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# Author Archives: Jan Sieber

## EPSRC DTP Studentships in Exeter, deadline January 2017

A number of PhD studentships are funded by the Engineering and Physical Sciences Research Council (EPSRC) Doctoral Training Partnership with Exeter to commence in September 2017. The projects are funded on a competitive basis. Usually the projects that receive the best applicants will be awarded the funding. The studentships will provide funding for a stipend which, is currently £14,296 per annum for 2016-2017, research costs and UK/EU tuition fees at Research Council UK rates for 42 months (3.5 years) for full-time students, pro rata for part-time students.

The link to the list of projects is here (note that the list is long, applied maths & dynamics projects are mixed with others):

http://www.exeter.ac.uk/postgraduate/research-degrees/mathematics/funding/

## Positions available (in Exeter and elsewhere)

A 3-year position as a Postdoctoral Research Fellow is available in the research group (working with Jan Sieber:

http://www.jobs.ac.uk/job/AUU269/postdoctoral-research-fellow/

Also, internationally, several tenure track/permanent positions are open:

McGill (tenure track, info from Tony Humphries):

http://www.mathjobs.org/jobs/jobs/9249

DTU Lyngby (permanent, info from Frank Schilder):

http://www.compute.dtu.dk/om_os/ledige_stillinger/job?id=4778215b-b1f1-4a38-b927-666abf94cbb8

## A one day study in Ergodic Theory and Dynamical Systems

**22nd October 2015**, CEMPS – University of Exeter, Organiser: Ana Rodrigues

###### Morning session (in Harrison Building, room HAR 171)

- 11:30 – 12:30 Paulo Varandas (UFBA, Brasil)
- 12:30 – 13:30 Thomas Jordan (Bristol, UK)

###### Afternoon session (in Laver Building, room Laver 212)

- 15:30 – 16:30 Peter Ashwin (Exeter, UK)
- 16:30 – 17:30 Yiwei Zhang (Exeter, UK)

###### Abstracts

###### Paulo Varandas – Topological methods for problems in ergodic theory

Many chaotic dynamical systems are ‘rich’ from the topological viewpoint. This richness can be expressed by the fact that pseudo-orbits are shadowed by true orbits for the dynamics (shadowing property) or that pieces of orbits are well approximated by a orbit (specification property). These properties are satisfied by uniformly hyperbolic dynamics and some weaker versions have been established for wide classes of non-uniformly hyperbolic dynamical systems. In this talk we shall recall some of these weaker notions of shadowing and specification and describe how these can be used as very usefull tools in some problems arising in ergodic theory.

###### Thomas Jordan – Minkowski’s question mark function

Minkowski’s question mark function is a homeomprphism from [0,1] to itself which maps quadratic irrationals into the rationals. We’ll show how to view this function as a conjugacy between dynamical systems and as an invariant measure for the Gauss map (x\to 1/x\mod 1). We’ll then outline how a combination of large deviations and methods from a paper of Kaufman can be used to show the Fourier-Stieltjes transform of this function decays polynomially and give a few consequences of this fact. (Joint work with Tuomas Sahlsten).

###### Peter Ashwin – Piecewise isometric dynamics; some puzzles and problems

I will introduce and discuss some aspects of the dynamics of piecewise isometries (PWIs). These are iterated maps that are geometrically very simple (just isometries) on a number of “atoms” – convex regions that form a partition of phase space. They can be seen generalizations of interval exchange transformations to higher dimensions. PWis may arise in a number of applications but are hard to understand using standard dynamical tools based around hyperbolicity. I will outline a few results and some unsolved problems related to the dynamics, geometry and measure of the various invariant subsets that arise for PWIs in two dimensions.

###### Yiwei Zhang – A glimpse of thermodynamics formalism for interval maps

I will take a short survey on the basic setting of thermodynamics formalism for interval maps. In particular, I will introduce the standard transfer operator method in the uniformly hyperbolic maps setting, and explain how the spectral structure of this operator links with the existence/uniqueness of equilibrium state and its exponential decay of correlation. I will also explain how to extend this method for the non-uniformly hyperbolic interval maps.

## European Dynamics Days Exeter 2015 updates

## Program updates & changes

Late changes to programme (pdf for download)

## Early Stage Researcher positions in EU ITN network

Two funded PhD positions are available as part of the ITN “Critical Transitions in Complex Systems” (a EU Horizon 2020 Innovative Training Network). The posts last for 36 months.

Application closing date is **28 April 2015**.

Topics:

- Intrinsic versus extrinsic extremes in financial markets (inquiries to Peter Ashwin)
- Delay effects in palaeoclimate time series (inquiries to Jan Sieber)

Note the eligibility criteria for EU Innovative Training Network positions. Usually UK residents are excluded, check http://ec.europa.eu/research/participants/portal/doc/call/h2020/h2020-msca-itn-2015/1622613-itn_2015_-_guide_for_applicants_v1_en.pdf#page=13 for details.

## Stefanie Zegowitz started postdoctoral position

Stefanie Zegowitz will be working with Ana Rodrigues. Her University homepage is http://emps.exeter.ac.uk/mathematics/staff/shz201.

## European Dynamics Days 2015 to be hosted in Exeter

The international conference “European Dynamics Days 2015” will be held at the University of Exeter during September 7th-11th 2015. Local organisers are

- Christian Bick (homepage at Rice)
- Peter Ashwin,
- Ana Rodrigues,
- Jan Sieber
- Jane Pratt (homepage in Physics and Astronomy.

The current homepage of the conference is http://emps.exeter.ac.uk/mathematics/research/csdc/dynamicsdays2015/