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The Lorentz attractor and Smale horseshoe are typical examples of fractal invariant sets for dynamical systems. Fractal objects are ubiquitous in dynamics, including invariant sets, invariant measures, invariant foliations et cetera.
Thermodynamical formalism is a powerful tool for studying dimensions of fractal objects. It originated in statistical mechanics, but currently it has applications to many area of mathematics including spectral theory, hyperbolic geometry and probability theory.
The goal of this conference is to bring together experts studying fractal objects in dynamics in order to review recent progress in the field and catalyze further research.
Early career participants will also have the opportunity to attend an introductory CIMPA school on Hyperbolic Groups and their Representations which will take place in Piriapolis, Uruguay the preceding week.
The workshop consits of 3 minicourses and several lectures.
The ICDG-Fez2016 conference seeks original and high quality contributions in the fields chosen as topics for the three sections of this conference:
The conference will cover, but is not limited to, the main themes: Algebra, Geometry, dynamical symmetries and conservation laws, mathematical physics and applications.
This in particular includes the themes: Deformation theory and quantization, Hom-algebras and n-ary algebraic structures, Hopf algebra, integrable systems and related mathematical structures, jet theory and Weil bundles, Lie theory and applications, noncommutative geometry, Lie algebras, and more.
The conference will focus on the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization and discrete and noncommutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, noncommutative dynamics, non-commutative geometry and applications in physics and beyond.
Randomness is inherent to models of the physical, biological, and social world. Random topology models are important in a variety of complicated models including quantum gravity and black holes, filaments of dark matter in astronomy, spatial statistics, and morphological models of shapes, as well as models appearing in social media. The probabilistic method, theory of point processes, and ideas from stochastic and integral geometry have been central tools for proofs and efficient algorithms to measure topological quantities, such as Betti numbers of random geometric complexes.
The workshop topics include: random simplicial complexes, topological invariants in Gaussian random fields, and topological aspects of phase transitions, and geometry and topology of hard disks. A major theme of this workshop will center around computational issues and numerical experiments based on existing models and implementations.
This workshop focuses on building bridges - by developing a unified point of view and by emphasizing cross-fertilization of ideas and techniques from geometry, topology and combinatorics. New experimental evidence is crucial to this goal. The workshop emphasizes the computational and algorithmic aspects of the problems in topics including: Concentration of maps and isoperimetry of waists in discrete setting, configuration Space/Test Map scheme and theorems of Tverbeg type, Equipartitions of measures, social choice, van Kampen-Haefliger-Weber theory for maps of simplicial complexes, combinatorics of homotopy colimits, and discrete Morse theory.
Last updated: 26 January 2016