Summer School and Conference on Real Algebraic Geometry and its Applications | (smr 1537)
    Go to day
    
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            08:30 - 10:00
        
        
        
            Registration
        
        
    
    Location: Main Building, Lobby - 
        
    
        08:30
    
    
        Registration
            1h30'        
    
    
 
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        08:30
    
    
        Registration
            1h30'        
    
    
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            14:00 - 14:15
        
        
        
            Opening
        
        
    
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        14:00
    
    
        Opening
            15'        
    
    
 
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        14:00
    
    
        Opening
            15'        
    
    
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            14:15 - 15:15
        
        
        
            Algebraic and semialgebraic sets (1)
        
        
    
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        14:15
    
    
        Algebraic and semialgebraic sets (1)
            1h0'        
    
    Speaker: M. Coste (Université de Rennes I, France) Material:  lecture notes lecture notes
 
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        14:15
    
    
        Algebraic and semialgebraic sets (1)
            1h0'        
    
    
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            15:15 - 15:30
        
        
        
            Break
        
        
    
    - 15:15 Break 15'
 
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            15:30 - 16:30
        
        
        
            Description of semialgebraic sets (1)
        
        
    
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        15:30
    
    
        Description of semialgebraic sets (1)
            1h0'        
    
    Speaker: C. Andradas Heranz (Universidad Complutense de Madrid, Spain) Material:  lecture notes lecture notes
 
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        15:30
    
    
        Description of semialgebraic sets (1)
            1h0'        
    
    
 
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            08:30 - 10:00
        
        
        
            Registration
        
        
    
    
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            09:00 - 10:00
        
        
        
            Topology of real algebraic curves (1)
        
        
    
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        09:00
    
    
        Topology of real algebraic curves (1)
            1h0'        
    
    Speaker: I. Itenberg (Université de Rennes I, France) Material:  lecture notes lecture notes
 
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        09:00
    
    
        Topology of real algebraic curves (1)
            1h0'        
    
    
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            10:00 - 10:15
        
        
        
            Break
        
        
    
    - 10:00 Break 15'
 
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            10:15 - 11:15
        
        
        
            Sums of squares, moments and optimization (1)
        
        
    
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        10:15
    
    
        Sums of squares, moments and optimization (1)
            1h0'        
    
    Speaker: M. Schweighofer (Université de Rennes I, France) Material:  transparencies transparencies
 
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        10:15
    
    
        Sums of squares, moments and optimization (1)
            1h0'        
    
    
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            11:15 - 11:30
        
        
        
            Break
        
        
    
    - 11:15 Break 15'
 
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            11:30 - 12:30
        
        
        
            Algebraic and semialgebraic sets (2)
        
        
    
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        11:30
    
    
        Algebraic and semialgebraic sets (2)
            1h0'        
    
    Speaker: M. Coste (Université de Rennes I, France) Material:  lecture notes lecture notes
 
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        11:30
    
    
        Algebraic and semialgebraic sets (2)
            1h0'        
    
    
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            12:30 - 14:00
        
        
        
            Lunch Break
        
        
    
    - 12:30 Lunch Break 1h30'
 
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            14:00 - 15:00
        
        
        
            Description of semialgebraic sets (2)
        
        
    
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        14:00
    
    
        Description of semialgebraic sets (2)
            1h0'        
    
    Speaker: C. Andradas Heranz (Universidad Complutense de Madrid, Spain) Material:  lecture notes lecture notes
 
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        14:00
    
    
        Description of semialgebraic sets (2)
            1h0'        
    
    
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            15:00 - 15:30
        
        
        
            Break
        
        
    
    - 15:00 Break 30'
 
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            15:30 - 16:30
        
        
        
            Topology of real algebraic curves (2)
        
        
    
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        15:30
    
    
        Topology of real algebraic curves (2)
            1h0'        
    
    Speaker: I. Itenberg (Université de Rennes I, France) Material:  lecture notes lecture notes
 
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        15:30
    
    
        Topology of real algebraic curves (2)
            1h0'        
    
    
 
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            09:00 - 10:00
        
        
        
            Topology of real algebraic curves (1)
        
        
    
    
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            09:00 - 10:00
        
        
        
            Sums of squares, moments and optimization (2)
        
        
    
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        09:00
    
    
        Sums of squares, moments and optimization (2)
            1h0'        
    
    Speaker: M. Schweighofer (Université de Rennes I, France) Material:  lecture notes lecture notes
 
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        09:00
    
    
        Sums of squares, moments and optimization (2)
            1h0'        
    
    
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            10:00 - 10:15
        
        
        
            Break
        
        
    
    - 10:00 Break 15'
 
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            10:15 - 11:15
        
        
        
            Algebraic and semialgebraic sets (3)
        
        
    
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        10:15
    
    
        Algebraic and semialgebraic sets (3)
            1h0'        
    
    Speaker: M. Coste (Université de Rennes I, France) Material:  lecture notes lecture notes
 
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        10:15
    
    
        Algebraic and semialgebraic sets (3)
            1h0'        
    
    
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            11:15 - 11:30
        
        
        
            Break
        
        
    
    - 11:15 Break 15'
 
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            11:30 - 12:30
        
        
        
            Description of semialgebraic sets (3)
        
        
    
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        11:30
    
    
        Description of semialgebraic sets (3)
            1h0'        
    
    Speaker: C. Andradas Heranz (Universidad Complutense de Madrid, Spain) Material:  lecture notes lecture notes
 
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        11:30
    
    
        Description of semialgebraic sets (3)
            1h0'        
    
    
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            12:30 - 14:00
        
        
        
            Lunch Break
        
        
    
    - 12:30 Lunch Break 1h30'
 
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            14:00 - 15:00
        
        
        
            Topology of real algebraic curves (3)
        
        
    
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        14:00
    
    
        Topology of real algebraic curves (3)
            1h0'        
    
    Speaker: I. Itenberg (Université de Rennes I, France) Material:  lecture notes lecture notes
 
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        14:00
    
    
        Topology of real algebraic curves (3)
            1h0'        
    
    
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            15:00 - 15:30
        
        
        
            Break
        
        
    
    - 15:00 Break 30'
 
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            15:30 - 16:30
        
        
        
            Sums of squares, moments and optimization (3)
        
        
    
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        15:30
    
    
        Sums of squares, moments and optimization (3)
            1h0'        
    
    Speaker: M. Schweighofer (Université de Rennes I, France) Material:  lecture notes lecture notes
 
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        15:30
    
    
        Sums of squares, moments and optimization (3)
            1h0'        
    
    
 
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            09:00 - 10:00
        
        
        
            Sums of squares, moments and optimization (2)
        
        
    
    
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            09:00 - 10:00
        
        
        
            Algebraic and semialgebraic sets (4)
        
        
    
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        09:00
    
    
        Algebraic and semialgebraic sets (4)
            1h0'        
    
    Speaker: M. Coste (Université de Rennes I, France) Material:  lecture notes lecture notes
 
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        09:00
    
    
        Algebraic and semialgebraic sets (4)
            1h0'        
    
    
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            10:00 - 10:15
        
        
        
            Break
        
        
    
    - 10:00 Break 15'
 
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            10:15 - 11:15
        
        
        
            Description of semialgebraic sets (4)
        
        
    
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        10:15
    
    
        Description of semialgebraic sets (4)
            1h0'        
    
    Speaker: C. Andradas Heranz (Universidad Complutense de Madrid, Spain) Material:  lecture notes lecture notes
 
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        10:15
    
    
        Description of semialgebraic sets (4)
            1h0'        
    
    
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            11:15 - 11:30
        
        
        
            Break
        
        
    
    - 11:15 Break 15'
 
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            11:30 - 12:30
        
        
        
            Sums of squares, moments and optimization (4)
        
        
    
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        11:30
    
    
        Sums of squares, moments and optimization (4)
            1h0'        
    
    Speaker: M. Schweighofer (Université de Rennes I, France) Material:  lecture notes lecture notes
 
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        11:30
    
    
        Sums of squares, moments and optimization (4)
            1h0'        
    
    
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            12:30 - 14:00
        
        
        
            Lunch Break
        
        
    
    - 12:30 Lunch Break 1h30'
 
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            14:00 - 15:00
        
        
        
            Topology of real algebraic curves (4)
        
        
    
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        14:00
    
    
        Topology of real algebraic curves (4)
            1h0'        
    
    Speaker: I. Itenberg (Université de Rennes I, France) Material:  lecture notes lecture notes
 
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        14:00
    
    
        Topology of real algebraic curves (4)
            1h0'        
    
    
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            15:00 - 15:30
        
        
        
            Break
        
        
    
    - 15:00 Break 30'
 
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            15:30 - 15:45
        
        
        
            Brief presentation of the Third World Academy of Sciences
        
        
    
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        15:30
    
    
        Brief presentation of the Third World Academy of Sciences
            15'        
    
    
 
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        15:30
    
    
        Brief presentation of the Third World Academy of Sciences
            15'        
    
    
 
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            09:00 - 10:00
        
        
        
            Algebraic and semialgebraic sets (4)
        
        
    
    
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            09:00 - 10:00
        
        
        
            Algebraic and semialgebraic sets (5)
        
        
    
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        09:00
    
    
        Algebraic and semialgebraic sets (5)
            1h0'        
    
    Speaker: M. Coste (Université de Rennes I, France) Material:  lecture notes lecture notes
 
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        09:00
    
    
        Algebraic and semialgebraic sets (5)
            1h0'        
    
    
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            10:00 - 10:15
        
        
        
            Break
        
        
    
    - 10:00 Break 15'
 
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            10:15 - 11:15
        
        
        
            Description of semialgebraic sets (5)
        
        
    
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        10:15
    
    
        Description of semialgebraic sets (5)
            1h0'        
    
    Speaker: C. Andradas Heranz (Universidad Complutense de Madrid, Spain) Material:  lecture notes lecture notes
 
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        10:15
    
    
        Description of semialgebraic sets (5)
            1h0'        
    
    
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            11:15 - 11:30
        
        
        
            Break
        
        
    
    - 11:15 Break 15'
 
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            11:30 - 12:30
        
        
        
            Sums of squares, moments and optimization (5)
        
        
    
    - 
        
    
        11:30
    
    
        Sums of squares, moments and optimization (5)
            1h0'        
    
    Speaker: M. Schweighofer (Université de Rennes I, France) Material:  lecture notes lecture notes
 
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        11:30
    
    
        Sums of squares, moments and optimization (5)
            1h0'        
    
    
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            12:30 - 14:00
        
        
        
            Lunch Break
        
        
    
    - 12:30 Lunch Break 1h30'
 
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            14:00 - 15:00
        
        
        
            Topology of real algebraic curves (5)
        
        
    
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        14:00
    
    
        Topology of real algebraic curves (5)
            1h0'        
    
    Speaker: I. Itenberg (Université de Rennes I, France) Material:  lecture notes lecture notes
 
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        14:00
    
    
        Topology of real algebraic curves (5)
            1h0'        
    
    
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            18:30 - 20:00
        
        
        
            Welcome, first contact
        
        
    
    Location: Adriatico Guest House (Terrace) - 
        
    
        18:30
    
    
        Welcome, first contact
            1h30'        
    
    
 
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        18:30
    
    
        Welcome, first contact
            1h30'        
    
    
 
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            09:00 - 10:00
        
        
        
            Algebraic and semialgebraic sets (5)
        
        
    
    
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            09:30 - 12:30
        
        
        
            Historic of RAGAAD, presentation of the various research groups
        
        
    
    Location: Adriatico Guest House Kastler Lecture Hall - 
        
    
        09:30
    
    
        Historic of RAGAAD, presentation of the various research groups
            3h0'        
    
    
 
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        09:30
    
    
        Historic of RAGAAD, presentation of the various research groups
            3h0'        
    
    
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            12:30 - 14:00
        
        
        
            Lunch Break
        
        
    
    Location: Adriatico Guest House Kastler Lecture Hall - 12:30 Lunch Break 1h30'
 
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            14:00 - 16:00
        
        
        
            Discussions about the network objectives, designation of a small working group in charge of the texts
        
        
    
    Location: Adriatico Guest House Kastler Lecture Hall - 
        
    
        14:00
    
    
        Discussions about the network objectives, designation of a small working group in charge of the texts
            2h0'        
    
    
 
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        14:00
    
    
        Discussions about the network objectives, designation of a small working group in charge of the texts
            2h0'        
    
    
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            16:00 - 16:30
        
        
        
            Break
        
        
    
    Location: Adriatico Guest House Kastler Lecture Hall - 16:00 Break 30'
 
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            16:30 - 17:00
        
        
        
            Espaces poids d'une algèbre de Malcev
        
        
    
    Location: Adriatico Guest House Kastler Lecture Hall - 
        
    
        16:30
    
    
        Espaces poids d'une algèbre de Malcev
            30'        
    
    Speaker: A. Koulibaly (University of Ouagadougou, Burkina Faso) 
 
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        16:30
    
    
        Espaces poids d'une algèbre de Malcev
            30'        
    
    
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            17:00 - 17:30
        
        
        
            Quasi-bigèbres de Lie et algèbres quasi-Batalin-Vilkovisky différentielles
        
        
    
    Location: Adriatico Guest House Kastler Lecture Hall - 
        
    
        17:00
    
    
        Quasi-bigèbres de Lie et algèbres quasi-Batalin-Vilkovisky différentielles
            30'        
    
    Speaker: M. Bangoura (University of Conakry, Guinea) 
 
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        17:00
    
    
        Quasi-bigèbres de Lie et algèbres quasi-Batalin-Vilkovisky différentielles
            30'        
    
    
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            17:30 - 18:30
        
        
        
            On classes of duo rings
        
        
    
    Location: Adriatico Guest House Kastler Lecture Hall - 
        
    
        17:30
    
    
        On classes of duo rings
            1h0'        
    
    Speaker: M. Sanghare (Université Cheikh Anta Diop de Dakar, Senegal) 
 
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        17:30
    
    
        On classes of duo rings
            1h0'        
    
    
 
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            09:30 - 12:30
        
        
        
            Historic of RAGAAD, presentation of the various research groups
        
        
    
    
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                - 
    
        
        
        
            09:00 - 09:30
        
        
        
            Extensions of partial operations and relations
        
        
    
    Location: Adriatico Guest House Kastler Lecture Hall - 
        
    
        09:00
    
    
        Extensions of partial operations and relations
            30'        
    
    Speaker: G. Kientega (University of Ouagadougou, Burkina Faso) 
 
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        09:00
    
    
        Extensions of partial operations and relations
            30'        
    
    
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            09:30 - 10:00
        
        
        
            Calculs différentiels sur des algèbres de dimension finie
        
        
    
    Location: Adriatico Guest House Kastler Lecture Hall - 
        
    
        09:30
    
    
        Calculs différentiels sur des algèbres de dimension finie
            30'        
    
    Speaker: A.B. Kpamegan (Université d'Abomey-Calavi, Cotonou, Bénin) 
 
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        09:30
    
    
        Calculs différentiels sur des algèbres de dimension finie
            30'        
    
    
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            10:00 - 10:30
        
        
        
            Differential algebra and applications
        
        
    
    Location: Adriatico Guest House Kastler Lecture Hall - 
        
    
        10:00
    
    
        Differential algebra and applications
            30'        
    
    Speaker: B. Sadik (University of Semlalia, Marrakech, Morocco) 
 
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        10:00
    
    
        Differential algebra and applications
            30'        
    
    
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            10:30 - 11:00
        
        
        
            Break
        
        
    
    Location: Adriatico Guest House Kastler Lecture Hall - 10:30 Break 30'
 
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            11:00 - 12:30
        
        
        
            Presentation by the working group of the synthesis of the discussions
        
        
    
    Location: Adriatico Guest House Kastler Lecture Hall - 
        
    
        11:00
    
    
        Presentation by the working group of the synthesis of the discussions
            1h30'        
    
    
 
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        11:00
    
    
        Presentation by the working group of the synthesis of the discussions
            1h30'        
    
    
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            12:30 - 14:00
        
        
        
            Lunch Break
        
        
    
    Location: Adriatico Guest House Kastler Lecture Hall - 12:30 Lunch Break 1h30'
 
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            14:00 - 14:30
        
        
        
            Algebraic structures in genetics
        
        
    
    Location: Adriatico Guest House Kastler Lecture Hall - 
        
    
        14:00
    
    
        Algebraic structures in genetics
            30'        
    
    Speaker: I. Katambe (University of Niamey, Niger) 
 
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        14:00
    
    
        Algebraic structures in genetics
            30'        
    
    
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            14:30 - 15:00
        
        
        
            Weak super-representations of Malcev super-algebras
        
        
    
    Location: Adriatico Guest House Kastler Lecture Hall - 
        
    
        14:30
    
    
        Weak super-representations of Malcev super-algebras
            30'        
    
    Speaker: M.-F. Ouedraogo (University of Ouagadougou, Burkina Faso) 
 
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        14:30
    
    
        Weak super-representations of Malcev super-algebras
            30'        
    
    
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            15:00 - 15:30
        
        
        
            Global analytic functions
        
        
    
    Location: Adriatico Guest House Kastler Lecture Hall - 
        
    
        15:00
    
    
        Global analytic functions
            30'        
    
    Speaker: F. Broglia (Università di Pisa, Italy) 
 
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        15:00
    
    
        Global analytic functions
            30'        
    
    
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            15:30 - 16:00
        
        
        
            Break
        
        
    
    Location: Adriatico Guest House Kastler Lecture Hall - 15:30 Break 30'
 
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            16:00 - 18:00
        
        
        
            Conclusions and official starting of the network
        
        
    
    Location: Adriatico Guest House Kastler Lecture Hall - 
        
    
        16:00
    
    
        Conclusions and official starting of the network
            2h0'        
    
    
 
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        16:00
    
    
        Conclusions and official starting of the network
            2h0'        
    
    
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            19:00 - 20:30
        
        
        
            Party
        
        
    
    Location: Main Building Cafeteria - 19:00 Party 1h30'
 
 
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            09:00 - 09:30
        
        
        
            Extensions of partial operations and relations
        
        
    
    
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            09:00 - 10:00
        
        
        
            Algorithms in real algebraic geometry (1)
        
        
    
    - 
        
    
        09:00
    
    
        Algorithms in real algebraic geometry (1)
            1h0'        
    
    Speaker: M.-F. Roy (Université de Rennes I, France) Material:  lecture notes lecture notes
 
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        09:00
    
    
        Algorithms in real algebraic geometry (1)
            1h0'        
    
    
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            10:00 - 10:15
        
        
        
            Break
        
        
    
    - 10:00 Break 15'
 
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            10:15 - 11:15
        
        
        
            Constrained optimization and quadratic mappings (1)
        
        
    
    - 
        
    
        10:15
    
    
        Constrained optimization and quadratic mappings (1)
            1h0'        
    
    Speaker: A. Agrachev (SISSA, Trieste, Italy) Material:  lecture notes lecture notes
 
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        10:15
    
    
        Constrained optimization and quadratic mappings (1)
            1h0'        
    
    
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            11:15 - 11:30
        
        
        
            Break
        
        
    
    - 11:15 Break 15'
 
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            11:30 - 12:30
        
        
        
            Geometry and computer vision (1)
        
        
    
    - 
        
    
        11:30
    
    
        Geometry and computer vision (1)
            1h0'        
    
    Speaker: Y. Yomdin (The Weizmann Ins. of Science, Rehovot, Israel) Material:  lecture notes lecture notes
 
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        11:30
    
    
        Geometry and computer vision (1)
            1h0'        
    
    
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            12:30 - 14:00
        
        
        
            Lunch Break
        
        
    
    - 12:30 Lunch Break 1h30'
 
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            14:00 - 15:00
        
        
        
            Applications of real algebraic geometry to computer-aided geometric design (1)
        
        
    
    - 
        
    
        14:00
    
    
        Applications of real algebraic geometry to computer-aided geometric design (1)
            1h0'        
    
    Speaker: L. Gonzalez-Vega (Universidad de Cantabria, Santander, Spain) Material:  transparencies transparencies
 
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        14:00
    
    
        Applications of real algebraic geometry to computer-aided geometric design (1)
            1h0'        
    
    
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            15:00 - 15:15
        
        
        
            Break
        
        
    
    - 15:00 Break 15'
 
- 
    
        
        
        
            15:15 - 16:45
        
        
        
            Computer Laboratory session
        
        
    
    Location: Computer Lab. (M) - 
        
    
        15:15
    
    
        Computer Laboratory session
            1h30'        
    
    
 
- 
        
    
        15:15
    
    
        Computer Laboratory session
            1h30'        
    
    
 
- 
    
        
        
        
            09:00 - 10:00
        
        
        
            Algorithms in real algebraic geometry (1)
        
        
    
    
- 
                
                - 
    
        
        
        
            09:00 - 10:00
        
        
        
            Algorithms in real algebraic geometry (2)
        
        
    
    - 
        
    
        09:00
    
    
        Algorithms in real algebraic geometry (2)
            1h0'        
    
    Speaker: M.-F. Roy (Université de Rennes I, France) Material:  lecture notes lecture notes
 
- 
        
    
        09:00
    
    
        Algorithms in real algebraic geometry (2)
            1h0'        
    
    
- 
    
        
        
        
            10:00 - 10:15
        
        
        
            Break
        
        
    
    - 10:00 Break 15'
 
- 
    
        
        
        
            10:15 - 11:15
        
        
        
            Polynomial system solving in the real case (1)
        
        
    
    - 
        
    
        10:15
    
    
        Polynomial system solving in the real case (1)
            1h0'        
    
    Speaker: F. Rouillier (Projet SPACES and Equipe Calfor, Paris, France) Material:  transparencies transparencies
 
- 
        
    
        10:15
    
    
        Polynomial system solving in the real case (1)
            1h0'        
    
    
- 
    
        
        
        
            11:15 - 11:30
        
        
        
            Break
        
        
    
    - 11:15 Break 15'
 
- 
    
        
        
        
            11:30 - 12:30
        
        
        
            Geometry and computer vision (2)
        
        
    
    - 
        
    
        11:30
    
    
        Geometry and computer vision (2)
            1h0'        
    
    Speaker: Y. Yomdin (The Weizmann Ins. of Science, Rehovot, Israel) Material:  lecture notes lecture notes
 
- 
        
    
        11:30
    
    
        Geometry and computer vision (2)
            1h0'        
    
    
- 
    
        
        
        
            12:30 - 14:00
        
        
        
            Lunch Break
        
        
    
    - 12:30 Lunch Break 1h30'
 
- 
    
        
        
        
            14:00 - 15:00
        
        
        
            Applications of real algebraic geometry to computer-aided geometric design (2)
        
        
    
    - 
        
    
        14:00
    
    
        Applications of real algebraic geometry to computer-aided geometric design (2)
            1h0'        
    
    Speaker: L. Gonzalez-Vega (Universidad de Cantabria, Santander, Spain) Material:  lecture notes lecture notes
 
- 
        
    
        14:00
    
    
        Applications of real algebraic geometry to computer-aided geometric design (2)
            1h0'        
    
    
- 
    
        
        
        
            15:00 - 15:15
        
        
        
            Break
        
        
    
    - 15:00 Break 15'
 
- 
    
        
        
        
            15:15 - 16:45
        
        
        
            Computer Laboratory session
        
        
    
    Location: Computer Lab. (M) - 
        
    
        15:15
    
    
        Computer Laboratory session
            1h30'        
    
    
 
- 
        
    
        15:15
    
    
        Computer Laboratory session
            1h30'        
    
    
 
- 
    
        
        
        
            09:00 - 10:00
        
        
        
            Algorithms in real algebraic geometry (2)
        
        
    
    
- 
                
                - 
    
        
        
        
            09:00 - 10:00
        
        
        
            Constrained optimization and quadratic mappings (2)
        
        
    
    - 
        
    
        09:00
    
    
        Constrained optimization and quadratic mappings (2)
            1h0'        
    
    Speaker: A. Agrachev (SISSA, Trieste, Italy) Material:  lecture notes lecture notes
 
- 
        
    
        09:00
    
    
        Constrained optimization and quadratic mappings (2)
            1h0'        
    
    
- 
    
        
        
        
            10:00 - 10:15
        
        
        
            Break
        
        
    
    - 10:00 Break 15'
 
- 
    
        
        
        
            10:15 - 11:15
        
        
        
            Polynomial system solving in the real case (2)
        
        
    
    - 
        
    
        10:15
    
    
        Polynomial system solving in the real case (2)
            1h0'        
    
    Speaker: F. Rouillier (Projet SPACES and Equipe Calfor, Paris, France) Material:  transparencies transparencies
 
- 
        
    
        10:15
    
    
        Polynomial system solving in the real case (2)
            1h0'        
    
    
- 
    
        
        
        
            11:15 - 11:30
        
        
        
            Break
        
        
    
    - 11:15 Break 15'
 
- 
    
        
        
        
            11:30 - 12:30
        
        
        
            Geometry and computer vision (3)
        
        
    
    - 
        
    
        11:30
    
    
        Geometry and computer vision (3)
            1h0'        
    
    Speaker: Y. Yomdin (The Weizmann Ins. of Science, Rehovot, Israel) Material:  lecture notes lecture notes
 
- 
        
    
        11:30
    
    
        Geometry and computer vision (3)
            1h0'        
    
    
- 
    
        
        
        
            12:30 - 14:00
        
        
        
            Lunch Break
        
        
    
    - 12:30 Lunch Break 1h30'
 
- 
    
        
        
        
            14:00 - 15:00
        
        
        
            Applications of real algebraic geometry to computer-aided geometric design (3)
        
        
    
    - 
        
    
        14:00
    
    
        Applications of real algebraic geometry to computer-aided geometric design (3)
            1h0'        
    
    Speaker: L. Gonzalez-Vega (Universidad de Cantabria, Santander, Spain) Material:  lecture notes lecture notes
 
- 
        
    
        14:00
    
    
        Applications of real algebraic geometry to computer-aided geometric design (3)
            1h0'        
    
    
- 
    
        
        
        
            15:00 - 15:15
        
        
        
            Break
        
        
    
    - 15:00 Break 15'
 
- 
    
        
        
        
            15:15 - 16:45
        
        
        
            Computer Laboratory session
        
        
    
    Location: Computer Lab. (M) - 
        
    
        15:15
    
    
        Computer Laboratory session
            1h30'        
    
    
 
- 
        
    
        15:15
    
    
        Computer Laboratory session
            1h30'        
    
    
 
- 
    
        
        
        
            09:00 - 10:00
        
        
        
            Constrained optimization and quadratic mappings (2)
        
        
    
    
- 
                
                - 
    
        
        
        
            09:00 - 10:00
        
        
        
            Constrained optimization and quadratic mappings (3)
        
        
    
    - 
        
    
        09:00
    
    
        Constrained optimization and quadratic mappings (3)
            1h0'        
    
    Speaker: A. Agrachev (SISSA, Trieste, Italy) Material:  lecture notes lecture notes
 
- 
        
    
        09:00
    
    
        Constrained optimization and quadratic mappings (3)
            1h0'        
    
    
- 
    
        
        
        
            10:00 - 10:15
        
        
        
            Break
        
        
    
    - 10:00 Break 15'
 
- 
    
        
        
        
            10:15 - 11:15
        
        
        
            Polynomial system solving in the real case (3)
        
        
    
    - 
        
    
        10:15
    
    
        Polynomial system solving in the real case (3)
            1h0'        
    
    Speaker: F. Rouillier (Projet SPACES and Equipe Calfor, Paris, France) Material:  transparencies transparencies
 
- 
        
    
        10:15
    
    
        Polynomial system solving in the real case (3)
            1h0'        
    
    
- 
    
        
        
        
            11:15 - 11:30
        
        
        
            Break
        
        
    
    - 11:15 Break 15'
 
- 
    
        
        
        
            11:30 - 12:30
        
        
        
            Geometry and computer vision (4)
        
        
    
    - 
        
    
        11:30
    
    
        Geometry and computer vision (4)
            1h0'        
    
    Speaker: Y. Yomdin (The Weizmann Ins. of Science, Rehovot, Israel) Material:  lecture notes lecture notes
 
- 
        
    
        11:30
    
    
        Geometry and computer vision (4)
            1h0'        
    
    
- 
    
        
        
        
            12:30 - 14:00
        
        
        
            Lunch Break
        
        
    
    - 12:30 Lunch Break 1h30'
 
- 
    
        
        
        
            14:00 - 15:00
        
        
        
            Applications of real algebraic geometry to computer-aided geometric design (4)
        
        
    
    - 
        
    
        14:00
    
    
        Applications of real algebraic geometry to computer-aided geometric design (4)
            1h0'        
    
    Speaker: L. Gonzalez-Vega (Universidad de Cantabria, Santander, Spain) Material:  lecture notes lecture notes
 
- 
        
    
        14:00
    
    
        Applications of real algebraic geometry to computer-aided geometric design (4)
            1h0'        
    
    
- 
    
        
        
        
            15:00 - 15:15
        
        
        
            Break
        
        
    
    - 15:00 Break 15'
 
- 
    
        
        
        
            15:15 - 16:45
        
        
        
            Computer Laboratory session
        
        
    
    Location: Computer Lab. (M) - 
        
    
        15:15
    
    
        Computer Laboratory session
            1h30'        
    
    
 
- 
        
    
        15:15
    
    
        Computer Laboratory session
            1h30'        
    
    
 
- 
    
        
        
        
            09:00 - 10:00
        
        
        
            Constrained optimization and quadratic mappings (3)
        
        
    
    
- 
                
                - 
    
        
        
        
            09:00 - 10:00
        
        
        
            Algorithms in real algebraic geometry (3)
        
        
    
    - 
        
    
        09:00
    
    
        Algorithms in real algebraic geometry (3)
            1h0'        
    
    Speaker: M.-F. Roy (Université de Rennes I, France) Material:  lecture notes lecture notes
 
- 
        
    
        09:00
    
    
        Algorithms in real algebraic geometry (3)
            1h0'        
    
    
- 
    
        
        
        
            10:00 - 10:15
        
        
        
            Break
        
        
    
    - 10:00 Break 15'
 
- 
    
        
        
        
            10:15 - 11:15
        
        
        
            Polynomial system solving in the real case (4)
        
        
    
    - 
        
    
        10:15
    
    
        Polynomial system solving in the real case (4)
            1h0'        
    
    Speaker: F. Rouillier (Projet SPACES and Equipe Calfor, Paris, France) Material:  transparencies transparencies
 
- 
        
    
        10:15
    
    
        Polynomial system solving in the real case (4)
            1h0'        
    
    
- 
    
        
        
        
            11:15 - 11:30
        
        
        
            Break
        
        
    
    - 11:15 Break 15'
 
- 
    
        
        
        
            11:30 - 12:30
        
        
        
            Constrained optimization and quadratic mappings (4)
        
        
    
    - 
        
    
        11:30
    
    
        Constrained optimization and quadratic mappings (4)
            1h0'        
    
    Speaker: A. Agrachev (SISSA, Trieste, Italy) Material:  lecture notes lecture notes
 
- 
        
    
        11:30
    
    
        Constrained optimization and quadratic mappings (4)
            1h0'        
    
    
- 
    
        
        
        
            12:30 - 14:00
        
        
        
            Lunch Break
        
        
    
    - 12:30 Lunch Break 1h30'
 
- 
    
        
        
        
            14:00 - 15:00
        
        
        
            Algorithms in real algebraic geometry (4)
        
        
    
    - 
        
    
        14:00
    
    
        Algorithms in real algebraic geometry (4)
            1h0'        
    
    Speaker: M.-F. Roy (Université de Rennes I, France) Material:  lecture notes lecture notes
 
- 
        
    
        14:00
    
    
        Algorithms in real algebraic geometry (4)
            1h0'        
    
    
 
- 
    
        
        
        
            09:00 - 10:00
        
        
        
            Algorithms in real algebraic geometry (3)
        
        
    
    
- 
                
                - 
    
        
        
        
            09:00 - 10:00
        
        
        
            On generalized critical values of polynomial maps (1)
        
        
    
    - 
        
    
        09:00
    
    
        On generalized critical values of polynomial maps (1)
            1h0'        
    
    Speaker: K. Kurdyka (Université de Savoie, Le Bourget-du-Lac, France) Material:  lecture notes lecture notes
 
- 
        
    
        09:00
    
    
        On generalized critical values of polynomial maps (1)
            1h0'        
    
    
- 
    
        
        
        
            10:00 - 10:15
        
        
        
            Break
        
        
    
    - 10:00 Break 15'
 
- 
    
        
        
        
            10:15 - 11:15
        
        
        
            On some subrings of formal power series
        
        
    
    - 
        
    
        10:15
    
    
        On some subrings of formal power series
            1h0'        
    
    Speaker: A. El Khadiri (Université Ibn Tofail, Kénitra, Morocco) Material:  lecture notes lecture notes
 
- 
        
    
        10:15
    
    
        On some subrings of formal power series
            1h0'        
    
    
- 
    
        
        
        
            11:15 - 11:30
        
        
        
            Break
        
        
    
    - 11:15 Break 15'
 
- 
    
        
        
        
            11:30 - 12:30
        
        
        
            Nilpotent bases for distributions generating special multi-flags, nilpotency orders, and related algorithmic & combinatorial issues
        
        
    
    - 
        
    
        11:30
    
    
        Nilpotent bases for distributions generating special multi-flags, nilpotency orders, and related algorithmic & combinatorial issues
            1h0'        
    
    Speaker: P. Mormul (University of Warsaw, Poland) 
 
- 
        
    
        11:30
    
    
        Nilpotent bases for distributions generating special multi-flags, nilpotency orders, and related algorithmic & combinatorial issues
            1h0'        
    
    
- 
    
        
        
        
            12:30 - 14:00
        
        
        
            Lunch Break
        
        
    
    - 12:30 Lunch Break 1h30'
 
- 
    
        
        
        
            14:00 - 15:00
        
        
        
            On topology of families of trajectories of analytic gradient vector fields (1)
        
        
    
    - 
        
    
        14:00
    
    
        On topology of families of trajectories of analytic gradient vector fields (1)
            1h0'        
    
    Speaker: Z.S. Szafraniec (University of Gdansk, Poland) 
 
- 
        
    
        14:00
    
    
        On topology of families of trajectories of analytic gradient vector fields (1)
            1h0'        
    
    
- 
    
        
        
        
            15:00 - 15:30
        
        
        
            Break
        
        
    
    - 15:00 Break 30'
 
- 
    
        
        
        
            15:30 - 16:30
        
        
        
            The existence of Morse functions on sets definable in o-minimal structures
        
        
    
    - 
        
    
        15:30
    
    
        The existence of Morse functions on sets definable in o-minimal structures
            1h0'        
    
    Speaker: Ta Le Loi (Dalat University, Vietnam) Material:  lecture notes lecture notes
 
- 
        
    
        15:30
    
    
        The existence of Morse functions on sets definable in o-minimal structures
            1h0'        
    
    
 
- 
    
        
        
        
            09:00 - 10:00
        
        
        
            On generalized critical values of polynomial maps (1)
        
        
    
    
- 
                
                - 
    
        
        
        
            09:00 - 10:00
        
        
        
            Virtual roots of real polynomials (1)
        
        
    
    - 
        
    
        09:00
    
    
        Virtual roots of real polynomials (1)
            1h0'        
    
    Speaker: H. Lombardi (Université de Franche-Comté, Besançon, France) 
 
- 
        
    
        09:00
    
    
        Virtual roots of real polynomials (1)
            1h0'        
    
    
- 
    
        
        
        
            10:00 - 10:15
        
        
        
            Break
        
        
    
    - 10:00 Break 15'
 
- 
    
        
        
        
            10:15 - 11:15
        
        
        
            On generalized critical values of polynomial maps (2)
        
        
    
    - 
        
    
        10:15
    
    
        On generalized critical values of polynomial maps (2)
            1h0'        
    
    Speaker: K. Kurdyka (Université de Savoie, Le Bourget-du-Lac, France) Material:  lecture notes lecture notes
 
- 
        
    
        10:15
    
    
        On generalized critical values of polynomial maps (2)
            1h0'        
    
    
- 
    
        
        
        
            11:15 - 11:30
        
        
        
            Break
        
        
    
    - 11:15 Break 15'
 
- 
    
        
        
        
            11:30 - 12:30
        
        
        
            Hankel form reduction and Berlekamp Massey algorithm
        
        
    
    - 
        
    
        11:30
    
    
        Hankel form reduction and Berlekamp Massey algorithm
            1h0'        
    
    Speaker: N. Chaouachi (Ben Atti) (Université Tunis II, Tunisia) 
 
- 
        
    
        11:30
    
    
        Hankel form reduction and Berlekamp Massey algorithm
            1h0'        
    
    
- 
    
        
        
        
            12:30 - 14:00
        
        
        
            Lunch Break
        
        
    
    - 12:30 Lunch Break 1h30'
 
- 
    
        
        
        
            14:00 - 15:00
        
        
        
            Joining two points in a compact connected component of an algebraic set via gradient trajectories
        
        
    
    - 
        
    
        14:00
    
    
        Joining two points in a compact connected component of an algebraic set via gradient trajectories
            1h0'        
    
    Speaker: D. D'Acunto (Universidad Complutense de Madrid, Spain) 
 
- 
        
    
        14:00
    
    
        Joining two points in a compact connected component of an algebraic set via gradient trajectories
            1h0'        
    
    
- 
    
        
        
        
            15:00 - 15:30
        
        
        
            Break
        
        
    
    - 15:00 Break 30'
 
- 
    
        
        
        
            15:30 - 16:30
        
        
        
            Description of the Jelonek set
        
        
    
    - 
        
    
        15:30
    
    
        Description of the Jelonek set
            1h0'        
    
    Speaker: A.H. Stasica (Jagiellonian University, Cracow, Poland) 
 
- 
        
    
        15:30
    
    
        Description of the Jelonek set
            1h0'        
    
    
 
- 
    
        
        
        
            09:00 - 10:00
        
        
        
            Virtual roots of real polynomials (1)
        
        
    
    
- 
                
                - 
    
        
        
        
            09:00 - 10:00
        
        
        
            Relative Poincaré lemma for singular varieties and quasi-homogeneity
        
        
    
    - 
        
    
        09:00
    
    
        Relative Poincaré lemma for singular varieties and quasi-homogeneity
            1h0'        
    
    Speaker: W. Domitrz (Warsaw University of Technology, Poland) 
 
- 
        
    
        09:00
    
    
        Relative Poincaré lemma for singular varieties and quasi-homogeneity
            1h0'        
    
    
- 
    
        
        
        
            10:00 - 10:15
        
        
        
            Break
        
        
    
    - 10:00 Break 15'
 
- 
    
        
        
        
            10:15 - 11:15
        
        
        
            On algebraic functions
        
        
    
    - 
        
    
        10:15
    
    
        On algebraic functions
            1h0'        
    
    Speaker: A. Benhissi (Faculté des Sciences de Monastir, Tunisia) 
 
- 
        
    
        10:15
    
    
        On algebraic functions
            1h0'        
    
    
- 
    
        
        
        
            11:15 - 11:30
        
        
        
            Break
        
        
    
    - 11:15 Break 15'
 
- 
    
        
        
        
            11:30 - 12:30
        
        
        
            Number of irreducible elements in Z/nZ
        
        
    
    - 
        
    
        11:30
    
    
        Number of irreducible elements in Z/nZ
            1h0'        
    
    Speaker: B. Kojok (University of Saint-Joseph, Beirut, Lebanon) 
 
- 
        
    
        11:30
    
    
        Number of irreducible elements in Z/nZ
            1h0'        
    
    
- 
    
        
        
        
            12:30 - 14:00
        
        
        
            Lunch Break
        
        
    
    - 12:30 Lunch Break 1h30'
 
- 
    
        
        
        
            14:00 - 15:00
        
        
        
            Real algebraic geometry from a metric viewpoint
        
        
    
    - 
        
    
        14:00
    
    
        Real algebraic geometry from a metric viewpoint
            1h0'        
    
    Speaker: L. Birbrair (Univ. Federal do Ceará, Fortaleza, Brazil) 
 
- 
        
    
        14:00
    
    
        Real algebraic geometry from a metric viewpoint
            1h0'        
    
    
- 
    
        
        
        
            15:00 - 15:15
        
        
        
            Break
        
        
    
    - 15:00 Break 15'
 
- 
    
        
        
        
            15:15 - 15:45
        
        
        
            A rational real Nuls Stellensatz for univariate polynomials
        
        
    
    - 
        
    
        15:15
    
    
        A rational real Nuls Stellensatz for univariate polynomials
            30'        
    
    Speaker: H. Warou (Université de Niamey, Niger) 
 
- 
        
    
        15:15
    
    
        A rational real Nuls Stellensatz for univariate polynomials
            30'        
    
    
- 
    
        
        
        
            15:45 - 16:00
        
        
        
            Break
        
        
    
    - 15:45 Break 15'
 
- 
    
        
        
        
            16:00 - 16:30
        
        
        
            Quantifier elimination for boolean products of real closed valuation rings
        
        
    
    - 
        
    
        16:00
    
    
        Quantifier elimination for boolean products of real closed valuation rings
            30'        
    
    Speaker: J.I. Guier Acosta (Universidad de Costa Rica, San Pedro, Costa Rica) 
 
- 
        
    
        16:00
    
    
        Quantifier elimination for boolean products of real closed valuation rings
            30'        
    
    
 
- 
    
        
        
        
            09:00 - 10:00
        
        
        
            Relative Poincaré lemma for singular varieties and quasi-homogeneity
        
        
    
    
- 
                
                - 
    
        
        
        
            09:00 - 10:00
        
        
        
            On the dual of a plane projective curve
        
        
    
    - 
        
    
        09:00
    
    
        On the dual of a plane projective curve
            1h0'        
    
    Speaker: D. Bouziane (Université Cadi Ayyad, Marrakech, Morocco) 
 
- 
        
    
        09:00
    
    
        On the dual of a plane projective curve
            1h0'        
    
    
- 
    
        
        
        
            10:00 - 10:15
        
        
        
            Break
        
        
    
    - 10:00 Break 15'
 
- 
    
        
        
        
            10:15 - 11:15
        
        
        
            Genericity of a_F and w_F regularity conditions and equisingularity of functions in a family of functions definable in o-minimal structures
        
        
    
    - 
        
    
        10:15
    
    
        Genericity of a_F and w_F regularity conditions and equisingularity of functions in a family of functions definable in o-minimal structures
            1h0'        
    
    Speaker: Ta Le Loi (Dalat University, Vietnam) Material:  lecture notes lecture notes
 
- 
        
    
        10:15
    
    
        Genericity of a_F and w_F regularity conditions and equisingularity of functions in a family of functions definable in o-minimal structures
            1h0'        
    
    
- 
    
        
        
        
            11:15 - 11:30
        
        
        
            Break
        
        
    
    - 11:15 Break 15'
 
- 
    
        
        
        
            11:30 - 12:30
        
        
        
            The theorem of the complement for a quasi subanalytic set
        
        
    
    - 
        
    
        11:30
    
    
        The theorem of the complement for a quasi subanalytic set
            1h0'        
    
    Speaker: A. El Khadiri (Université Ibn Tofail, Kénitra, Morocco) Material:  lecture notes lecture notes
 
- 
        
    
        11:30
    
    
        The theorem of the complement for a quasi subanalytic set
            1h0'        
    
    
- 
    
        
        
        
            12:30 - 14:00
        
        
        
            Lunch Break
        
        
    
    - 12:30 Lunch Break 1h30'
 
- 
    
        
        
        
            14:00 - 15:00
        
        
        
            Estimates on the number of complex zeros of solutions of linear differential equations via real algebraic geometry
        
        
    
    - 
        
    
        14:00
    
    
        Estimates on the number of complex zeros of solutions of linear differential equations via real algebraic geometry
            1h0'        
    
    Speaker: A. Grigoriev (SISSA, Trieste, Italy) Material:  lecture notes lecture notes
 
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        14:00
    
    
        Estimates on the number of complex zeros of solutions of linear differential equations via real algebraic geometry
            1h0'        
    
    
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            15:00 - 15:30
        
        
        
            Break
        
        
    
    - 15:00 Break 30'
 
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            15:30 - 16:30
        
        
        
            Definable incomplete expansions of ordered fields without open-definable gaps
        
        
    
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        15:30
    
    
        Definable incomplete expansions of ordered fields without open-definable gaps
            1h0'        
    
    Speaker: M. Moniri (Tarbiat Modarres University, Tehran, Iran) 
 
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        15:30
    
    
        Definable incomplete expansions of ordered fields without open-definable gaps
            1h0'        
    
    
 
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            09:00 - 10:00
        
        
        
            On the dual of a plane projective curve
        
        
    
    
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            09:00 - 10:00
        
        
        
            Density of subanalytic sets and Whitney conditions
        
        
    
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        09:00
    
    
        Density of subanalytic sets and Whitney conditions
            1h0'        
    
    Speaker: G. Valette (Université de Provence, Marseille, France) 
 
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        09:00
    
    
        Density of subanalytic sets and Whitney conditions
            1h0'        
    
    
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            10:00 - 10:15
        
        
        
            Break
        
        
    
    - 10:00 Break 15'
 
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            10:15 - 11:15
        
        
        
            On topology of families of trajectories of analytic gradient vector fields (2)
        
        
    
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        10:15
    
    
        On topology of families of trajectories of analytic gradient vector fields (2)
            1h0'        
    
    Speaker: Z.S. Szafraniec (University of Gdansk, Poland) 
 
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        10:15
    
    
        On topology of families of trajectories of analytic gradient vector fields (2)
            1h0'        
    
    
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            11:15 - 11:30
        
        
        
            Break
        
        
    
    - 11:15 Break 15'
 
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            11:30 - 12:30
        
        
        
            Virtual roots of real polynomials (2)
        
        
    
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        11:30
    
    
        Virtual roots of real polynomials (2)
            1h0'        
    
    Speaker: H. Lombardi (Université de Franche-Comté, Besançon, France) 
 
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        11:30
    
    
        Virtual roots of real polynomials (2)
            1h0'        
    
    
 
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            09:00 - 10:00
        
        
        
            Density of subanalytic sets and Whitney conditions
        
        
    
    
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