Synchronous activities:
Mini-courses
- Elena Celledoni (Norwegian University of Science and Technology, Norway)
[bg_collapse view=”button-orange” color=”#4a4949″ expand_text=” Some topics on deep learning and numerical analysis” collapse_text=”Show Less” ]
Title: Some topics on deep learning and numerical analysis
Session 1 (Tuesday): Deep learning as optimal control and structure preserving deep learning.
Session 2 (Thursday): An introduction to shape analysis and deep learning for optimal reparametrizations of shapes.
Resume of the course and references
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- Eva Miranda (Universitat Politècnica de Catalunya, Spain, CRM-Observatoire de Paris) and Daniel Peralta-Salas (ICMAT-CSIC, Spain) and
[bg_collapse view=”button-orange” color=”#4a4949″ expand_text=”Looking at Euler flows through a contact mirror: From universality to Turing completeness” collapse_text=”Show Less” ]
Title: Looking at Euler flows through a contact mirror: From universality to Turing completeness
Abstract: The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. Recently, Tao launched a programme to address the global existence problem for the Euler and Navier-Stokes equations based on the concept of universality. Inspired by this proposal, in this course we show that the stationary Euler equations exhibit several universality features, In the sense that, any non-autonomous flow on a compact manifold can be extended to a smooth stationary solution of the Euler equations on some Riemannian manifold of possibly higher dimension. A key point in the proof is looking at the h-principle in contact geometry through a contact mirror, unveiled by Sullivan, Etnyre and Ghrist more than two decades ago. Another application of this contact mirror concerns the study of singular periodic orbits (including escape orbits in Celestial mechanics joint with Cédric Oms) that we briefly discuss. We end up this minicourse addressing an apparently different question: What kind of physics might be non-computational? The universality result above yields the Turing completeness of the steady Euler flows on a 17-dimensional sphere, But, can this result be improved? We will give a positive answer in dimension three, discuss some applications and new constructions using billiard-type maps
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Invited Talks
- Michael Barton (Basque Center of Applied Mathematics, Spain)
[bg_collapse view=”button-orange” color=”#4a4949″ expand_text=”Motion planning for 5-axis CNC machining of free-form surfaces” collapse_text=”Show Less” ]
Title: Motion planning for 5-axis CNC machining of free-form surfaces
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- Volker Branding (University of Vienna, Austria)
[bg_collapse view=”button-orange” color=”#4a4949″ expand_text=”The supersymmetric nonlinear sigma model as a geometric variational problem” collapse_text=”Show Less” ]
Title: The supersymmetric nonlinear sigma model as a geometric variational problem
Abstract: The supersymmetric nonlinear sigma model is an important model in modern quantum field theory whose action functional is fixed by the invariance under various symmetries. In the physics literature it is usually formulated in terms of supergeometry. However, when abandoning the invariance under supersymmetry transformations, it can also be studied using well-established tools from the geometric calculus of variation. Following this approach one obtains an action functional that involves a map between two manifolds and a vector spinor defined along that map.
In the case of a Riemannian domain its critical points couple the harmonic map equation to spinor fields, these became known as Dirac-harmonic maps and variants thereof in the mathematics literature. If the domain manifold is Lorentzian, the critical points couple the wave map equation to spinor fields.
In this talk we will present various geometric and analytic results on Dirac-harmonic maps and their extensions. Moreover, we will discuss the difficulties that arise when trying to prove existence results and in which cases these can be overcome.
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- Dariusz Chru?ci?ski (Nicolaus Copernicus University, Poland)
[bg_collapse view=”button-orange” color=”#4a4949″ expand_text=” Universal Constraint for Relaxation Rates for Quantum Dynamical Semigroup” collapse_text=”Show Less” ]
Title: Universal Constraint for Relaxation Rates for Quantum Dynamical Semigroup
Abstract: A general property of relaxation rates in open quantum systems is discussed. We propose a constraint for relaxation rates that universally holds in fairly large classes of quantum dynamics. It is conjectured that this constraint is universal, i.e., it is valid for all quantum dynamical semigroups. The conjecture is supported by numerical analysis. Moreover, we show that the conjectured constraint is tight by providing a concrete model that saturates the bound. This constraint provides, therefore, a physical manifestation of complete positivity. Our conjecture also has two important implications: it provides (i) a universal constraint for the spectra of quantum channels and (ii) a necessary condition to decide whether a given channel is consistent with Markovian evolution.
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- Marco Gualtieri (University of Toronto, Canada)
[bg_collapse view=”button-orange” color=”#4a4949″ expand_text=”Geometric quantization and Noncommutative algebraic geometry” collapse_text=”Show Less” ]
Title: Geometric quantization and Noncommutative algebraic geometry
Abstract: The quantization of the integer multiples of a symplectic structure via the choice of a Kahler polarization lead us to the homogeneous coordinate rings familiar in algebraic geometry. I will explain how this framework may be deformed, making contact with noncommutative algebraic geometry. The main tool will be the deformation of the Kahler polarization to a generalized Kahler polarization. This is joint work with Francis Bischoff (arXiv:2108.01658).
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- Bruno Mera (IST, University of Lisbon, Portugal
[bg_collapse view=”button-orange” color=”#4a4949″ expand_text=”Kähler geometry and Chern insulators” collapse_text=”Show Less” ]
Title: Kähler geometry and Chern insulators
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- José Senovilla (Universidad del Pais Vasco, Spain)
[bg_collapse view=”button-orange” color=”#4a4949″ expand_text=”Elementary geometric quantities and gravitational energy” collapse_text=”Show Less” ]
Title: Elementary geometric quantities and gravitational energy
Abstract: Gravity manifests itself as curvature of spacetime. Curvature’s strength can be measured by considering the variations of the basic geometric quantities (area, volume, radius) of small balls with respect to their counterparts in flat spacetime. These variations are directly related, via the Einstein field equations, to the energy density of matter at the ball’s centre. In this talk I consider what happens when the matter energy density vanishes. Elementary geometric measurements still feel the effect of pure gravity, and the resulting changes should still be related to the gravitational strength or, in simple words, to the gravitational energy density. This leads to a novel prescription for the quasi-local energy of the pure gravitational field.
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Contributed talks
- Álvaro Rodríguez Abella (ICMAT, Spain)
[bg_collapse view=”button-orange” color=”#4a4949″ expand_text=”Lagrangian reduction by fibered actions in Field Theory” collapse_text=”Show Less” ]
Title: Lagrangian reduction by fibered actions in Field Theory
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- Jordi Gaset (Universitat Autònoma de Barcelona, Spain)
[bg_collapse view=”button-orange” color=”#4a4949″ expand_text=”Equivalent Lagrangians in Contact Mechanics” collapse_text=”Show Less” ]
Title: Equivalent Lagrangians in Contact Mechanics
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- Asier López-Gordón (ICMAT, Spain)
[bg_collapse view=”button-orange” color=”#4a4949″ expand_text=”Mechanical systems with external forces. Symmetries, reduction and Hamilton-Jacobi theory” collapse_text=”Show Less” ]
Title: Mechanical systems with external forces. Symmetries, reduction and Hamilton-Jacobi theory
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- Charlotte Kirchhoff-Lukat (KU Leuven, Belgium)
[bg_collapse view=”button-orange” color=”#4a4949″ expand_text=”Coisotropic A-branes in Symplectic Manifolds” collapse_text=”Show Less” ]
Title: Coisotropic A-branes in Symplectic Manifolds
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- Clarice Netto (IMPA, Brasil)
[bg_collapse view=”button-orange” color=”#4a4949″ expand_text=”Courant-Nijenhuis algebroids” collapse_text=”Show Less” ]
Title: Courant-Nijenhuis algebroids
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- Matteo Raffaelli (TU Wien, Austria)
[bg_collapse view=”button-orange” color=”#4a4949″ expand_text=”Curvature-adapted submanifolds of bi-invariant Lie groups” collapse_text=”Show Less” ]
Title: Curvature-adapted submanifolds of bi-invariant Lie groups
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- Frederico Rossi ( Università di Milano-Bicocca, Italy)
[bg_collapse view=”button-orange” color=”#4a4949″ expand_text=”Indefinite Nilsolitons and Einstein Solvmanifolds” collapse_text=”Show Less” ]
Title: Indefinite Nilsolitons and Einstein Solvmanifolds
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- Alfonso Giuseppe Tortorella (KU Leuven, Belgium)
[bg_collapse view=”button-orange” color=”#4a4949″ expand_text=”Deformations of Symplectic Foliations” collapse_text=”Show Less” ]
Title: Deformations of Symplectic Foliations
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- Alexandre Anahory Simões (ICMAT, Spain)
[bg_collapse view=”button-orange” color=”#4a4949″ expand_text=”Mechanical nonholonomic trajectories are Riemannian geodesics!” collapse_text=”Show Less” ]
Title: Mechanical nonholonomic trajectories are Riemannian geodesics!
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Asynchronous activities:
- Posters in pdf format
- Video-Poster
All these communications will be available in a meeting forum, where it will be possible to interact in writing. See how to submit an abstract here.