3rd Bremen Winter School and Symposium: Diffusion on Fractals and Non-linear Dynamics

By Jens Rademacher
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24 Mar. - 02 Apr. 2015

The winter school and symposium, which was jointly organised by the Dynamics and Geometry and Applied Analysis groups in the math department of the University of Bremen, bridged a rather disparate set of topics: diffusion on fractals, quasi-crystals, non-linear waves and chaotic dynamics. Somewhat surprisingly, this worked out rather well.


The larger part of the participants

The main organiser was Tony Samuel, with support by Malte Koch, Kurt Falk, Marc Keßeböhmer, Tobias Oertel-Jäger and the author.
Uni Bremen's MINTernational guest lecturer program and M8 PostDoc Initiative Plus as well as the DFG Scientific Network - Skew Product Dynamics and Multifractal Analysis provided funding for this event.

This was the third event in a series of winter schools held at the University of Bremen in the past three years and - with over 60 international participants - the largest, hosting main speakers from Finland, France, Germany, Italy, Japan, Romania, the USA and the UK. The event featured plenary lectures, mini-lecture courses, seminar talks, open problem sessions and a public lecture. Further details can be found below and on the event's website.

  
Ian Melbourne lecturing and Daniel Lenz in an open problem session

For various reasons the winter school part and symposium with research talks ended up being intermingled in the schedule and the course lectures were attended by practically all participants, not just the graduate students. The enthusiasm largely turned the problem sessions, originally intended for course work of the graduate students, into discussion sessions -- which added to the planned open problem sessions for discussing research problems... and yet, everybody seemed to enjoy hijacking the format, and discussions beyond the topical borders emerged. Participants and speakers also liked the long (90 min) course plenary lectures, which provided the time for details and background information.

  
Discussions during the coffee break

The lecture courses: Jun Kigami discussed the notion of Laplacians defined by Dirichlet forms on fractals, while Ben Hambly took a more probabilistic perspective defining and analysing diffusion via Brownian motion on fractal sets. Sergey Zelik introduced the world of spatio-temporally chaotic attractors for dissipative PDEs and Margaret Beck discussed stability of nonlinear waves, focusing on nonlinear stability via pointwise Green's functions. Johannes Kellendonk gave insights into the analysis of quasicrystals via dynamical systems and non-commutative geometry, and Ian Melbourne lectured on stochastic limits for deterministic fast-slow systems.

Further plenary lectures (full titles here) were held by Michael Baake (aperiodic order), Uta Freiberg (diffusion on fractals), Kumiko Hattori (non-Markov processes on fractals), Daniel Lenz (aperiodic order), Daniel Meyer (fractals and geometry) Erin Pearse (lattice-type fractals) and John Rock (complex dimensions). A number of shorter talks, e.g., by Gerhard Keller (skew-product flows), rounded up the symposium part.

  
Bremer Knipp and Labskaus

Social activities were equally well attended, though the trip to wade in the Wattenmeer of the nearby North Sea coast was prevented by a storm—luckily early enough. The four conference dinners gave everybody the opportunity to try Bremen specialties, such as Knipp, Green kale and Labskaus (ok, that one you can also get in Hamburg).... And then there is Beck's beer and the better local brew of Haake Beck, which was tried for many hours in Bremen's nightlife.

    
Waiting in the rain (hey, it's Bremen), visiting the Schnoor quarters and John Rock happy about Bremen's cathedral

An unchallenged highlight of the event was Margaret Beck's public lecture, which had a high attendence including a surprisingly large number of non-workshop attendees. She got everybody to marvel at "Vortices and the Navier-Stokes Equation" and to think about "Understanding Solutions of Equations That We Can't Actually Solve."

    
Margaret Beck and part of the audience of the public lecture, and afterwards (Jun Kigami in the center)


Jens Rademacher

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