Description
The Abdus Salam International Centre for Theoretical Physics (ICTP) is orgamzing a "Fifth International Conference and School Geometry, Dynamics, Integrable Systems - GDIS 2014: Bicentennial of The Great Poncelet Theorem and Billiard Dynamics", to be held at ICTP, Trieste, Italy, from 16 June to 27 June 2014. 

The main aim of the school is to introduce young participants into these exciting topics and prepare 
them for the week long conference to follow the school. The first week on the activity is devoted to a school that will give an overview of recent developments and interrelations between geometry and dynamical systems, with a special focus on mathematical billiards and integrable systems. The school will provide a background in algebraic geometry, theory of measured foliations and flat surfaces, the discrete integrable systems, 2-2 correspondences, the QR T maps, and the mechanical background of the billiard systems. The second week will be an international conference, where leading experts will report on the newest developments in the field of integrable dynamical systems and their geometry. The event will mark the bicentennial of the great Poncelet theorem. 

 
Topics 
Mathematical Billiards 
Flat surfaces and exchange transformations 
Classical Integrable Systems 
Algebro-Geometric Methods in Dynamical Systems 
N onholonomic mechanics 
Rigid-Body and Multi-Body Dynamics 
Go to day
  • Monday, 16 June 2014
    • 08:30 - 10:00 Registration of the participants at Adriatico Guest House ( Adriatico Guest House - Kastler Lecture Hall Area (Lower Level 1) )
    • 10:00 - 10:30 Opening 30' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: V. Dragovic and F.R. Villegas
      Material: Video
    • 10:30 - 12:00 Lyapunov exponents 1h30' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: M. Viana (IMPA, Rio de Janeiro, Brazil)
      Material: Video
    • 12:00 - 14:30 Lunch break ( Adriatico Guest House Kastler Lecture Hall )
    • 14:30 - 16:00 Poncelet theorem and mathematical billiards 1h30' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: S. Tabachnikov (The Pennsylvania State University, University Park PA, USA)
      Material: Video
    • 16:00 - 16:30 Coffee break ( Adriatico Guest House Kastler Lecture Hall )
    • 16:30 - 17:30 SEMINAR: Poincaré Theory for compact abelian one-dimensional solenoidal groups 1h0' ( Adriatico Guest House Kastler Lecture Hall )
      Abstract The notion of Poincaré rotation number for homeomorphisms of the unit circle is generalized to the case of homeomorphisms of a general compact abelian one–dimensional solenoidal group, which is also a one–dimensional foliated space; specifically, the theory is developed for the algebraic universal covering space of the circle (the adèle class group of the rationals).  Poincaré's dynamical classification theorem is also generalized to homeomorphisms of solenoids whose rotation element is an irrational element (i.e., monothetic generator) of the given group.
      Speaker: Alberto Verjovsky (Instituto de Matemáticas UNAM Cuernavaca, México)
      Material: Video
  • Tuesday, 17 June 2014
    • 08:30 - 10:00 Pencils of Conics and Biquadratics, Integrability, and Poncelet Theorem 1h30' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: V. Dragovic (Mathematical Institute Sanu, Serbia & The University of Texas at Dallas, USA)
      Material: Video
    • 10:00 - 10:30 Break ( Adriatico Guest House Kastler Lecture Hall )
    • 10:30 - 12:00 Poncelet theorem and mathematical billiards 1h30' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: S. Tabachnikov (The Pennsylvania State University, University Park PA, USA)
      Material: Video
    • 12:00 - 14:30 Lunch break ( Adriatico Guest House Kastler Lecture Hall )
    • 14:30 - 16:00 Lyapunov exponents 1h30' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: M. Viana (IMPA, Rio de Janeiro, Brazil)
      Material: Video
    • 16:00 - 16:30 Coffee break ( Adriatico Guest House Kastler Lecture Hall )
    • 16:30 - 18:00 Tutorial 1h30' ( Adriatico Guest House Kastler Lecture Hall )
  • Wednesday, 18 June 2014
    • 08:30 - 10:00 Lyapunov exponents 1h30' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: M. Viana (IMPA, Rio de Janeiro, Brazil)
      Material: Video
    • 10:00 - 10:30 Break ( Adriatico Guest House Kastler Lecture Hall )
    • 10:30 - 12:00 Pencils of Conics and Biquadratics, Integrability, and Poncelet Theorem 1h30' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: V. Dragovic (Mathematical Institute Sanu, Serbia & The University of Texas at Dallas, USA)
      Material: Video
    • 12:00 - 14:30 Lunch break ( Adriatico Guest House Kastler Lecture Hall )
    • 14:30 - 16:00 Poncelet theorem and mathematical billiards 1h30' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: S. Tabachnikov (The Pennsylvania State University, University Park PA, USA)
      Material: Video
    • 16:00 - 16:30 Coffee break ( Adriatico Guest House Kastler Lecture Hall )
  • Thursday, 19 June 2014
    • 08:30 - 10:00 Poncelet theorem and mathematical billiards 1h30' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: S. Tabachnikov (The Pennsylvania State University, University Park PA, USA)
      Material: Video
    • 10:00 - 10:30 Break ( Adriatico Guest House Kastler Lecture Hall )
    • 10:30 - 12:00 Lyapunov exponents 1h30' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: M. Viana (IMPA, Rio de Janeiro, Brazil)
      Material: Video
    • 12:00 - 14:30 Lunch break ( Adriatico Guest House Kastler Lecture Hall )
    • 14:30 - 16:00 Pencils of Conics and Biquadratics, Integrability, and Poncelet Theorem 1h30' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: V. Dragovic (Mathematical Institute Sanu, Serbia & The University of Texas at Dallas, USA)
      Material: Video
    • 16:00 - 16:30 Coffee break ( Adriatico Guest House Kastler Lecture Hall )
    • 16:30 - 18:00 Tutorial "Kowalevski top" 1h30' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: K. Kukic (University of Belgrade, Belgrade, Serbia)
    • 19:30 - 21:30 Get together ( Adriatico Guest House Kastler Lecture Hall )
  • Friday, 20 June 2014
    • 08:30 - 10:00 Poncelet theorem and mathematical billiards 1h30' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: S. Tabachnikov (The Pennsylvania State University, University Park PA, USA)
      Material: Video
    • 10:00 - 10:30 Break ( Adriatico Guest House Kastler Lecture Hall )
    • 10:30 - 12:00 Higher-dimensional Poncelet porisms 1h30' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: M. Radnovic (Mathematical Institute Sanu, Serbia & University of Sydney, Australia)
      Material: Video
    • 12:00 - 14:30 Lunch break ( Adriatico Guest House Kastler Lecture Hall )
    • 14:30 - 16:00 Pencils of Conics and Biquadratics, Integrability, and Poncelet Theorem 1h30' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: V. Dragovic (Mathematical Institute Sanu, Serbia & The University of Texas at Dallas, USA)
      Material: Video
    • 16:00 - 16:30 Coffee break ( Adriatico Guest House Kastler Lecture Hall )
    • 16:30 - 18:00 Tutorial 1h30' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: A.K. Adabrah and E. Hooton (University of Texas at Dallas, USA)
  • Monday, 23 June 2014
    • 08:30 - 09:20 Registration 50' ( Adriatico Guest House Kastler Lecture Hall )
    • 09:20 - 09:50 Opening 30' ( Adriatico Guest House Kastler Lecture Hall )
      Material: Video
    • 09:50 - 10:30 Conservation Laws of Generalized Billiards That Are Polynomial in Momenta 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: V. Kozlov (Moscow State University, Moscow, Russian Federation)
      Material: Video
    • 10:30 - 10:40 Break ( Adriatico Guest House Kastler Lecture Hall )
    • 10:40 - 11:20 The Neumann potential on the sphere and the geodesics on an ellipsoid 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: A. Albouy (IMCCE CNRS UMR, Observatoire de Paris, France)
    • 11:20 - 11:30 Break ( Adriatico Guest House Kastler Lecture Hall )
    • 11:30 - 12:10 A Theorem of Jacobi on complete integrals and its stochastic deformation 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: J.C. Zambrini (Universidade de Lisboa, Lisboa, Portugal)
      Material: Video
    • 12:10 - 15:00 Lunch break ( Adriatico Guest House Kastler Lecture Hall )
    • 15:00 - 15:40 Topological methods in nonholonomic mechanics 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: A. Borisov (Udmurt State University, Izhevsk, Russian Federation)
      Material: Video
    • 15:40 - 15:50 Coffee break ( Adriatico Guest House Kastler Lecture Hall )
    • 15:50 - 16:30 Billiards in the three body problem 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: S. Bolotin (University of Wisconsin, Madison WI, USA)
      Material: Video
    • 16:30 - 16:40 Break ( Adriatico Guest House Kastler Lecture Hall )
    • 16:40 - 17:20 Integrable line congruences and double reflection nets 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: M. Radnovic (Mathematical Institute Sanu, Serbia & University of Sydney, Australia)
      Material: Video
    • 18:00 - 19:00 SPECIAL PUBLIC LECTURE "On explicitly solvable ODE's" 1h0' ( Leonardo da Vinci Building Main Lecture Hall )
      Abstract: We discuss the problem of integration of ODE systems by quadratures. The main classical results on exact integration of general nonlinear systems are the Euler-Jacobi theorem on the integrating factor and the Lie theorem on the solvable algebra of symmetries. We present a general theory uniting these two approaches. We generalize Darboux's classical results on the integrability of linear non-autonomous systems with an incomplete set of particular solutions. Special attention is paid to linear Hamiltonian systems. We also discuss the general problem of integrability of autonomous ODE systems in an n-dimensional space which admit an algebra of symmetry fields of dimension greater than or equal to n.
      Speaker: V. Kozlov (Moscow State University, Moscow, Russian Federation)
  • Tuesday, 24 June 2014
    • 09:00 - 09:40 A family of locally integrable billiards 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: D. Treschev (V.A. Steklov Mathematical Institute, Moscow, Russian Federation)
      Material: Video
    • 09:40 - 09:50 Break ( Adriatico Guest House Kastler Lecture Hall )
    • 09:50 - 10:30 Virtual billiards and Heisenberg model in pseudo-Euclidean spaces 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: B. Jovanovic (Institute of Mathematics SANU, Belgrade, Serbia)
      Material: Video
    • 10:30 - 10:40 Break ( Adriatico Guest House Kastler Lecture Hall )
    • 10:40 - 11:20 Grassmannians and multi-soliton solutions to KP-II: an algebraic geometric approach 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: S. Abenda (University of Bologna, Bologna, Italy)
      Material: Video
    • 11:20 - 11:30 Break ( Adriatico Guest House Kastler Lecture Hall )
    • 11:30 - 12:10 Integrability and non-integrability of pentagram maps 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: B. Khesin (University of Toronto, Toronto Ontario, Canada)
      Material: Video
    • 12:10 - 15:00 Lunch break ( Adriatico Guest House Kastler Lecture Hall )
    • 15:00 - 15:40 The controllability and self-propulsion of bodies with an invariable shell in a fluid 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: A. Kilin (Udmurt State University, Izhevsk, Russian Federation)
      Material: Video
    • 15:40 - 15:50 Coffee break ( Adriatico Guest House Kastler Lecture Hall )
    • 15:50 - 16:30 Two Integrable Systems related to the Euler fluid equations on a rotating sphere 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: H. Dullin (University of Sydney, Sydney, Australia)
      Material: Video
    • 16:30 - 16:40 Break ( Adriatico Guest House Kastler Lecture Hall )
    • 16:40 - 17:20 Applications of the Kowalevski-Painleve method to the motion of a rigid body in an ideal fluid 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: V. Dragovic and B. Gajic (Institute of Mathematics SANU, Serbia & The University of Texas at Dallas, USA)
      Material: Video
  • Wednesday, 25 June 2014
    • 09:00 - 09:40 The Submerged Rigid Body: Application to Guidance and Navigation for Autonomous Underwater Vehicles 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: M. Chyba (University of Hawaii at Manoa, Honolulu, USA)
      Material: Video
    • 09:40 - 09:50 Break ( Adriatico Guest House Kastler Lecture Hall )
    • 09:50 - 10:30 Integrable geodesic flows on 2-torus: formal solutions and variational principle 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: A. Mironov (Sobolev Institute of Mathematics, Novosibirsk, Russian Federation)
      Material: Video
    • 10:30 - 10:40 Break ( Adriatico Guest House Kastler Lecture Hall )
    • 10:40 - 11:20 On symmetries of singular implicit ODEs 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: S. Agafonov (UNESP Universidade Estadual Paulista, Sao Jose, Brazil)
      Material: Video
    • 11:20 - 11:30 Break ( Adriatico Guest House Kastler Lecture Hall )
    • 11:30 - 12:10 Poncelet theorem and Painleve?-VI 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: V. Shramchenko (University of Sherbrooke, Sherbrooke QC, Canada)
      Material: Video
    • 12:10 - 15:00 Lunch break ( Adriatico Guest House Kastler Lecture Hall )
    • 16:00 - 17:30 Poster session - oral presentations 1h30' ( Adriatico Guest House Kastler Lecture Hall )
    • 17:30 - 19:00 Poster session - stand presentations 1h30' ( Adriatico Guest House - Kastler Lecture Hall Area (Lower Level 1) )
      Refreshments will be available in the poster session area
  • Thursday, 26 June 2014
    • 09:00 - 09:40 Superintegrable systems on a plane and sphere 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: I. Mamaev (Udmurt State University, Izhevsk, Russian Federation)
      Material: Video
    • 09:40 - 09:50 Break ( Adriatico Guest House Kastler Lecture Hall )
    • 09:50 - 10:30 Superintegrable systems on Euclidean plane, sphere and hyperbolic plane 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: C. Gonera (University of Lodz, Lodz, Poland)
      Material: Slides Video
    • 10:30 - 10:40 Break ( Adriatico Guest House Kastler Lecture Hall )
    • 10:40 - 11:20 Poncelet Porism for Biquadratic Curves 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: G. Khimshiashvili (Ilia State University, Tbilisi, Georgia)
      Material: Video
    • 11:20 - 11:30 Break ( Adriatico Guest House Kastler Lecture Hall )
    • 11:30 - 12:10 Simultaneous separation for the Neumann and Chaplygin systems 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: A. Tsyganov (St.Petersburg State University, St.Petersburg, Russian Federation)
      Material: Video
    • 12:10 - 15:00 Lunch break ( Adriatico Guest House Kastler Lecture Hall )
    • 15:00 - 15:40 Classical Images and Quantum Symmetries in Annular Domain 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: O. Pashaev (Izmir Institute of Technology, zmir, Turkey)
      Material: Video
    • 15:40 - 15:50 Coffee break ( Adriatico Guest House Kastler Lecture Hall )
    • 15:50 - 16:30 Dynamics and Control of a Spherical Robot with an Axisymmetric Pendulum Actuator 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: T. Ivanova (Udmurt State University, Izhevsk, Russian Federation)
      Material: Video
  • Friday, 27 June 2014
    • 09:00 - 09:40 Physical measures for partially hyperbolic diffeomorphisms 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: S. Luzzatto (ICTP, Trieste, Italy)
      Material: Video
    • 09:40 - 09:50 Break ( Adriatico Guest House Kastler Lecture Hall )
    • 09:50 - 10:30 Algebraic Frobenius manifolds, classical W-algebras and semiuniversal deformation of simple singularties 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: Y. Dinar (University of Khartoum, Sudan & Sultan Qaboos University, Oman)
      Material: Video
    • 10:30 - 10:40 Break ( Adriatico Guest House Kastler Lecture Hall )
    • 10:40 - 11:20 Algebraic-geometric integrability of pentagram maps 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: F. Soloviev (University of Toronto, Toronto Ontario, Canada)
      Material: Video
    • 11:20 - 11:30 Break ( Adriatico Guest House Kastler Lecture Hall )
    • 11:30 - 12:10 On Poncelet's closure theorem 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: W. Mozgawa (Maria Curie-Sklodowska University, Lublin, Poland)
      Material: Video
    • 12:20 - 13:00 Generic hyperelliptic Prym varieties and separation of variables in some algebraic integrable systems 40' ( Adriatico Guest House Kastler Lecture Hall )
      Speaker: Y. Fedorov (Universidad Politecnica de Cataluna, Barcelona, Spain)
      Material: Video
    • 13:00 - 15:00 Lunch break ( Adriatico Guest House Kastler Lecture Hall )
    • 15:00 - 18:00 END OF THE ACTIVITY ( Adriatico Guest House Kastler Lecture Hall )