration des points”

Abstract :

Dès son article princeps sur ce qui allait devenir la notion de
catégorie abélienne (Duality forgroups Bull.AMS 1950), Mac-Lane soulignait
la nécessité d’aller au-delà du cas additif/abélien et de trouver un
axiome simple qui permettrait de conceptualiser de façon uniforme les
propriétés de la catégorie des groupes, des anneaux, des  K-algèbres etc.
Il indiquait alors l’obtention des isomorphismes de Noether comme un bon
test de réussite de ce genre de conceptualisation. C’est ce que fait
précisément la notion de catégorie protomodulaire.

Une des façons de l’introduire est de le faire via la «fibration des
points» qui se révèle avoir, par ailleurs, une remarquable puissance
classificatrice puisqu’elle permet de caractériser les catégories
additives, essentiellement affines, arithmétiques, les catégories de
Mal’cev, naturellement Mal’cev, de Gumm, protomodulaires et fortement
protomodulaires.

Click here for link to Recording of Prof. BOURN’s Talk

plus here for Notes of Presentation (Incomplete)

—oOo—

1.00 – 2: 30:PM : Lunch Interval

—oOo—

2:30 – 3:30 PM : Professor Thomas STREICHER (Darmstadt)

Title : FIBERED THEORY of GEOMETRIC MORPHISMS

Abstract :

Geometric morphisms were introduced originally by analogy with
continuous maps and locale morphisms. But as pointed out by Jean
Benabou in his Montreal lectures 1974 their definition can be
motivated in terms of “good” properties of fibrations. Later in
J.-L. Moens’ Thesis (1982) there was established a 1-1-correspondence
between geometric morphisms and so-called geometric fibrations.

After revisiting this fibered theory of geometric morphisms we
consider generalisations which allow one to formulate the theory of
triposes (Hyland et.al. around 1982) in more geometric terms. This
allows one to reformulate an open problem in the theory of triposes in
more elementary terms.

Click here for link to Recording of Prof. STREICHER’s Talk

plus here for Notes of Presentation

—oOo—

3:30 – 4:30 PM : Professor Andree C. EHRESMANN (Amiens)

Title :  DES ESPECES DE STRUCTURES LOCALES AUX DISTRUCTURES ET SYSTEMES GUIDABLES

Abstract :

Le premier article original que Jean Benabou a publié (en 1957) portait
sur les treillis locaux, reflétant son intérêt pour les travaux de Charles
Ehresmann sur les structures locales et les topologies sans points.
Je parlerai brièvement de ces travaux de Charles, et en particulier de son
important article de 1957 où il définit le cadre catégorique des espèces de
structures locales ; il y démontre le “Théorème d’élargissement complet” d’une
espèce de structures locales, dont la preuve unit une sorte d’extension de Kan à
un théorème de faisceau associé sur une “catégorie locale”.
En imitant les méthodes utilisées dans cet article, j’ai introduit (dans
ma thèse en 1962) la notion de “distructure” qui donne un cadre catégorique pour
l’étude des “fonctions généralisées”. Je l’exposerai en termes plus modernes et
montrerai comment elle permet de retrouver les distributions de Schwartz, de
manière à pouvoir définir des distributions sur des variétés de dimension
infinie. Les distructures ont des applications aux problèmes de contrôle.

Click here for link to Recording of Prof. EHRESMANN’s Talk   (Not yet uploaded. Link not yet active)

plus here for Overheads of Presentation

—oOo—

7:30 PM : Colloquium Dinner

—oOo—

SATURDAY 4th June 2011

9:45  – 10: 45 AM :  Professor Martin HYLAND (Univerity of Cambridge)

Title :   KLEISLI BICATEGORIES

The importance of the notion of Bicategory is widely
recognised. It has many applications and points the way
to higher category theory. Kleisli Bicategories give a setting for many sophisticated mathematical
notions. A survey of these examples illustrates the
significance of the choices made in Jean Benabou’s
Introduction to Bicategories.

Click here for link to Recording of Prof. HYLAND’s Talk   (Not yet uploaded. Link not yet active)

plus here for Notes of his Presentation and related documentation

—oOo—

10 : 45 AM : Pause

—oOo—

11: 00- 11.40 : Jacques ROUBAUD :  (Working) Title : REMEMBRANCE OF CATEGORIES’ PAST

Personal Recollections and reminiscences of Jean Benabou (En Francais)

Click here for link to Recording of  Jacques ROUBAUD’s Talk   (Not yet uploaded. Link not yet active)

—oOo—

11:45 – 1:30 PM : Lunch Interval

—oOo—

1: 30 – 2:30 PM : Professor Andre JOYAL (UQUAM)

Title :  UNIVERSAL  FIBRATIONS

Abstract:

A universal (minimal) Kan fibration was recently constructed by Voevodsky to
model Martin-Lof type theory. We shall construct a universal left fibration
and a universal Grothendieck fibration between quasi-categories.

Click here for link to Recording of Prof.JOYAL’s Talk   (Not yet uploaded. Link not yet active)

plus here for Notes of his Presentation and related documentation

—oOo—

2:30  PM :  Professor Jean BENABOU

Title :  A NEW APPROACH TO THE NOTION OF “BEING CARTESIAN”

Abstract:

Cartesian functors and maps were introduced by Grothendieck in
1960-61 for prefibrations and fibrations. Since then they have been studied
essentially only in the case of fibrations.
I shall present general definitions covering many other situations, which reduce to the classical ones in the previous cases, and give important examples which do not fit in the classical setting, and shall prove many results which were not known even in the case of fibrations.
Some of these results need assumptions, much weaker than fibrations or even
prefibrations, namely prefoliations and foliations, which I shall introduce and study briefly, with a focus on examples and counter examples.

Followed by Discussion

Click here for link to Recording of Prof. BENABOU’s Talk   (Not yet uploaded. Link not yet active)

plus here for Notes of his Presentation and related documentation

—oOo—

5:00  PM : Closure of The Colloquium.

—oOo—

Thursday 2nd June 2011

University Paris 7 Denis Diderot

First Meeting of June 2nd-30th 2011 Program of PHILMATH INTERSEM

Theme of 2011 Program : The Notions of Simplicity and Complexity of Proof

2011 Program of Seminars organised within the Framework of The Ideals of Proof Program and Chair D’Excellence (Prof. Mic DETLEFSEN, University of Paris 7 and University of Notre Dame USA)

See also separate section of Archive Catalogue for Ideals of Proof Program events for details of this program and of the 2010 PhilMath Intersem Program.

2nd June 2011  14:00 hrs Univ Paris 7 Denis Diderot.  Batiment Condorcet Salle 454A Klee

Speakers :

Prof Mic DETLEFSEN : “Complexities of Proof”

Click here for link to recording

Prof. Timothy McCARTHY: “Normativity and Mechanism”

Click here for link to recording

Click here for link to accompanying text/overheads/notes

Prof. Andrew ARANA : Towards a measure of the difficulty of following proofs”

Click here for link to recording

Click here for link to accompanying text/overheads/notes

—oOo—

Friday 3rd June 2011

Bristol University : 9 Woodlands Road Bristol, England.

Bristol University Philosophy Department Departmental Seminar Speaker :

Frank ARTZENIUS

Title : To be Advised.

—oOo—

Monday 6th June 2011

Second Meeting of June 2nd-30th 2011 Program of PHILMATH INTERSEM

Theme of 2011 Program : The Notions of Simplicity and Complexity of Proof

14: 00 – 18:00 hrs Conference Room, MSH Lorraine,  91 Avenue de La Liberation, Nancy, France

Speaker :

Prof. John STILLWELL  :  “Ideal Elements in Geometry”

Click here for link to recording of Talk

Click here for link to accompanying text/overheads/notes

—oOo—

Wednesday 8th June 2011

Third Meeting of June 2nd-30th 2011 Program of PHILMATH INTERSEM

Theme of 2011 Program : The Notions of Simplicity and Complexity of Proof

14: 00 – 18:00 hrs Conference Room, MSH Lorraine,  91 Avenue de La Liberation, Nancy, France

Speaker :

Prof. John STILLWELL  :  “Ideal Elements in Number Theory, Analysis and Algebraic Geometry”

Click here for link to recording of Talk  (This recording is unfortunately incomplete)

Click here for link to accompanying text/overheads/notes

—oOo—

Wednesday 8th June 2011

Institut de Mathematique de JUSSIEU

175 Rue du Chevalaret Paris Salle 7 D 01

Groupe de Travail : ALGEBRE ET TOPOLOGIE HOMOTOPIQUES

LECTURE IV of A Series of Lectures by Professor Andre JOYAL (UQUAM)

INTRODUCTION TO QUASI-CATEGORIES IV

Click here for Link to recording of Talk

Click here for Link to Speakers Overheads

 

—oOo—

Thursday 9th June 2011

University of Paris 7  Paris-Diderot Bat. Condorcet  Salle 612B Klein

REHSEIS/SPHERE Seminar “Histoire des Sciences, Histoire du Texte”  (Convenor Karine CHEMLA)

Details of program TBA

—oOo—

Friday 10th June 2011

Bristol University : 9 Woodlands Road Bristol, England.

Bristol University Philosophy Department Departmental Seminar Speaker :

Natalie GOLD (Edinburgh) Title :

To be Advised.

—oOo—

Friday 10th June 2011

Fourth Meeting of June 2nd-30th 2011 Program of PHILMATH INTERSEM

Theme of 2011 Program : The Notions of Simplicity and Complexity of Proof

14: 00 – 18:00 hrs : Batiment Condorcet Universite Paris 7 Diderot Salle Klimt 366a

Speakers :

Dr Jeff KETLAND (Munich) “Speed-up, Explanation and Indispensability”

Click here for link to recording of Talk

Click here for link to accompanying text/overheads/notes

—oOo—

Dr Richard PETTIGREW (Bristol) : “Ketland and the epistemological consequences of speed-up”

Click here for link to recording of Talk

Click here for link to accompanying text/overheads/notes

—oOo—

Tuesday 14th June 2011

Fifth Meeting of June 2nd-30th 2011 Program of PHILMATH INTERSEM

Theme of 2011 Program : The Notions of Simplicity and Complexity of Proof

14: 00 – 18:00 hrs : Batiment Condorcet Universite Paris 7 Diderot Salle Klimt 366a

Speakers :

Prof Kevin KELLY : “A Topological Theory of Simplicity and Its Connection with Truth”

(Prof Kelly’s talk was unfortunately not recorded)

Prof. Pierre CARTIER (CNRS and IHES) : “On  “Monstrous” Proofs and what we should say about them”

Click here for link to recording of talk

Click here for link to accompanying text/overheads/notes

—oOo—

Tuesday 14th June – Friday 17th June 2011

1. Laboratoire APC (Astrophysique Partiucles et Cosmologie) University Paris
International Workshop on Cosmological Frontiers in Fundamental Physics

A Workshop jointly organised by the Laboratoire APC of Paris 7, The Permiter Institute of Canada and The International Solvay Institute (Brussels, Belgium)

The purpose of this Workshop is to enable leading researchers to discuss and exchange ideas on recent developments at the interface of modern cosmology and fundamental physics.  It is the Fifth in a series of joint workshops organised by the Perimeter Institute, The International Solvay Institutes and the Laboratoire APC.

Further information and full details of Program to be added.

—oOo—

2.  14 – 17 June 2011

University of Paris 7  Paris-Diderot Bat. Condorcet  Salle 612B Klein

REHSEIS/SPHERE Seminar in History and Philosophy of Mathematics 3 Day Colloquium :

Colloque Apollonius on Ancient Mathematics.  Details and Program to be added.

—oOo—

Wednesday 15th June 2011

Institut de Mathematique de JUSSIEU

175 Rue du Chevalaret Paris Salle 7 D 01

Groupe de Travail : ALGEBRE ET TOPOLOGIE HOMOTOPIQUES

LECTURE IV of A Series of Lectures by Professor Andre JOYAL (UQUAM)

INTRODUCTION TO QUASI-CATEGORIES V

Click here for Link to recording of Talk

Click here for Link to Speakers Overheads

—oOo—

Wednesday 15th – Saturday 18th June 2011

MATHEMATICS AND COMPUTATION IN MUSIC

A Series of Seminars and Events Organised by IRCAM

For Details of Program see  http://mcm2011.ircam.fr/drupal/files/MCM2011-Program.pdf

—oOo—

Thursday 16th – Friday 17th June 2011

REHSEIS – Universite Paris 7 Diderot – Batiment Condorcet Salle KLIMT 366A

Le Paradoxe des Jumeaux

Einstein’s Twin Paradox 1911 – 2011 A Centenary Conference

Day One Thursday 16th June 2011

Talk 1 : Jean-Marc LEVY-LEBLOND (University of Nice)

Peut-On deparadoxifier les Jumeaux ?

Click here for Link to recording of Talk

Click here for Link to Speakers Overheads

Further details of Program to be added

—oOo—

Thursday 16th June 2011

Sixth Meeting of June 2nd-30th 2011 Program of PHILMATH INTERSEM

Theme of 2011 Program : The Notions of Simplicity and Complexity of Proof

14: 00 – 18:00 hrs : Batiment Condorcet Universite Paris 7 Diderot Salle Klimt 3

Speakers :

Prof Gilles DOWEK (Paris 7) : “What could and what should a good notion of proof complexity measure ?”

Click here for link to recording of talk

Click here for link to accompanying text/overheads/notes

Guillaume BUREL (Paris 7) ; “The impact of theories on proof complexity”

Click here for link to recording of talk

Click here for link to accompanying text/overheads/notes

—oOo—

Monday 20th June 2011

University Paris 7 Denis Diderot 14:00 -18:00 hrs Batiment Condorcet. Salle Klee 366a

Seventh Meeting of June 2nd-30th 2011 Program of PHILMATH INTERSEM

Theme of 2011 Program : The Notions of Simplicity and Complexity of Proof.

Speaker : Prof : Michael RATHJEN : “On the (unreasonable?) effectiveness of ideal elements”

Click here for link to recording of talk

Click here for link to accompanying text, notes, overheads

—oOo—

Wednesday 22nd June 2011

Institut de Mathematique de JUSSIEU

175 Rue du Chevalaret Paris Salle 7 D 01

Groupe de Travail : ALGEBRE ET TOPOLOGIE HOMOTOPIQUES

LECTURE IV of A Series of Lectures by Professor Andre JOYAL (UQUAM)

INTRODUCTION TO QUASI-CATEGORIES VI

Click here for Link to recording of Talk

Click here for Link to Speakers Overheads

 

—oOo—

Thursday 23rd June 2011

University Paris 7 Denis Diderot 14:00 -18:00 hrs Batiment Condorcet. Salle Klee 366a

Eighth Meeting of June 2nd-30th 2011 Program of PHILMATH INTERSEM

Theme of 2011 Program : The Notions of Simplicity and Complexity of Proof

Speaker : Prof. Matthias BAAZ (Vienna) : “A Logical View on the simplicity of Proofs”

Click here for link to recording of talk

Click here for link to accompanying text, notes, overheads

—oOo—

25- 26 June 2011

The Centre for History and Philosophy of Science, Technology and Medicine (CHPSTM), University of Aberdeen, Scotland.

Workshop on ‘Quantum States: ontic or epistemic?’

Program of the CHPSTM workshop:

All talks held in MacRobert 268, University of Aberdeen main campus (Old Aberdeen).

Saturday 25 June:

14:00-14:45 Guido Bacciagaluppi (Aberdeen), Aspects of the ‘Bornian’ and ‘Schrödingerian’ views of the wavefunction

14:45-15:30 Jonathan Oppenheim (Cambridge) [via videolink?], title TBA

15:30-16:00 coffee 16:00-16:45

Jonathan Barrett (Royal Holloway, London), title TBA

16:45-17:30 Paul Busch (York), title TBA

17:30-18:15 Ilja Schmelzer (Banjul, Gambia) [TBC], The paleoclassical interpretation of quantum theory

19:00-ca. 22:00 dinner

—oOo—

Sunday 26 June: 09:15 -10:00

Alberto Montina (Perimeter Institute, Ontario), Ontological dimension and quantum information complexity

10:00-10:45 Hans Westman (Sydney), Two failed (?) attempts at digesting the indigestible wavefunction

10:45-11:15 coffee

11:15-12:00 Harald Atmanspacher (IGPP, Freiburg i. Br.), title TBA

12:00-12:45 Alexei Grinbaum (CEA, Saclay), What is epistemic besides quantum states?

12:45-14:45 lunch

14:45-15:30 Christopher Fuchs (Perimeter Institute, Ontario), A quantum state just IS a probability distribution

15:30-16:15 Jos Uffink (Utrecht), Entropy, entanglement and utility

Further details and links to recordings of Talks and speakers overheads to be added.

—oOo—

Sunday 26th June – Saturday 2nd July 2011

Isle of Skye Scotland Summer School on New Developments in Noncommutative Algebra and Its Applications

Program and further details to be added.

—oOo—

Monday 27th June 2011

University Paris 7 Denis Diderot 14:00 -18:00 hrs Batiment Condorcet. Salle Klee 366a

Ninth Meeting of June 2nd-30th 2011 Program of PHILMATH INTERSEM

Theme of 2011 Program : The Notions of Simplicity and Complexity of Proof

Speaker : Prof. Sam BAAS (UCSD) : “Expressibility and Derivability, and the complexity of Proofs”

Click here for link to recording of talk

Click here for link to accompanying text, notes, overheads

—oOo—

Monday 27th June – Tuesday 28th June 2011

Jerusalem, Israel

The Van Leer Institute

Cosmological and Conscious Time : An International Workshop

Further Details to be Added

—oOo—

Monday 27th June – Wednesday 29th June 2011

Robert Gordon University Aberdeen Scotland

Quantum Interactions 2011

An International Conference on the Applications of Quantum Theory to Artificial Intelligence Studies, Cognitive Science, Complex Systems Theory and Biology and Decision Theory

Further Details and Program to be added.

—oOo—

Wednesday 29th June 2011

Institut de Mathematique de JUSSIEU

175 Rue du Chevalaret Paris Salle 7 D 01

Groupe de Travail : ALGEBRE ET TOPOLOGIE HOMOTOPIQUES

LECTURE IV of A Series of Lectures by Professor Andre JOYAL (UQUAM)

INTRODUCTION TO QUASI-CATEGORIES VII

—oOo—

Thursday 30th June 2011

University Paris 7 Denis Diderot 14:00 -18:00 hrs Batiment Condorcet. Salle Klee 366a

Tenthand Final Meeting of June 2nd-30th 2011 Program of PHILMATH INTERSEM

Theme of 2011 Program : The Notions of Simplicity and Complexity of Proof

Speaker : Prof. Jeremy AVIGAD: “Simplicity, Extensionality and Functions as Objects”

Click here for link to recording of talk

Click here for link to accompanying text, notes, overheads

—oOo—

Many further events for June 2011 to be added.