The ALEA in Europe Young Researcher's workshop aims at bringing together Ph.D. students and young postdoc researchers of the ALEA-Network. The 2015 edition is organised at the university of Bath in partnership with the EPSRC Centre for Doctoral Training SAMBa.
In addition to the two mini-courses and two invited talks detailed below, the participants will have the opportunity to expose some open problems and discuss them in small groups during two dedicated sessions.
We welcome any young researcher interested in participating to the workshop. There is no registration fee. However, note that we have no funding for participants' travel and accomodation. Only lunches and coffee breaks will be provided.
If you want to participate, please email the organisers Dorka Fekete and Cécile Mailler mentioning your full name, your institution and a link to your webpage (alternatively a short description of your research).
The term ``Analytic Combinatorics'', coined by Ph. Flajolet and B. Sedgewick, combines powerful analytic methods from complex analysis with the field of enumerative com- binatorics. The link between these fields is provided by generating functions, which are a priori only defined as formal power series. However, in many applications they can also be interpreted as analytic power series with a non-zero radius of convergence. Analyzing the analytic properties enables us to gain insights on the underlying coefficients.
After a brief introduction into these methods, we will apply them to the classical study of lattice paths. The enumeration of lattice paths is a classical topic in combinatorics which is still a very active field of research. They have many applications in chemistry, physics, mathematics and computer science. For example lattice paths are used as the solution of integer programming problems, in cryptanalysis, in crystallography and as models in queueing theory.
We will start by recalling some important and useful results from the theory of Markov Processes, e.g. semi-groups, infinitesimal generators, reversibility and necessary and sufficient conditions for the existence of stationary distributions.
Once we have laid the foundations, we introduce some classical examples of interacting particle systems like the Ising model, the simple exclusion process and the zero-range process.
Depending on the time remaining and the interest of the audience, we will point out relations to statistical mechanics and the theory of large deviations.
The investigation of large random combinatorial objects has spawned a very active research field in the study of local and scaling limits of random planar maps. After a general introduction, we shall focus on an object named the Uniform Infinite Quadrangulation of the Half-Plane (UIHPQ), which arises as a local limit of random quadrangulations with a boundary whose size and perimeter are sent to infinity. We present a wide range of results obtained in joint work with N. Curien, and discuss their consequences concerning an annealed model of self-avoiding walks on large random quadrangulations.
We will introduce some simple tools to understand the most famous properties of branching random walks. We will then explore a more advanced model with spatially dependent branching. A key observation will be that even though expected values are totally misleading at first, if we are slightly cleverer about what quantity to look at then expectations tell us (almost) everything.
(*) The Numerical Analysis Seminar of the Maths Department on the 11th of December can be of interest to some of the participants. It will be held at 1:15pm in the Wolfson Lecture Theatre. The speaker is Martin Redmann (Max Planck Institute, Magdebourg, Germany). The title of the talk is ``Model order reduction for linear controlled SDEs with Lévy Noise'', more information can be found on the Numerical Analysis Seminar webpage.
Axel Bacher (University of Paris 13, France)
Anne Briquet (University of Lorraine, France)
Alessandra Caraceni (University of Orsay, France)
Gwendal Collet (TU Vienna, Austria)
Christina Diehl (University of Frankfurt, Germany)
Mathieu Dien (University of Paris 6, France)
Sarah Eugène (University of Paris 6 & Inria, France)
Dorka Fekete (University of Bath, UK)
Julian Gerstenberg (Leibniz University of Hannover, Germany)
Mitchell Gooding (University of Oxford, UK)
Emma Horton (University of Bath, UK)
Vincent Jugé (Mines ParisTech & University of Paris 7, France)
Marcus Kaiser (University of Bath, UK)
Andrea Kuntschik (University of Frankfurt, Germany)
Marie-Louise Lackner (TU Vienna, Austria)
Cécile Mailler (University of Bath, UK)
Sam Moore (University of Bath, UK)
Quentin de Mourgues (University of Paris 13, France)
Noela Müller (University of Frankfurt, Germany)
Steven Pagett (University of Bath, UK)
Samu Potka (KTH Stockholm, Sweden)
Alexander Roberts (Uiversity of Oxford, UK)
Matt Roberts (University of Bath, UK)
Ben Robinson (University of Bath, UK)
Nicolas Rolin (University of Paris 13, France)
Fiona Skerman (University of Bristol, UK)
Erik Thörnblad (University of Uppsala, Sweden)
Alexandra Ugolnikova (University of Paris 13, France)
Michael Wallner (TU Vienna, Austria)
Thomas Wong (University of Paris 13, France)
Kit Yates (University of Bath, UK)
Dominic Yeo (University of Oxford, UK)
The closest airport to Bath is Bristol airport. Once there, you can take either the A4 bus to Bath or the Airport Flyer bus to Bristol main train station (Temple Meads) and then the train to Bath. The A4 bus is a big green bus that runs every 30 minutes in day time and every hour early morning and late evening; it costs £20 a return (pay to the driver in cash) and takes you directly to Bath, near the train station, in 50 minutes. The Airport Flyer is more frequent, costs approximately £7 (pay to the driver in cash) and takes you to Bristol Temple Meads in 20 minutes. There, you can buy a single trip to Bath for approximately £7. The overall journey will take approximately 50 minutes.
If you can't find a convenient flight to Bristol airport, it's most likely that you'll find a flight to London. The most convenient airport to come to Bath is definitely London Heathrow. From there, there are different options to join Bath. You can take the Heathrow Express to London Paddington (approx. 30 minutes) and there take a direct train to Bath (90 minutes). You can book your train tickets online, for example on the First Great Western website. The second option is coach: National Express runs regular direct buses from Heathrow to Bath, the fastest ones take two hours and this option is generally cheaper that the previous one - you can book your tickets online on the National Express website. The third option is to take the RailAir bus from Heathrow to Reading and there a direct train to Bath. It takes approximately two hours.
The university is not very far from the train station and, looking at a map, you could be tempted to walk there. Be aware that the university is on top of a steep hill and the walk up might not be as pleasant as it seems: the walk down, on the other hand, is very pleasant and offers nice views on the city (at least when it's not raining).
To go from the train station to the university, you can take the bus (U1 or U18) and pay to the driver when you jump on. The bus stop is in front of the bus station, near the Sainsbury's local. The U1 and the U18 are run by two different companies, meaning that if you buy a return, it will only be accepted in the corresponding company for the way back. The university is the last stop of the bus.
The workshop will take place in the Wolfson Lecture theatre. It is in the 4W building, on the lowest floor. From the bus stop, walk up the stairs onto the parade (follow the people that were on the same bus). Continue walking straight until you pass the Librairy on your right. Continue straight after the Librairy. The 4W building will then be on your left (with glass automated doors). Enter the building: the Tiki café is on your right and the Student services on your left. Take the stairs in front of you to the lowest level: the Wolfson theatre is on your left, after the pigeon holes and the lifts.
Bath is a very touristy place and December can be quite busy. We advise the participants to book their hotel as soon as possible. Possible hotels are the Parade Park hotel, the Premier Inn, and the Travelodge (City Center or Waterside). The YMCA also offers low budget accomodation (private rooms are available). We also recommend the official Bath tourist information website for finding and booking accommodation.