BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Valentin Lychagin (University of Tromsø\, Norway) DTSTART:20220124T153000Z DTEND:20220124T163000Z DTSTAMP:20260422T213050Z UID:Wisla22WinterSchoolWorkshop/1 DESCRIPTION:Title: Continuum Mechanics of Media with Inner Structure\ nby Valentin Lychagin (University of Tromsø\, Norway) as part of Differen tial Geometry and its applications: fluid dynamics\, dispersive systems\, image processing\n\n\nAbstract\nShort description:\nContinuum mechanics on Riemannian manifolds\n-Thermodynamics of Newtonian media.\n-Conservation laws\, Navier-Stokes and Euler equations.\nContinuum mechanics of media wi th inner structures\nContinuum mechanics of molecular media\n LOCATION:https://researchseminars.org/talk/Wisla22WinterSchoolWorkshop/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter J. Olver (University of Minnesota\, USA) DTSTART:20220124T170000Z DTEND:20220124T180000Z DTSTAMP:20260422T213050Z UID:Wisla22WinterSchoolWorkshop/2 DESCRIPTION:Title: Fractalization and Quantization in Dispersive Systems< /a>\nby Peter J. Olver (University of Minnesota\, USA) as part of Differen tial Geometry and its applications: fluid dynamics\, dispersive systems\, image processing\n\n\nAbstract\nThese talks will survey recent results on linear and nonlinear dispersive wave equations on periodic domains. The T albot effect\, also known as dispersive quantization. The evolution\, thro ugh spatially periodic linear dispersion\, of rough initial data produces fractal\, non-differentiable profiles at irrational times and\, for asympt otically polynomial dispersion relations\, quantized structures at rationa l times. Such phenomena have been observed in dispersive wave models\, op tics\, and quantum mechanics\, and lead to intriguing connections with exp onential sums arising in number theory. Ramifications and recent progres s on the analysis\, numerics\, and extensions to nonlinear wave models\, b oth integrable and non-integrable\, will be presented. Related results fo r the Fermi-Pasta-Ulam-Tsingou problem of the dynamics of nonlinear mass-s pring chains and the Lamb model for radiation damping of a vibrating body in an energy conducting medium will also be discussed.\n LOCATION:https://researchseminars.org/talk/Wisla22WinterSchoolWorkshop/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentin Lychagin (University of Tromsø\, Norway) DTSTART:20220125T153000Z DTEND:20220125T163000Z DTSTAMP:20260422T213050Z UID:Wisla22WinterSchoolWorkshop/3 DESCRIPTION:Title: Continuum Mechanics of Media with Inner Structure\ nby Valentin Lychagin (University of Tromsø\, Norway) as part of Differen tial Geometry and its applications: fluid dynamics\, dispersive systems\, image processing\n\n\nAbstract\nShort description:\nContinuum mechanics on Riemannian manifolds\n-Thermodynamics of Newtonian media.\n-Conservation laws\, Navier-Stokes and Euler equations.\nContinuum mechanics of media wi th inner structures\nContinuum mechanics of molecular media\n LOCATION:https://researchseminars.org/talk/Wisla22WinterSchoolWorkshop/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter J. Olver (University of Minnesota\, USA) DTSTART:20220125T170000Z DTEND:20220125T180000Z DTSTAMP:20260422T213050Z UID:Wisla22WinterSchoolWorkshop/4 DESCRIPTION:Title: Fractalization and Quantization in Dispersive Systems< /a>\nby Peter J. Olver (University of Minnesota\, USA) as part of Differen tial Geometry and its applications: fluid dynamics\, dispersive systems\, image processing\n\n\nAbstract\nThese talks will survey recent results on linear and nonlinear dispersive wave equations on periodic domains. The T albot effect\, also known as dispersive quantization. The evolution\, thro ugh spatially periodic linear dispersion\, of rough initial data produces fractal\, non-differentiable profiles at irrational times and\, for asympt otically polynomial dispersion relations\, quantized structures at rationa l times. Such phenomena have been observed in dispersive wave models\, op tics\, and quantum mechanics\, and lead to intriguing connections with exp onential sums arising in number theory. Ramifications and recent progres s on the analysis\, numerics\, and extensions to nonlinear wave models\, b oth integrable and non-integrable\, will be presented. Related results fo r the Fermi-Pasta-Ulam-Tsingou problem of the dynamics of nonlinear mass-s pring chains and the Lamb model for radiation damping of a vibrating body in an energy conducting medium will also be discussed.\n LOCATION:https://researchseminars.org/talk/Wisla22WinterSchoolWorkshop/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentin Lychagin (University of Tromsø\, Norway) DTSTART:20220126T153000Z DTEND:20220126T163000Z DTSTAMP:20260422T213050Z UID:Wisla22WinterSchoolWorkshop/5 DESCRIPTION:Title: Continuum Mechanics of Media with Inner Structure\ nby Valentin Lychagin (University of Tromsø\, Norway) as part of Differen tial Geometry and its applications: fluid dynamics\, dispersive systems\, image processing\n\n\nAbstract\nShort description:\nContinuum mechanics on Riemannian manifolds\n-Thermodynamics of Newtonian media.\n-Conservation laws\, Navier-Stokes and Euler equations.\nContinuum mechanics of media wi th inner structures\nContinuum mechanics of molecular media\n LOCATION:https://researchseminars.org/talk/Wisla22WinterSchoolWorkshop/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter J. Olver (University of Minnesota\, USA) DTSTART:20220126T170000Z DTEND:20220126T180000Z DTSTAMP:20260422T213050Z UID:Wisla22WinterSchoolWorkshop/6 DESCRIPTION:Title: Symmetry\, invariance\, and equivalence in image proce ssing\nby Peter J. Olver (University of Minnesota\, USA) as part of Di fferential Geometry and its applications: fluid dynamics\, dispersive syst ems\, image processing\n\n\nAbstract\nSymmetry recognition is fundamental in human vision and thus also plays a key role in image processing algorit hms. These talks will survey old and new mathematical perspectives on sym metry\, invariance\, and equivalence based on transformation groups and gr oupoids. Cartan's solution to the equivalence and symmetry problem for su bmanifolds relies on the associated geometric invariants\, through what is now known as the differential invariant signature. Applications arise in art\, computer vision\, medicine\, geometry\, and beyond\, including auto mated assembly of broken objects: jigsaw puzzles\, egg shells\, broken bon es\, and lithics (stone age tools).\n LOCATION:https://researchseminars.org/talk/Wisla22WinterSchoolWorkshop/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentin Lychagin (University of Tromsø\, Norway) DTSTART:20220127T153000Z DTEND:20220127T163000Z DTSTAMP:20260422T213050Z UID:Wisla22WinterSchoolWorkshop/7 DESCRIPTION:Title: Continuum Mechanics of Media with Inner Structure\ nby Valentin Lychagin (University of Tromsø\, Norway) as part of Differen tial Geometry and its applications: fluid dynamics\, dispersive systems\, image processing\n\n\nAbstract\nShort description:\nContinuum mechanics on Riemannian manifolds\n-Thermodynamics of Newtonian media.\n-Conservation laws\, Navier-Stokes and Euler equations.\nContinuum mechanics of media wi th inner structures\nContinuum mechanics of molecular media\n LOCATION:https://researchseminars.org/talk/Wisla22WinterSchoolWorkshop/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter J. Olver (University of Minnesota\, USA) DTSTART:20220127T170000Z DTEND:20220127T180000Z DTSTAMP:20260422T213050Z UID:Wisla22WinterSchoolWorkshop/8 DESCRIPTION:Title: Symmetry\, invariance\, and equivalence in image proce ssing\nby Peter J. Olver (University of Minnesota\, USA) as part of Di fferential Geometry and its applications: fluid dynamics\, dispersive syst ems\, image processing\n\n\nAbstract\nSymmetry recognition is fundamental in human vision and thus also plays a key role in image processing algorit hms. These talks will survey old and new mathematical perspectives on sym metry\, invariance\, and equivalence based on transformation groups and gr oupoids. Cartan's solution to the equivalence and symmetry problem for su bmanifolds relies on the associated geometric invariants\, through what is now known as the differential invariant signature. Applications arise in art\, computer vision\, medicine\, geometry\, and beyond\, including auto mated assembly of broken objects: jigsaw puzzles\, egg shells\, broken bon es\, and lithics (stone age tools).\n LOCATION:https://researchseminars.org/talk/Wisla22WinterSchoolWorkshop/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Klas Modin (Chalmers University of Technology & University of Goth enburg\, Sweden) DTSTART:20220128T153000Z DTEND:20220128T163000Z DTSTAMP:20260422T213050Z UID:Wisla22WinterSchoolWorkshop/9 DESCRIPTION:Title: Introduction to Geometric Hydrodynamics\nby Klas M odin (Chalmers University of Technology & University of Gothenburg\, Swede n) as part of Differential Geometry and its applications: fluid dynamics\, dispersive systems\, image processing\n\n\nAbstract\nIn three lectures I trace the work of three legends of mathematics and mechanics: Euler\, Poin caré\, and Arnold. This leads up to the aim of the lectures: to explain A rnold’s discovery from 1966 that solutions to Euler’s equations for th e motion of an incompressible fluid correspond to geodesics on the infinit e-dimensional Riemannian manifold of volume preserving diffeomorphisms. In many ways\, this discovery is the foundation for the field of geometric h ydrodynamics\, which today encompasses much more than just Euler’s equat ions\, with deep connections to many other fields such as optimal transpor t\, shape analysis\, and information theory.\n LOCATION:https://researchseminars.org/talk/Wisla22WinterSchoolWorkshop/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Klas Modin (Chalmers University of Technology & University of Goth enburg\, Sweden) DTSTART:20220128T170000Z DTEND:20220128T180000Z DTSTAMP:20260422T213050Z UID:Wisla22WinterSchoolWorkshop/10 DESCRIPTION:Title: Introduction to Geometric Hydrodynamics\nby Klas Modin (Chalmers University of Technology & University of Gothenburg\, Swed en) as part of Differential Geometry and its applications: fluid dynamics\ , dispersive systems\, image processing\n\n\nAbstract\nIn three lectures I trace the work of three legends of mathematics and mechanics: Euler\, Poi ncaré\, and Arnold. This leads up to the aim of the lectures: to explain Arnold’s discovery from 1966 that solutions to Euler’s equations for t he motion of an incompressible fluid correspond to geodesics on the infini te-dimensional Riemannian manifold of volume preserving diffeomorphisms. I n many ways\, this discovery is the foundation for the field of geometric hydrodynamics\, which today encompasses much more than just Euler’s equa tions\, with deep connections to many other fields such as optimal transpo rt\, shape analysis\, and information theory.\n LOCATION:https://researchseminars.org/talk/Wisla22WinterSchoolWorkshop/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Boris Khesin (University of Toronto\, Canada) DTSTART:20220129T153000Z DTEND:20220129T163000Z DTSTAMP:20260422T213050Z UID:Wisla22WinterSchoolWorkshop/11 DESCRIPTION:Title: Hamiltonian Fluid Dynamics\nby Boris Khesin (Univ ersity of Toronto\, Canada) as part of Differential Geometry and its appli cations: fluid dynamics\, dispersive systems\, image processing\n\n\nAbstr act\nThe course outlines group-theoretic and Hamiltonian approaches to hyd rodynamics. We start by describing the Eulerian dynamics of an ideal fluid and the Korteweg—de Vries equation of shallow water from the group-theo retic and geometric points of view. The Hamiltonian framework will allow u s to visualize the geometry of Casimirs for the Euler equation and helicit y of vector fields\, as well as to recover the motion of point vortices\, vortex filaments and membranes.\n LOCATION:https://researchseminars.org/talk/Wisla22WinterSchoolWorkshop/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Boris Khesin (University of Toronto\, Canada) DTSTART:20220129T170000Z DTEND:20220129T180000Z DTSTAMP:20260422T213050Z UID:Wisla22WinterSchoolWorkshop/12 DESCRIPTION:Title: Hamiltonian Fluid Dynamics\nby Boris Khesin (Univ ersity of Toronto\, Canada) as part of Differential Geometry and its appli cations: fluid dynamics\, dispersive systems\, image processing\n\n\nAbstr act\nThe course outlines group-theoretic and Hamiltonian approaches to hyd rodynamics. We start by describing the Eulerian dynamics of an ideal fluid and the Korteweg—de Vries equation of shallow water from the group-theo retic and geometric points of view. The Hamiltonian framework will allow u s to visualize the geometry of Casimirs for the Euler equation and helicit y of vector fields\, as well as to recover the motion of point vortices\, vortex filaments and membranes.\n LOCATION:https://researchseminars.org/talk/Wisla22WinterSchoolWorkshop/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Klas Modin (Chalmers University of Technology & University of Goth enburg\, Sweden) DTSTART:20220131T153000Z DTEND:20220131T163000Z DTSTAMP:20260422T213050Z UID:Wisla22WinterSchoolWorkshop/13 DESCRIPTION:Title: Introduction to Geometric Hydrodynamics\nby Klas Modin (Chalmers University of Technology & University of Gothenburg\, Swed en) as part of Differential Geometry and its applications: fluid dynamics\ , dispersive systems\, image processing\n\n\nAbstract\nIn three lectures I trace the work of three legends of mathematics and mechanics: Euler\, Poi ncaré\, and Arnold. This leads up to the aim of the lectures: to explain Arnold’s discovery from 1966 that solutions to Euler’s equations for t he motion of an incompressible fluid correspond to geodesics on the infini te-dimensional Riemannian manifold of volume preserving diffeomorphisms. I n many ways\, this discovery is the foundation for the field of geometric hydrodynamics\, which today encompasses much more than just Euler’s equa tions\, with deep connections to many other fields such as optimal transpo rt\, shape analysis\, and information theory.\n LOCATION:https://researchseminars.org/talk/Wisla22WinterSchoolWorkshop/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Boris Khesin (University of Toronto\, Canada) DTSTART:20220131T170000Z DTEND:20220131T180000Z DTSTAMP:20260422T213050Z UID:Wisla22WinterSchoolWorkshop/14 DESCRIPTION:Title: Hamiltonian Fluid Dynamics\nby Boris Khesin (Univ ersity of Toronto\, Canada) as part of Differential Geometry and its appli cations: fluid dynamics\, dispersive systems\, image processing\n\n\nAbstr act\nThe course outlines group-theoretic and Hamiltonian approaches to hyd rodynamics. We start by describing the Eulerian dynamics of an ideal fluid and the Korteweg—de Vries equation of shallow water from the group-theo retic and geometric points of view. The Hamiltonian framework will allow u s to visualize the geometry of Casimirs for the Euler equation and helicit y of vector fields\, as well as to recover the motion of point vortices\, vortex filaments and membranes.\n LOCATION:https://researchseminars.org/talk/Wisla22WinterSchoolWorkshop/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Ian Roulstone (University of Surrey\, UK) DTSTART:20220201T153000Z DTEND:20220201T163000Z DTSTAMP:20260422T213050Z UID:Wisla22WinterSchoolWorkshop/15 DESCRIPTION:Title: Monge–Ampère Geometry and the Navier–Stokes Equa tions\nby Ian Roulstone (University of Surrey\, UK) as part of Differe ntial Geometry and its applications: fluid dynamics\, dispersive systems\, image processing\n\n\nAbstract\nIn this series of three lectures\, we sha ll apply ideas from Monge–Ampère geometry to the partial differential equations governing incompressible fluid flow in two and three spatial dim ensions. Despite the apparent randomness of turbulent flows\, vortices pla y a key role in determining the structure and evolution of the flow. We sh all show how almost-complex structures in four and six dimensions are natu rally associated with regimes in which vorticity dominates over strain and \, furthermore\, how such flows are associated with Riemannian metrics of positive scalar curvature. In turn\, these insights suggest a route to obt aining topological information about vortex structures.\n LOCATION:https://researchseminars.org/talk/Wisla22WinterSchoolWorkshop/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Volodya Roubtsov (University of Angers\, France) DTSTART:20220201T170000Z DTEND:20220201T180000Z DTSTAMP:20260422T213050Z UID:Wisla22WinterSchoolWorkshop/16 DESCRIPTION:Title: Introduction to Hamiltonian Mechanics\nby Volodya Roubtsov (University of Angers\, France) as part of Differential Geometry and its applications: fluid dynamics\, dispersive systems\, image process ing\n\n\nAbstract\nI shall give a short account of Hamiltonian methods of classical mechanics. After a minimal reminder from symplectic geometry\, I shall concentrate on explicit examples of mechanical systems and shall de monstrate main features of the Hamiltonian approach and Liouville integrab ility: a construction of action-angle variables for the chosen examples. M y lectures do not contain new results and have a fully methodological flav or.\n LOCATION:https://researchseminars.org/talk/Wisla22WinterSchoolWorkshop/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Ian Roulstone (University of Surrey\, UK) DTSTART:20220202T153000Z DTEND:20220202T163000Z DTSTAMP:20260422T213050Z UID:Wisla22WinterSchoolWorkshop/17 DESCRIPTION:Title: Monge–Ampère Geometry and the Navier–Stokes Equa tions\nby Ian Roulstone (University of Surrey\, UK) as part of Differe ntial Geometry and its applications: fluid dynamics\, dispersive systems\, image processing\n\n\nAbstract\nIn this series of three lectures\, we sha ll apply ideas from Monge–Ampère geometry to the partial differential equations governing incompressible fluid flow in two and three spatial dim ensions. Despite the apparent randomness of turbulent flows\, vortices pla y a key role in determining the structure and evolution of the flow. We sh all show how almost-complex structures in four and six dimensions are natu rally associated with regimes in which vorticity dominates over strain and \, furthermore\, how such flows are associated with Riemannian metrics of positive scalar curvature. In turn\, these insights suggest a route to obt aining topological information about vortex structures.\n LOCATION:https://researchseminars.org/talk/Wisla22WinterSchoolWorkshop/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Ian Roulstone (University of Angers\, France) DTSTART:20220202T170000Z DTEND:20220202T180000Z DTSTAMP:20260422T213050Z UID:Wisla22WinterSchoolWorkshop/18 DESCRIPTION:Title: Introduction to Hamiltonian Mechanics\nby Ian Rou lstone (University of Angers\, France) as part of Differential Geometry an d its applications: fluid dynamics\, dispersive systems\, image processing \n\n\nAbstract\nI shall give a short account of Hamiltonian methods of cla ssical mechanics. After a minimal reminder from symplectic geometry\, I sh all concentrate on explicit examples of mechanical systems and shall demon strate main features of the Hamiltonian approach and Liouville integrabili ty: a construction of action-angle variables for the chosen examples. My l ectures do not contain new results and have a fully methodological flavor. \n LOCATION:https://researchseminars.org/talk/Wisla22WinterSchoolWorkshop/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Volodya Roubtsov (University of Surrey\, UK) DTSTART:20220203T153000Z DTEND:20220203T163000Z DTSTAMP:20260422T213050Z UID:Wisla22WinterSchoolWorkshop/19 DESCRIPTION:Title: Monge–Ampère Geometry and the Navier–Stokes Equa tions\nby Volodya Roubtsov (University of Surrey\, UK) as part of Diff erential Geometry and its applications: fluid dynamics\, dispersive system s\, image processing\n\n\nAbstract\nIn this series of three lectures\, we shall apply ideas from Monge–Ampère geometry to the partial differenti al equations governing incompressible fluid flow in two and three spatial dimensions. Despite the apparent randomness of turbulent flows\, vortices play a key role in determining the structure and evolution of the flow. We shall show how almost-complex structures in four and six dimensions are n aturally associated with regimes in which vorticity dominates over strain and\, furthermore\, how such flows are associated with Riemannian metrics of positive scalar curvature. In turn\, these insights suggest a route to obtaining topological information about vortex structures.\n LOCATION:https://researchseminars.org/talk/Wisla22WinterSchoolWorkshop/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Volodya Roubtsov (University of Angers\, France) DTSTART:20220203T170000Z DTEND:20220203T180000Z DTSTAMP:20260422T213050Z UID:Wisla22WinterSchoolWorkshop/20 DESCRIPTION:Title: Introduction to Hamiltonian Mechanics\nby Volodya Roubtsov (University of Angers\, France) as part of Differential Geometry and its applications: fluid dynamics\, dispersive systems\, image process ing\n\n\nAbstract\nI shall give a short account of Hamiltonian methods of classical mechanics. After a minimal reminder from symplectic geometry\, I shall concentrate on explicit examples of mechanical systems and shall de monstrate main features of the Hamiltonian approach and Liouville integrab ility: a construction of action-angle variables for the chosen examples. M y lectures do not contain new results and have a fully methodological flav or.\n LOCATION:https://researchseminars.org/talk/Wisla22WinterSchoolWorkshop/20/ END:VEVENT END:VCALENDAR