This is a four day school at the PhD level. It will consist of lecture series by Mohamed Abouzaid (Columbia), , Joana Cirici (Barcelona), Alexander Suciu (Northeastern University), Craig Westerland (University of Minnesota), Hisham Sati (NYUAbu Dhabi) and Paolo Salvatore (Roma Tor Vergata).
The topics of the school will center around Topology and Geometry.
The first MIMS school was held in 2012 under the title "Operads and Configuration Spaces".
Organizing Commitee:
Sonia Ghorbal, Sadok Kallel, Paolo Salvatore, Hisham Sati,
Scientific Commitee:
Paolo Salvatore, Hisham Sati, Sadok Kallel
Sponsors:
MIMS, International Mathematical Union (IMU), Club of Innovation and Scientific Research (Dubai), GE2RI (Universite de Tunis).
Mohamed Abuzaid
Flow categories for symplectic topology
CohenJonesSegal introduced the notion of flow categoriesto construct homotopy types associated to Morse functions. In particular, they proved that the stable homotopy type of a manifold may be recovered from what they call a "framed flow category." I will revisit their construction, adapting it to the needs of symplectic topology, which requires considering Morse theory in the infinite dimensional setting. This is joint work with Andrew Blumberg.
Joana Cirici
Weights on cohomology and application to formality
Paolo Salvatore
Formality in Algebra and Topology
An algebraic structure (commutative algebra, operad..) with a differential is called formal if it is equivalent to its homology in the derived sense. Two related famous formality results are due to Kontsevich: the formality conjecture in deformation quantization and the formality of the little discs operad. We review the obstruction theory to formality in a general setting, and focus particularly on algebraic structures originating from topological spaces. Then we report on some recent nonformality results related to euclidean configuration spaces.
Hisham Sati
Twisted generalized cohomology and applications
Twisted forms of various generalized cohomology theories have been gaining prominence in recent years, both for mathematics as well as for applications in physics. We will survey this area, starting with twisted de Rham cohomology and twisted Ktheory, and then generalizing to more recently constructed theories such as twisted elliptic cohomology, twisted Morava Ktheory and Etheory, and twisted iterated algebraic Ktheory of the topological Ktheory spectrum. I will describe the construction of the latter theories and then give geometric/differential refinements of a few and present computational techniques, which will be illustrated with examples. We will also highlight connections to twisted higher tangential structures, such as String and higher structures. We end with applications (to physics), including Tduality as an isomorphism of twisted cohomology theories, fields as Chern characters of elements of such theories, and charges of branes as pushforwards.
Alex Suciu
Geometry and topology of cohomology jump loci
The cohomology jumping loci of a space come in two basic flavors: the characteristic varieties, which are the jump loci for homology with coefficients in rank 1 local systems, and the resonance varieties, which are the jump loci for the homology of cochain complexes arising from multiplication by degree 1 classes in the cohomology ring. The geometry of these varieties, and the interplay between them sheds new light on the topology of the original space and that of its abelian covers.
Craig Westerland
Arithmetic statistics and the homology of moduli spaces
Adnene Chergui (Short communication), Universite Houari Boumedienne, Alger
On LeviCivita's theorem for degenerate semiriemannian manifolds
Mehdi Nabil, Universite Cadi Ayyad, Marrakech.
Cohomology of coinvariant forms
Let M be a differentiable manifold and $\Gamma$ a group acting on M by diffeomorphisms. We call a $\Gamma$coinvariant form on M any linear combination of differential forms of the type $\omega\gamma^*\omega$ with $\omega\in\Omega^*(M)$ and $\gamma\in\Gamma$. The space of such forms is denoted $\Omega^*(M)_\Gamma$, it is a subcomplex of $(\Omega^*(M),d)$ we therefore write $H^p(\Omega^*(M)_\Gamma)$ for its $p$th cohomology group. We study the action of the group $\Gamma$ on the manifold M in various situations by observing the relationship of this newly introduced complex with the complex of $\Gamma$invariant forms on M; $\Omega^*(M)^\Gamma$ and the complex of diffenrential forms $\Omega^*(M)$ and illustrating the interplay between their respective cohomologies by means of direct sum decompositions or exact sequences, depending on the case of study. This eventually leads to some cohomological obstructions for the existence of certain group actions (Isometric actions or properly discontinuous actions). Travail en collaboration avec Abdelhak Abouqateb et Mohamed Boucetta.
913 July  9h10h20  10:5012h10  14h15h  15h1016h10  16h4517h45  
Monday 
Cirici  Coffe break  Suciu  lunch  Westerland  Abouzaid  Coffe break  Sati 
Tuesday 
Abouzaid  Cirici  lunch  Abouzaid  Suciu  Salvatore  
Wed. 
Suciu  Westerland  lunch 
Tunis visit: Bardo Museum

Tunis visit: Bardo Museum

19h30 Dinner Medina 

Thursday 
Westerland  Cirici  lunch  Sati  Salvatore 
Short coms: 1. A. Chergui 2. N. Mehdi 

Friday 
Guided Tour of Tunis or short trip 
Participant  Institution 

Mohammed Abouzaid  Columbia University 
Mouadh Akriche  IPEIBizerte 
Marwa Assili  FST 
Naoufel BATTIKH  Faculté des sciences de Tunis 
Aziz Ben Ouali  Institut préparatoire aux études d'ingénieurs de Monastir 
Marwa Bouali  Tunis El Manar University 
Mohamed Amine Boubatra  Faculty of science of Tunis 
Moez Bouzouita  institut préparatoire du kairouan 
Abdelkerim Chaabani  FST 
Esma Chelbi  école normale supérieure 
Adnene Chergui  Universite Boumedienne Alger 
Seifallah Cherif  IPEIManar 
Joana Cirici  University of Barcelona 
Abderraouf Dorai  TPEIELMANAR 
Moncef Ghazel  IPEIMANAR 
Sonia Ghorbal  Faculté des sciences de Tunis 
HASSINE Holia  FST 
saihi ines  Faculté des sciences de Tunis 
Nawal Irz  Faculté des Sciences de Tunis 
Hatem Issaoui  IPEIN 
Fatma Kadi  ENS KoubaAlgeria 
Sadok Kallel  American University of Sharjah 
soula maroi  facuté de science de sfax 
Mohammed El Amine Mekki  Université Mustapha Stambouli 
Mehdi Nabil  Cadi Ayyad University, Marrakesh 
Roberto Pagaria  SNS Pisa 
Andrea Pizzi  Roma Tor Vergata 
Alessio Ranallo  University Roma II, Tor Vergata 
Jammazi Refki  FST El Manar 
Chaabane REJEB  Institut préparatoire aux études d'ingénieurs El Manar 
HASNA RIAHI  ENIT 
Rhaiem Saber  FST 
Rebhi salem  FST 
Paolo Salvatore  Roma Tor Vergata 
Hisham Sati  New York University, Abu Dhabi 
Alexander Suciu  Northwestern University 
Walid Taamallah  IPEIEM 
Oumaima Tibssirte  Cadi Ayyad University, Marrakesh 
Marwa Troudi  Faculté des sciences de Tunis 
Craig Westerland  University of Minnesota 
Mhamdi Zeinab  Faculte de science Sfax 
safa zouari  institut préparatoire à l'étude scientifique et technologique 