- Date: November 23, 2018
- Speaker: Renzo. L Ricca
Geometric devils in topological dynamics
Geometric and topological features play an important role in many physical systems, especially in fluid dynamics where forces drive continuous deformation. The benign influence of geometry, which is the muscular actor in topological dynamics, has sometimes a more devilish nature. Here we show how two different types of singularities that may emerge during the evolution of magnetic fields and soap films are responsible for the spontaneous reorganization and energy change of these systems.
A first example is given by the inflexional instability of magnetic knots that under conservation of self-linking number brings inflexional magnetic knots to inflexion-free braids through an integrable singularity of torsion. A second example is given by the continuous deformation of a soap film Möbius band to a 2-sided disk by a drastic change of the soap film topology through a twisted fold catastrophe. These are examples of generic behaviors that trigger energy relaxation in a wide variety of different physical contexts.
 Moffatt, H.K. & Ricca, R.L. (1992) Helicity and the Călugăreanu invariant. Proc. R. Soc. A 439, 411-429.
 Ricca, R.L. (2005) Inflexional disequilibrium of magnetic flux tubes. Fluid Dyn. Res. 36, 319-332.
 Goldstein, R.E., Moffatt, H.K., Pesci, A.I. & Ricca, R.L. (2010) A soap film Möbius strip changes topology with a twist singularity. Proc. Natnl. Acad. Sci. USA 107, 21979-21984.
inflexion, singularity, self-linking, twist, knots, braids, topological change, Möbius band, 2-sided disk
- Date: November 30, 2018
- Speaker: Sergio Rajsbaum
A very elementary introduction to the combinatorial topology approach to distributed computing
An introductory lecture following the approach of the book by Herlihy, Kozlov, Rajsbaum "Distributed Computing through Combinatorial Topology", Elsevier-Morgan Kaufmann, based on the notions of indistinguishability and perspectives. Illustrating the use of simplicial complexes via simple examples. No preliminary knowledge either about topology or about distributed computing.
distributed computing, combinatorial topology
-   10 am (Mexico City)
-   4 pm (London)
-   12 pm (Beijing)