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:20260404T100013Z UID:Wisla22WinterSchoolWorkshop/1 DESCRIPTION:Title: Continuum Mechanics of Media with Inner Structu re\nby Valentin Lychagin (University of Tromsø\, Norway) as part of D ifferential Geometry and its applications: fluid dynamics\, dispersive sys tems\, image processing\n\n\nAbstract\nShort description:\nContinuum mecha nics on Riemannian manifolds\n-Thermodynamics of Newtonian media.\n-Conser vation laws\, Navier-Stokes and Euler equations.\nContinuum mechanics of m edia with inner structures\nContinuum mechanics of molecular media\n LOCATION:https://stable.researchseminars.org/talk/Wisla22WinterSchoolWorks hop/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter J. Olver (University of Minnesota\, USA) DTSTART:20220124T170000Z DTEND:20220124T180000Z DTSTAMP:20260404T100013Z UID:Wisla22WinterSchoolWorkshop/2 DESCRIPTION:Title: Fractalization and Quantization in Dispersive S ystems\nby Peter J. Olver (University of Minnesota\, USA) as part of D ifferential Geometry and its applications: fluid dynamics\, dispersive sys tems\, image processing\n\n\nAbstract\nThese talks will survey recent resu lts on linear and nonlinear dispersive wave equations on periodic domains. The Talbot effect\, also known as dispersive quantization. The evolution \, through spatially periodic linear dispersion\, of rough initial data pr oduces fractal\, non-differentiable profiles at irrational times and\, for asymptotically polynomial dispersion relations\, quantized structures at rational times. Such phenomena have been observed in dispersive wave mode ls\, optics\, and quantum mechanics\, and lead to intriguing connections w ith exponential sums arising in number theory. Ramifications and recent progress on the analysis\, numerics\, and extensions to nonlinear wave mod els\, both integrable and non-integrable\, will be presented. Related res ults for the Fermi-Pasta-Ulam-Tsingou problem of the dynamics of nonlinear mass-spring chains and the Lamb model for radiation damping of a vibratin g body in an energy conducting medium will also be discussed.\n LOCATION:https://stable.researchseminars.org/talk/Wisla22WinterSchoolWorks hop/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentin Lychagin (University of Tromsø\, Norway) DTSTART:20220125T153000Z DTEND:20220125T163000Z DTSTAMP:20260404T100013Z UID:Wisla22WinterSchoolWorkshop/3 DESCRIPTION:Title: Continuum Mechanics of Media with Inner Structu re\nby Valentin Lychagin (University of Tromsø\, Norway) as part of D ifferential Geometry and its applications: fluid dynamics\, dispersive sys tems\, image processing\n\n\nAbstract\nShort description:\nContinuum mecha nics on Riemannian manifolds\n-Thermodynamics of Newtonian media.\n-Conser vation laws\, Navier-Stokes and Euler equations.\nContinuum mechanics of m edia with inner structures\nContinuum mechanics of molecular media\n LOCATION:https://stable.researchseminars.org/talk/Wisla22WinterSchoolWorks hop/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter J. Olver (University of Minnesota\, USA) DTSTART:20220125T170000Z DTEND:20220125T180000Z DTSTAMP:20260404T100013Z UID:Wisla22WinterSchoolWorkshop/4 DESCRIPTION:Title: Fractalization and Quantization in Dispersive S ystems\nby Peter J. Olver (University of Minnesota\, USA) as part of D ifferential Geometry and its applications: fluid dynamics\, dispersive sys tems\, image processing\n\n\nAbstract\nThese talks will survey recent resu lts on linear and nonlinear dispersive wave equations on periodic domains. The Talbot effect\, also known as dispersive quantization. The evolution \, through spatially periodic linear dispersion\, of rough initial data pr oduces fractal\, non-differentiable profiles at irrational times and\, for asymptotically polynomial dispersion relations\, quantized structures at rational times. Such phenomena have been observed in dispersive wave mode ls\, optics\, and quantum mechanics\, and lead to intriguing connections w ith exponential sums arising in number theory. Ramifications and recent progress on the analysis\, numerics\, and extensions to nonlinear wave mod els\, both integrable and non-integrable\, will be presented. Related res ults for the Fermi-Pasta-Ulam-Tsingou problem of the dynamics of nonlinear mass-spring chains and the Lamb model for radiation damping of a vibratin g body in an energy conducting medium will also be discussed.\n LOCATION:https://stable.researchseminars.org/talk/Wisla22WinterSchoolWorks hop/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentin Lychagin (University of Tromsø\, Norway) DTSTART:20220126T153000Z DTEND:20220126T163000Z DTSTAMP:20260404T100013Z UID:Wisla22WinterSchoolWorkshop/5 DESCRIPTION:Title: Continuum Mechanics of Media with Inner Structu re\nby Valentin Lychagin (University of Tromsø\, Norway) as part of D ifferential Geometry and its applications: fluid dynamics\, dispersive sys tems\, image processing\n\n\nAbstract\nShort description:\nContinuum mecha nics on Riemannian manifolds\n-Thermodynamics of Newtonian media.\n-Conser vation laws\, Navier-Stokes and Euler equations.\nContinuum mechanics of m edia with inner structures\nContinuum mechanics of molecular media\n LOCATION:https://stable.researchseminars.org/talk/Wisla22WinterSchoolWorks hop/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter J. Olver (University of Minnesota\, USA) DTSTART:20220126T170000Z DTEND:20220126T180000Z DTSTAMP:20260404T100013Z UID:Wisla22WinterSchoolWorkshop/6 DESCRIPTION:Title: Symmetry\, invariance\, and equivalence in imag e processing\nby Peter J. Olver (University of Minnesota\, USA) as par t of Differential Geometry and its applications: fluid dynamics\, dispersi ve systems\, image processing\n\n\nAbstract\nSymmetry recognition is funda mental in human vision and thus also plays a key role in image processing algorithms. These talks will survey old and new mathematical perspectives on symmetry\, invariance\, and equivalence based on transformation groups and groupoids. Cartan's solution to the equivalence and symmetry problem for submanifolds relies on the associated geometric invariants\, through what is now known as the differential invariant signature. Applications a rise in art\, computer vision\, medicine\, geometry\, and beyond\, includi ng automated assembly of broken objects: jigsaw puzzles\, egg shells\, bro ken bones\, and lithics (stone age tools).\n LOCATION:https://stable.researchseminars.org/talk/Wisla22WinterSchoolWorks hop/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentin Lychagin (University of Tromsø\, Norway) DTSTART:20220127T153000Z DTEND:20220127T163000Z DTSTAMP:20260404T100013Z UID:Wisla22WinterSchoolWorkshop/7 DESCRIPTION:Title: Continuum Mechanics of Media with Inner Structu re\nby Valentin Lychagin (University of Tromsø\, Norway) as part of D ifferential Geometry and its applications: fluid dynamics\, dispersive sys tems\, image processing\n\n\nAbstract\nShort description:\nContinuum mecha nics on Riemannian manifolds\n-Thermodynamics of Newtonian media.\n-Conser vation laws\, Navier-Stokes and Euler equations.\nContinuum mechanics of m edia with inner structures\nContinuum mechanics of molecular media\n LOCATION:https://stable.researchseminars.org/talk/Wisla22WinterSchoolWorks hop/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter J. Olver (University of Minnesota\, USA) DTSTART:20220127T170000Z DTEND:20220127T180000Z DTSTAMP:20260404T100013Z UID:Wisla22WinterSchoolWorkshop/8 DESCRIPTION:Title: Symmetry\, invariance\, and equivalence in imag e processing\nby Peter J. Olver (University of Minnesota\, USA) as par t of Differential Geometry and its applications: fluid dynamics\, dispersi ve systems\, image processing\n\n\nAbstract\nSymmetry recognition is funda mental in human vision and thus also plays a key role in image processing algorithms. These talks will survey old and new mathematical perspectives on symmetry\, invariance\, and equivalence based on transformation groups and groupoids. Cartan's solution to the equivalence and symmetry problem for submanifolds relies on the associated geometric invariants\, through what is now known as the differential invariant signature. Applications a rise in art\, computer vision\, medicine\, geometry\, and beyond\, includi ng automated assembly of broken objects: jigsaw puzzles\, egg shells\, bro ken bones\, and lithics (stone age tools).\n LOCATION:https://stable.researchseminars.org/talk/Wisla22WinterSchoolWorks hop/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Klas Modin (Chalmers University of Technology & University of Goth enburg\, Sweden) DTSTART:20220128T153000Z DTEND:20220128T163000Z DTSTAMP:20260404T100013Z UID:Wisla22WinterSchoolWorkshop/9 DESCRIPTION:Title: Introduction to Geometric Hydrodynamics\nby Klas Modin (Chalmers University of Technology & University of Gothenburg\ , Sweden) as part of Differential Geometry and its applications: fluid dyn amics\, dispersive systems\, image processing\n\n\nAbstract\nIn three lect ures I trace the work of three legends of mathematics and mechanics: Euler \, Poincaré\, and Arnold. This leads up to the aim of the lectures: to ex plain Arnold’s discovery from 1966 that solutions to Euler’s equations for the motion of an incompressible fluid correspond to geodesics on the infinite-dimensional Riemannian manifold of volume preserving diffeomorphi sms. In many ways\, this discovery is the foundation for the field of geom etric hydrodynamics\, which today encompasses much more than just Euler’ s equations\, with deep connections to many other fields such as optimal t ransport\, shape analysis\, and information theory.\n LOCATION:https://stable.researchseminars.org/talk/Wisla22WinterSchoolWorks hop/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Klas Modin (Chalmers University of Technology & University of Goth enburg\, Sweden) DTSTART:20220128T170000Z DTEND:20220128T180000Z DTSTAMP:20260404T100013Z UID:Wisla22WinterSchoolWorkshop/10 DESCRIPTION:Title: Introduction to Geometric Hydrodynamics\nb y Klas Modin (Chalmers University of Technology & University of Gothenburg \, Sweden) as part of Differential Geometry and its applications: fluid dy namics\, dispersive systems\, image processing\n\n\nAbstract\nIn three lec tures I trace the work of three legends of mathematics and mechanics: Eule r\, Poincaré\, and Arnold. This leads up to the aim of the lectures: to e xplain Arnold’s discovery from 1966 that solutions to Euler’s equation s for the motion of an incompressible fluid correspond to geodesics on the infinite-dimensional Riemannian manifold of volume preserving diffeomorph isms. In many ways\, this discovery is the foundation for the field of geo metric hydrodynamics\, which today encompasses much more than just Euler ’s equations\, with deep connections to many other fields such as optima l transport\, shape analysis\, and information theory.\n LOCATION:https://stable.researchseminars.org/talk/Wisla22WinterSchoolWorks hop/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Boris Khesin (University of Toronto\, Canada) DTSTART:20220129T153000Z DTEND:20220129T163000Z DTSTAMP:20260404T100013Z UID:Wisla22WinterSchoolWorkshop/11 DESCRIPTION:Title: Hamiltonian Fluid Dynamics\nby Boris Khesi n (University of Toronto\, Canada) as part of Differential Geometry and it s applications: fluid dynamics\, dispersive systems\, image processing\n\n \nAbstract\nThe course outlines group-theoretic and Hamiltonian approaches to hydrodynamics. We start by describing the Eulerian dynamics of an idea l fluid and the Korteweg—de Vries equation of shallow water from the gro up-theoretic and geometric points of view. The Hamiltonian framework will allow us to visualize the geometry of Casimirs for the Euler equation and helicity of vector fields\, as well as to recover the motion of point vort ices\, vortex filaments and membranes.\n LOCATION:https://stable.researchseminars.org/talk/Wisla22WinterSchoolWorks hop/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Boris Khesin (University of Toronto\, Canada) DTSTART:20220129T170000Z DTEND:20220129T180000Z DTSTAMP:20260404T100013Z UID:Wisla22WinterSchoolWorkshop/12 DESCRIPTION:Title: Hamiltonian Fluid Dynamics\nby Boris Khesi n (University of Toronto\, Canada) as part of Differential Geometry and it s applications: fluid dynamics\, dispersive systems\, image processing\n\n \nAbstract\nThe course outlines group-theoretic and Hamiltonian approaches to hydrodynamics. We start by describing the Eulerian dynamics of an idea l fluid and the Korteweg—de Vries equation of shallow water from the gro up-theoretic and geometric points of view. The Hamiltonian framework will allow us to visualize the geometry of Casimirs for the Euler equation and helicity of vector fields\, as well as to recover the motion of point vort ices\, vortex filaments and membranes.\n LOCATION:https://stable.researchseminars.org/talk/Wisla22WinterSchoolWorks hop/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Klas Modin (Chalmers University of Technology & University of Goth enburg\, Sweden) DTSTART:20220131T153000Z DTEND:20220131T163000Z DTSTAMP:20260404T100013Z UID:Wisla22WinterSchoolWorkshop/13 DESCRIPTION:Title: Introduction to Geometric Hydrodynamics\nb y Klas Modin (Chalmers University of Technology & University of Gothenburg \, Sweden) as part of Differential Geometry and its applications: fluid dy namics\, dispersive systems\, image processing\n\n\nAbstract\nIn three lec tures I trace the work of three legends of mathematics and mechanics: Eule r\, Poincaré\, and Arnold. This leads up to the aim of the lectures: to e xplain Arnold’s discovery from 1966 that solutions to Euler’s equation s for the motion of an incompressible fluid correspond to geodesics on the infinite-dimensional Riemannian manifold of volume preserving diffeomorph isms. In many ways\, this discovery is the foundation for the field of geo metric hydrodynamics\, which today encompasses much more than just Euler ’s equations\, with deep connections to many other fields such as optima l transport\, shape analysis\, and information theory.\n LOCATION:https://stable.researchseminars.org/talk/Wisla22WinterSchoolWorks hop/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Boris Khesin (University of Toronto\, Canada) DTSTART:20220131T170000Z DTEND:20220131T180000Z DTSTAMP:20260404T100013Z UID:Wisla22WinterSchoolWorkshop/14 DESCRIPTION:Title: Hamiltonian Fluid Dynamics\nby Boris Khesi n (University of Toronto\, Canada) as part of Differential Geometry and it s applications: fluid dynamics\, dispersive systems\, image processing\n\n \nAbstract\nThe course outlines group-theoretic and Hamiltonian approaches to hydrodynamics. We start by describing the Eulerian dynamics of an idea l fluid and the Korteweg—de Vries equation of shallow water from the gro up-theoretic and geometric points of view. The Hamiltonian framework will allow us to visualize the geometry of Casimirs for the Euler equation and helicity of vector fields\, as well as to recover the motion of point vort ices\, vortex filaments and membranes.\n LOCATION:https://stable.researchseminars.org/talk/Wisla22WinterSchoolWorks hop/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Ian Roulstone (University of Surrey\, UK) DTSTART:20220201T153000Z DTEND:20220201T163000Z DTSTAMP:20260404T100013Z UID:Wisla22WinterSchoolWorkshop/15 DESCRIPTION:Title: Monge–Ampère Geometry and the Navier–Stok es Equations\nby Ian Roulstone (University of Surrey\, UK) as part of Differential Geometry and its applications: fluid dynamics\, dispersive sy stems\, image processing\n\n\nAbstract\nIn this series of three lectures\, we shall apply ideas from Monge–Ampère geometry to the partial differ ential equations governing incompressible fluid flow in two and three spat ial dimensions. Despite the apparent randomness of turbulent flows\, vorti ces 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 a re naturally associated with regimes in which vorticity dominates over str ain and\, furthermore\, how such flows are associated with Riemannian metr ics of positive scalar curvature. In turn\, these insights suggest a route to obtaining topological information about vortex structures.\n LOCATION:https://stable.researchseminars.org/talk/Wisla22WinterSchoolWorks hop/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Volodya Roubtsov (University of Angers\, France) DTSTART:20220201T170000Z DTEND:20220201T180000Z DTSTAMP:20260404T100013Z UID:Wisla22WinterSchoolWorkshop/16 DESCRIPTION:Title: Introduction to Hamiltonian Mechanics\nby Volodya Roubtsov (University of Angers\, France) as part of Differential G eometry and its applications: fluid dynamics\, dispersive systems\, image processing\n\n\nAbstract\nI shall give a short account of Hamiltonian meth ods of classical mechanics. After a minimal reminder from symplectic geome try\, I shall concentrate on explicit examples of mechanical systems and s hall demonstrate main features of the Hamiltonian approach and Liouville i ntegrability: a construction of action-angle variables for the chosen exam ples. My lectures do not contain new results and have a fully methodologic al flavor.\n LOCATION:https://stable.researchseminars.org/talk/Wisla22WinterSchoolWorks hop/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Ian Roulstone (University of Surrey\, UK) DTSTART:20220202T153000Z DTEND:20220202T163000Z DTSTAMP:20260404T100013Z UID:Wisla22WinterSchoolWorkshop/17 DESCRIPTION:Title: Monge–Ampère Geometry and the Navier–Stok es Equations\nby Ian Roulstone (University of Surrey\, UK) as part of Differential Geometry and its applications: fluid dynamics\, dispersive sy stems\, image processing\n\n\nAbstract\nIn this series of three lectures\, we shall apply ideas from Monge–Ampère geometry to the partial differ ential equations governing incompressible fluid flow in two and three spat ial dimensions. Despite the apparent randomness of turbulent flows\, vorti ces 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 a re naturally associated with regimes in which vorticity dominates over str ain and\, furthermore\, how such flows are associated with Riemannian metr ics of positive scalar curvature. In turn\, these insights suggest a route to obtaining topological information about vortex structures.\n LOCATION:https://stable.researchseminars.org/talk/Wisla22WinterSchoolWorks hop/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Ian Roulstone (University of Angers\, France) DTSTART:20220202T170000Z DTEND:20220202T180000Z DTSTAMP:20260404T100013Z UID:Wisla22WinterSchoolWorkshop/18 DESCRIPTION:Title: Introduction to Hamiltonian Mechanics\nby Ian Roulstone (University of Angers\, France) as part of Differential Geom etry and its applications: fluid dynamics\, dispersive systems\, image pro cessing\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 shal l demonstrate main features of the Hamiltonian approach and Liouville inte grability: a construction of action-angle variables for the chosen example s. My lectures do not contain new results and have a fully methodological flavor.\n LOCATION:https://stable.researchseminars.org/talk/Wisla22WinterSchoolWorks hop/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Volodya Roubtsov (University of Surrey\, UK) DTSTART:20220203T153000Z DTEND:20220203T163000Z DTSTAMP:20260404T100013Z UID:Wisla22WinterSchoolWorkshop/19 DESCRIPTION:Title: Monge–Ampère Geometry and the Navier–Stok es Equations\nby Volodya Roubtsov (University of Surrey\, UK) as part of Differential Geometry and its applications: fluid dynamics\, dispersive systems\, image processing\n\n\nAbstract\nIn this series of three lecture s\, we shall apply ideas from Monge–Ampère geometry to the partial dif ferential equations governing incompressible fluid flow in two and three s patial dimensions. Despite the apparent randomness of turbulent flows\, vo rtices play a key role in determining the structure and evolution of the f low. We shall show how almost-complex structures in four and six dimension s are naturally associated with regimes in which vorticity dominates over strain and\, furthermore\, how such flows are associated with Riemannian m etrics of positive scalar curvature. In turn\, these insights suggest a ro ute to obtaining topological information about vortex structures.\n LOCATION:https://stable.researchseminars.org/talk/Wisla22WinterSchoolWorks hop/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Volodya Roubtsov (University of Angers\, France) DTSTART:20220203T170000Z DTEND:20220203T180000Z DTSTAMP:20260404T100013Z UID:Wisla22WinterSchoolWorkshop/20 DESCRIPTION:Title: Introduction to Hamiltonian Mechanics\nby Volodya Roubtsov (University of Angers\, France) as part of Differential G eometry and its applications: fluid dynamics\, dispersive systems\, image processing\n\n\nAbstract\nI shall give a short account of Hamiltonian meth ods of classical mechanics. After a minimal reminder from symplectic geome try\, I shall concentrate on explicit examples of mechanical systems and s hall demonstrate main features of the Hamiltonian approach and Liouville i ntegrability: a construction of action-angle variables for the chosen exam ples. My lectures do not contain new results and have a fully methodologic al flavor.\n LOCATION:https://stable.researchseminars.org/talk/Wisla22WinterSchoolWorks hop/20/ END:VEVENT END:VCALENDAR