LMS SHORT COURSE ON SYMPLECTIC GEOMETRY

LMS-EPSRC SHORT COURSE ON SYMPLECTIC GEOMETRY

The workshop starts on Monday morning at 8:58. Most of you will arrive on Sunday and for those of you who stay at the Royal Hotel the dinner will be provided. If you arrive by train then the hotel is within walking distance from the station. If you arrive by plane then either take a taxi or the bus 727 from the Airport to the central bus station (again within a walking distance from the hotel).

Daily plan:

All classes in Fraser Noble Lecture Theatre 3

09:00 - 10:00 Kędra
10:10 - 11:10 Oancea
11:10 - 11:40 Tea/Coffe
11:40 - 12:40 Coates
12:40 - 14:00 Lunch
14:00 - 16:00 Catching up classes
16:00 - 16:30 Tea/Coffe
16:30 - 17:30 Guest lecture

Exceptions: On Monday we start two minutes earlier with a few welcome words from Kędra. Wednesday afternoon is free (after lunch); the workshop finishes on Friday after lunch.

Guest lectures

All lectures at Fraser Noble Lecture Theatre 3 at 16:30

Monday: Gabriel Paternain - The contact geometry of the restricted 3-body problem with a movie.
Tuesday: Paul Biran - Lagrangian topology from the geometric and categorical viewpoints
Thursday: Ivan Smith - Homological algebra of symplectic topology

Socialising

The reception will be on Tuesday at 19:00 at Howies Restaurant.

Lecture notes

Coates: An introduction to quantum cohomology.
Kędra: Examples of symplectic manifolds and the same notes without colours.
Oancea: Floer homology 1, 2, 3, 4, 5.

Additional reading: Delzant's paper about symplectic actions of Lie groups.
McDuff-Salamon "Introduction to symplectic topology" and "Quantum cohomology and symplectic topology", Hofer-Zehnder "Symplectic invariants and Hamiltonian dynamics", Arnol'd "Mathematical methods of classical mechanics"

Practical information

The temperature in summer in Aberdeen is about 15C and it can change a lot during the day (say 10C in the morning, 20C at noon and 7C in the evening). The same refers to sun and rain. In short, you should expect sun, rain, wind, cold, hot, hale, rainbows, clouds, fog. However, there are no thunderstorms here.

Accommodation: The Royal Hotel in the town centre -- map.
Eating: Lunch will be provided for all registered participants (you will get vouchers). For those of you who stay in Royal Hotel there will be breakfast and dinner at the Hotel (except for Tuesday when we will all have the conference dinner). At the hotel you will be asked in the morning to choose your evening meal from the menu for up to £ 20 (that is, you need to pay for anything above that limit).
Classes: The Institute of Mathematics, Fraser Noble Building the Old Aberdeen Campus - No 7 on this map or on this map . It is 35 minutes walk ( map 1, map 2) from the hotel. You can also take a bus, weekly ticket is perhaps the cheapest option. Tickets can by bought on a bus but you need to have exact amount of money. Take the bus 1 or 2 (red line - direction Danestone or Ashwood, but NOT Garthdee) from Union Street to King Street/Regent Walk (which you can see on the above maps). A good orientation point is the new library (under construction) which is a big cube made glass; Fraser Noble building is next to it. Notice that Monday July 11 is a public holiday in Aberdeen so buses may be less frequent.
You can use wi-fi at the campus provided you are eduroam user.
What else to do:
visit the Art gallery or Maritime Museum etc, take a walk and watch dolphins or another walk on the campus,
enjoy the winter gardens or have a pint.

Course outline and prerequisites

Symplectic geometry is one of the fastest developing branches of mathematics. It originated from classical mechanics and most of the early motivation came from Hamiltonian dynamics. The major breakthrough took place in the 1980's when Gromov and Floer introduced the analysis of PDE to the subject. Since then the development of symplectic geometry is constantly impressive.

The course aims to attract students working in geometry, topology, analysis of PDE and mathematical physics. It will provide the students with an overview of the subject and it will ntroduce the recent research techniques and problems. In particular, we wish the students to appreciate the interplay of different branches of mathematics ranging from algebraic topology to analysis of partial differential equations.

There will be three lecture series, five lectures each:

Examples of symplectic manifolds and group actions (by J.Kedra - University of Aberdeen)
Floer homology (by A.Oancea - CNRS and University of Strasbourg)
Gromov-Witten theory (by T.Coates - Imperial College London)

In addition there will be three guest lectures by P.Biran (ETH Zurich), G.Paternain (Cambridge) and I.Smith (Cambridge). Lecture notes and further details will appear here some time in June.

Application

Applications should be made using the registration form available via the Society's website. The closing date for applications is Friday 27 May 2011. Numbers will be limited and those interested are advised to make an early application. All applicants will be contacted approximately two weeks after this deadline; we will not be able to give information about individual applications before then.

Fees

All research students registered at a UK university will be charged a registration fee of £100. They will not be charged for subsistence costs.

UK-based postdocs will be charged a registration fee of £100, plus half the subsistence costs (£225) £325 in total.

All others (overseas students and postdocs, those working in industry) will be charged a registration fee of £250 plus the full subsistence costs (£450), £700 in total.

All participants must pay their own travel costs (for EPSRC funded students, this should be covered by their DTA). Fees are not payable until a place on the course is offered. In the event of over-subscription preference will be given to UK-based research students.