Events & Calendar

Conference in the honour of Said Zarati
Oct 26, 2016 to Oct 30, 2016

Location : IHET, Tunis, Tunisia

This is a conference in algebraic topology celebrating Said Zarati's 65th birthday.

It will take place at the Institut des Hautes Etudes Touristiques de SidiDhrif in Tunis.

Registration is now open.

About Said Zarati

Saïd Zarati is a mathematician, specializing in Algebraic Topology, who studied at Tunis El Manar University then at Paris-Sud University where he defended his "thèse d'Etat" under the supervision of Jean Lannes. Back to Tunisia, he was appointed "Maître de Conférences" (1984) then Professor at Tunis El Manar University (1999).

He is an internationally recognized expert in the theory of unstable modules over the Steenrod algebra whose growth was boosted at the beginning of the eighties by works on the Sullivan conjecture. In particular, using the interactions between this theory and commutative algebra, he proved in 1996, jointly with Dorra Bourguiba, the Landweber-Stong conjecture about the depth of certain rings of invariants.

Saïd Zarati has founded a research unit in algebraic topology at the Faculty of Sciences of Tunis (FST) and is today the head of the research laboratory LATAO. He has supervised several Masters and Ph.D. theses; and his students (from all academic levels) have widely acclaimed his teaching skills.

He was Chairman of the Department of Mathematics of the FST for quite a while and has always been very active within the Tunisian Mathematical Society of which he was a founding member.

Presentation Said Zarati

Saïd Zarati est un mathématicien, spécialisé en Topologie Algébrique, qui a été formé à l'Université de Tunis El Manar puis a continué ses études à l'Université Paris-Sud où il a soutenu sa Thèse d'Etat sous la direction de Jean Lannes. De retour en Tunisie, il a été nommé Maître de Conférences (1984) puis Professeur (1999) à l'Université de Tunis El Manar.

C'est un spécialiste internationalement reconnu de la théorie des modules instables sur l'algèbre de Steenrod dont le développement a été accéléré au début des années 80 par les travaux sur la conjecture de Sullivan ; en utilisant les interactions entre cette théorie et l'algèbre commutative il a notamment résolu en 1996, avec Dorra Bourguiba, la conjecture de Landweber-Stong concernant la profondeur de certains anneaux d'invariants.

Saïd Zarati a créé une Unité de Recherche en Topologie Algébrique à la Faculté des Sciences de Tunis et est aujourd'hui Directeur du Laboratoire de Recherche LATAO. Il a encadré plusieurs DEA et thèses ; ses étudiants (à tous les niveaux) ont unanimement salué ses compétences pédagogiques.

Il a été longtemps Directeur du Département de Mathématiques de la FST et a toujours été un membre très actif au sein de la Société Mathématiques de Tunisie dont il est un des membres fondateurs.

 

 

 
 

Organizing Commitee:
Dorra Bourguiba, Jean Lannes , Ines Saihi, Lionel Schwartz, Nadia Hmida.

Scientific Commitee:
Dorra Bourguiba, Jean Lannes , Ines Saihi, Lionel Schwartz, Nadia Hmida.

Sponsors:
MIMS, Latao, LAGA

  • Jaume Aguade (U.A. Barcelona)
  • Jean Barge (Paris 7)
  • Carles Broto (U.A. Barcelona)
  • Natalia Castellana (U.A. Barcelona)
  • François-Xavier Dehon  (Nice)
  • Vincent Franjou (U. Nantes)
  • Nguyen Dang Ho Hai (Hue)
  • Hans-Werner Henn (U. Strasbourg)
  • Nguyen Huu Viet Hung (Hanoi)
  • Najib Idrissi (Universite de Lille 1)
  • Sadok Kallel (A.U. Sharjah)
  • Paolo Salvatore (Roma II)
  • Frank Neumann (Leicester)
  • Geoffrey Powell (Angers)
  • Pierre Vogel (Paris 7)

 

Titles and Abstracts:

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Jaume Aguadé

Generalized invariants of reflection groups

The invariant theory of finite reflection groups in positive characteristic dividing the order of the group displays a series of phenomena which do not appear when the order of the group is a unit in the base field. Some of these phenomena are not yet well understood. Generalized invariants and stable invariants are two of these phenomena. They were defined by Kac in 1985 based on work of Demazure in 1973, to provide a purely Weyl group explanation of the mod p cohomology of the compact connected Lie groups. These generalized and stable invariants seem to be very hard to compute and they are only known in a few trivial cases. We will present some computations which cover all groups in rank two.

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Jean Barge

Sturm, Sylvester, Hermite

On rappellera les travaux  (datant du milieu du 19-ieme siècle) de Sturm et Sylvester qui expriment le nombre de racines réelles d’un polynôme ( à coefficients réels) dans un intervalle donné, en terme de signatures. Puis la méthode d’Hermite qui conduit à un résultat analogue. On expliquera d’une façon plus moderne pourquoi ces deux approches sont très liées.

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Carles Broto

Fusion systems, groups, partial groups and simplicial sets

Motivated by the theory of fusion systems, Chermak introduces the concept of partial group and locality. We take the point of view of the nerve of a partial group and explore the insight of the homotopy theory of simplicial sets. As an application we generalize a calculation by J. Lannes of the homotopy fixed points for the action of a finite $p$-group on the $p$-completed classifying space of a finite group in the context of fusion systems. This is joint work with Alex Gonzalez.

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Natalia Castellana

Complex representations of p-local finite and compact structures

If G is a finite group, the regular representation provides a faithful unitary embedding of G, that is, a monomorphism of G into a unitary group U(n). For compact Lie groups, this statement is proven as a consequence of the Theorem of Peter and Weyl on the density of irreducible characters in the space of continuos class functions.  Such a monomorphism induces a map between classifying spaces with nice properties and structural implications on the cohomology of classifying spaces of compact Lie groups.

When working at a prime p, there are homotopical analogues to classifying spaces of compact Lie groups. First the notion of p-compact group was defined by Dwyer and Wilkerson and later Broto, Levi and Oliver introduced the notion of fusion system at a prime p, and the corresponding classifying space for it.

In this talk I will go through the results obtained in several joint projects with different authors concerning the
existence/construction of unitary representations for fusion systems and its classifying spaces in an homotopical setting

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Cameron Crowe

Algebraic Structures with Structure Constants and Homotopical Algebra

Given a chain complex V, we may form the chain complex of multilinear operations on V with n inputs and m outputs, for any integers n=0,1,2,... and m=0,1,2,...  Operations with zero inputs and m outputs are choices of elements in the n-fold tensor product of V.  Operations with n inputs and 0 outputs are linear maps, bilinear pairings and so forth.  And operations with 0 inputs and 0 outputs are choices of constants in the ground field.  The collection of all these chain complexes of operations for all n and m we denote End(V), the space endomorphisms on V.  The space of endomorphisms on V is an algebra under composition, permutation of inputs and outputs, tensor product and so on.  We may consider abstract algebras of operations at the level End(V) and form the category of such objects.

The idea of a kind of algebra structure may be encoded in an abstract algebra, P, of operations, and algebra structures of type P on V are tantamount to representations of P, that is maps of algebras of operations P-->End(V). One can do homotopy theory in the category of algebras of operations.  Thus we can describe two algebra structures as being "homotopic" if their structure maps are homotopic.  We show, for example, that homotopic algebra structures have equal structure constants.  We can also transfer algebra structures on one chain complex to a second, chain homotopy equivalent chain complex such that the structure maps are equivalent in another sense.  This theory generalizes current theories involving algebras over operads, props, properads, cyclic operads and so forth by adding constants, pairings and so forth. 

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François-Xavier Dehon

Künneth formula for ordinary homology and the detection of homotopy classes of maps

The aim of my talk is to explain how ordinary homology with integer coefficients can be used to detect homotopy classes of maps whose source is the classifying space of some abelian group. The first obstacle to this program is the weakness of the Künneth formula.

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Vincent Franjou

Lannes' T Functor as Harish-Chandra restriction
(joint work with Nguyen Dang Ho Hai \& Lionel Schwartz)

Polynomial algebras over a prime field appear as cohomology of elementary abelian groups, and carry an action of the Steenrod algebra commuting with the action of square matrices by linear substitution of the variables. We study Lannes' T-functor on their Steenrod algebra summands in terms of modular representation of matrices."

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Nguyen Dang Ho Hai

Deligne-Lusztig characters and the action of Lannes' T-functor on injective unstable modules

The talk describes the eigenvalues and eigenvectors of the induced action of Lannes' T-functor on the Grothendieck ring of reduced injective unstable modules by using the Deligne-Lusztig characters of the general linear group.

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Hans-Werner Henn

On the mod-2 cohomology of general linear and orthogonal groups over finite
fields of odd characteristic

(joint work with Jean Lannes)

Let K be a finite field of odd characteristic. We will discuss the mod-2 cohomology of the semidirect product
GL_n(K)\rtimes Z/2 with Z/2 acting on GL_n(K) via sending a matrix to the inverse of its tranposed matrix.
Understanding this cohomology as an unstable algebra over the Steenrod algebra is closely related to
constructions appearing in the work of Lannes and Zarati on derived functors of destabilization in the 1980's.

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Nguyen Huu Viet Hung

The generalized algebraic conjecture on spherical classes and the Lannes-Zarati homomorphism

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Najib Idrissi

The Lambrechts–Stanley Model of Configuration Spaces
 
We prove the validity over ℝ of a CDGA model of configuration spaces for simply connected manifolds with vanishing Euler characteristic, answering a conjecture of Lambrechts–Stanley. We get as a result that the real homotopy type of such configuration spaces only depends on a Poincaré duality model of the manifold. We moreover prove that our model is compatible with the action of the Fulton–MacPherson operad when the manifold is framed, by relying on Kontsevich’s proof of the formality of the little disks operads. We use this more precise result to get a complex computing factorization homology of framed manifolds.

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Sadok Kallel

On the topology of complements of diagonal arrangements

For X a connected finite simplicial complex we consider the space D of configurations of $n$ ordered points of X such that no d+1 of them are equal, and B the analogous space of configurations of unordered points. These reduce to the standard configuration spaces of distinct points when d=1. We describe the homotopy groups of D (resp. B) in terms of the homotopy (resp. homology) groups of X through a range which is generally sharp. It is noteworthy that the fundamental group of the configuration space B abelianizes as soon as we allow points to collide (i.e. d greater than 2). This is joint work with Ines Saihi.

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Frank Neumann

Spectral sequences for Hochschild cohomology and graded centers of differential graded categories

The Hochschild cohomology of a differential graded algebra or more generally of a differential graded category admits a natural map to the graded center of its derived category: the characteristic homomorphism.  We interpret it as an edge homomorphism in a spectral sequence. This gives a conceptual explanation of the possible failure of the characteristic homomorphism to be injective or surjective. To illustrate this, we will discuss several examples from geometry and topology, like modules over the dual numbers, coherent sheaves over algebraic curves, as well as examples related to free loop spaces and string topology. This is joint work with Markus Szymik (NTNU Trondheim).

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Geoffrey Powell

Essential extensions, the nilpotent filtration and the Arone-Goodwillie tower

The aim of this talk is to study spaces which have reduced mod 2 cohomology which is nilpotent by using the spectral sequence associated to the Arone-Goodwillie tower for iterated loop space functors. For example, this provides information upon the first two non-trivial layers of the nilpotent filtration of the cohomology, since the homological algebra of the category of unstable modules localized away from nilpotents forces a non-trivial differential.

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Paolo Salvatore

Formality of euclidean configuration spaces of 4 points in characteristic 2.

We address the question of formality of 4 point configuration space in R^n over F_2 in the sense of cochain DGA. For n>3 the space is intrinsically formal. For n=2 the space is not formal, and for n=3 it is formal. Both computations were done by obstruction theory using MATLAB software. We comment on the non-trivial algorithms implemented.

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Pierre Vogel

Localisations en algèbre et en topologie

La classification des plongements en codimension 2 entre variétés différentiables fait intervenir des notions de localisation en topologie algébrique et en algèbre. En particulier, il apparait dans cette classification des groupes de chirurgie d'un anneau $A$ qui est le localisé (au sens de Cohn) d'un anneau de groupe $Z[G]$, $G$ etant le groupe fondamental d'un certain espace. Malheureusement, le localisé d'un tel anneau de groupe est en général très difficile à décrire.   Dans cet exposé on donnera une description complète du localisé de $Z[G]$
lorsque $G$ est un groupe fini et on montrera une relation précise entre cette localisation d'anneau et la localisation de certain espaces.
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Les conferences Vendredi et Samedi commencent plus tot, a 8H50
 

   9:00  10-10:50  

11:20-

12:10

   14:00  15h00    16h00

 Wednesday

9h45
Ouverture
Jean   Barge  lunch  Franjou Hai    Powell

 Thursday

 Aguade    Castellana   Broto  lunch  Kallel Idrissi    Salvatore

 Friday

Hung   Henn   Dehon  lunch        

 Saturday

 Crowe  Neumann   Vogel  lunch        
List of participants to this conference
Oct 26, 2016 to Oct 30, 2016

Participant Institution
RIAHI Abdessalem fst
Jaume Aguade U. A. Barcelona
Mouadh Akriche IPEI Bizerte, université de Carthage
abbassi arwa Université de Kairouan
Jean Barge Paris 7
Aziz Ben Ouali Université de Monastir
Dorra Bourguiba FST
moez bouzouita IPEIK
Carles Broto U. A. Barcelona
Natalia Castellana U. A. Barcelona
Cameron Crowe City University of New York
Francois-Xavier Dehon U. de Nice
Vincent Franjou U. de Nantes
Islam GARBOUJ Université de Tunis el Manar
Moncef Ghazel IPEIM
Sonia Ghorbal Faculté des Sciences de Tunis
Paul Goerss Northwestern U.
Nguyen Dang Ho Hai Hue
Holia HASSINE facullté des sciences de tunis
Hans-Werner Henn U. Strasbourg
Nguyen H.V Hung Hanoi
Nejib Idrissi Universite de Lille 1
Sadok Kallel AUS
Saïma Khenissy ISBST, Université de la Manouba
Jean Lannes University of Paris 8
Ncib Lotfi ENIT
Mohammed El Amine Mekki Université d'Oran 1
Rafed Moussa Ecole Polytechnique de Tunisie
Hmida Nadia INSAT-Université de Carthage
Frank Neumann U. Leicester
Le Chi Quyet NGUYEN U. Angers
Hélène Pérennou Université de Nantes
Geoffrey Powell U. Angers
Chaabane REJEB Institut préparatoire aux études d'ingénieurs El Manar
Ines Saihi Université de Tunis ENSIT
Paolo Salvatore University of Roma II
Nabil Sayari Université de Moncton
kossentini sayed fst
Lionel Schwartz Universite de Paris 13
Abdessatar Souissi IPEST
Walid Taamallah IPEIB
Faouzi THABET ISSAT Gabès.Tunisia
Pierre Vogel Paris 7
Saïd Zarati F S. Tunis
Contact
Email : secretary@mims.tn