Entrance hall of the ICMS Workshop

Representation theory and symplectic singularities

Apr 04, 2016 - Apr 08, 2016

ICMS, 15 South College Street

Organisers

Name Institution
Gordon, Iain University of Edinburgh
Levy, Paul Lancaster University
Tange, Rudolf University of Leeds

A conference in honour of Sasha Premet's 60th birthday

Group photograph

Workshop Delegates at Pollock Halls

Three key themes of the workshop will be: finite W-algebras; representation theory and in- variant theory of reductive groups and their Lie algebras; and representation theory of symplectic singularities.

Finite W-algebras
 Finite W-algebras are natural quantizations of Slodowy slices to nilpotent orbits in simple Lie algebras. They were introduced (in full generality) by Premet in an influential paper [1]. Progress has been rapid in the fifteen or so years of the subject’s existence. One of the leaders in this area is Ivan Losev, who classified the irreducible finite-dimensional modules; proved the existence of one-dimensional modules in classical types; and determined, in terms of dimensions of irreducible representations of finite W -algebras, the Goldie ranks of primitive ideals of universal enveloping algebras of simple Lie algebras.

Modular representation theory and invariant theory of reductive groups and their Lie algebras Very early on in the history of W-algebras, Premet related reduced enveloping algebras and finite W-algebras by describing the former as matrix algebras over certain modular analogues of the latter. This powerful result allowed for known properties of finite W-algebras (especially the existence of 1-dimensional modules) to be used to prove a long-standing conjecture for modular Lie algebras (the existence of modules with dimension equal to the multiplicative lower bound in the Kac-Weisfeiler conjecture, “KW2”). In the other direction, in his work on the Gelfand- Kirillov conjecture [2] Premet used known results in characteristic p (non-rationality of invariants) to disprove (outside types A, C, G2) the long-standing GK conjecture in characteristic zero, namely that the skew-field of fractions of U(g) is isomorphic to the skew-field of fractions of a Weyl algebra over a transcendental extension of the ground field. These two examples exhibit some of the classic features of Premet’s most influential work, especially in the stunning use of reduction mod p methods and the deep relationship between algebra and geometry. These features are also reflected in the design of the workshop.

Representation theory of symplectic singularities Symplectic singularities were introduced by Beauville, extending the notion of symplectic manifold in the same way that rational Gorenstein singularities extend the class of Calabi-Yau manifolds. Two classes of examples are intersections of Slodowy slices and nilpotent orbit closures in simple complex Lie algebras, and quotient singularities C2n/Γ, where Γ is a finite subgroup of Sp2n(C). These classes of symplectic singularity are quantized by, respectively, finite W-algebras and (spherical subalgebras of) symplectic reflection algebras, indicating the omnipresence of quantized symplectic structures in representation theory. Quantizations of symplectic varieties in positive characteristic are especially interesting because of the presence of a large p-centre, similar to the situation for the universal enveloping algebra of a restricted Lie algebra.

The organisers are grateful for financial support from

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Arrangements

It is anticipated that the workshop will begin with registration on Monday morning 4 April and close around lunchtime on Friday 8 April. Please take these timings into account when booking your travel.

 

Participation

Invited Speakers - ALL invited speakers have been sent out invitations on behalf of ICMS and the Scientific Organisers.

A list of speakers can be found here http://www.maths.lancs.ac.uk/~levyp/RTSS/

Public applications to this workshop are now CLOSED.

PLEASE NOTE THAT ALL PUBLIC APPLICANTS ARE EXPECTED TO BOOK AND PAY FOR THEIR OWN ACCOMMODATION AND COVER THEIR OWN TRAVEL COSTS (with the exception of the 7 PhD student funded places available at this workshop).

 

Venue and Talks

The workshop will be held at 15 South College Street, Edinburgh. You may also find this map useful for the workshop. All lectures will be held in the Newhaven Lecture Theatre. The Lecture Theatre is equipped with a data projector, computer, visualiser (the new generation of overhead projectors) and two blackboards. The projector and one board may be used simultaneously. It is best to bring your presentation on a memory stick to use in our ICMS computer. Alternatively, it is possible for you to use your own laptop with our data projector, but please be aware that you may have to alter your laptop resolutions/settings.

 

UK Visas

If you are travelling from overseas you may require an entry visa. A European visa does not guarantee entry to the UK. Please use this link to the UK Visas site to find out if you need a visa and if so how to apply for one.

 

Travel

Information about travel to the UK and Edinburgh is available here. Please note that it is your responsibility to have adequate travel insurance to cover medical and other emergencies that may occur on your trip.

A taxi directly from the airport will cost approximately 20.00 GBP to the city centre for a one-way journey. There is also a bus service direct from the airport to the city centre which will cost 4.50 single or 7.50 GBP return - the Airlink 100. This is a frequent service (every 10 minutes during peak times) and will bring you close to Waverley Railway Station and the workshop venue.

Lothian buses charge £1.50 for a single, £4.00 for a day ticket. Please note that the exact fare is required and no change is given.

If travelling by train, please note that Edinburgh has several railway stations; Waverley Railway Station being the main station and closest to the workshop venue at 15 South College Street. If you alight at Edinburgh Waverley, the meeting venue is an easy 10 minute walk over North and South Bridge. The other railway stations are Haymarket and Edinburgh Park but please note that these stations are at the West End of the city centre.

 

Accommodation

ICMS will organise accommodation for all invited speakers. Other participants should arrange their own. You can find a list of accommodation close to ICMS here.

 

Catering

The workshop grant will cover refreshments throughout the event, a lunch on Monday and an informal wine reception on Monday evening.

 

Workshop Dinner

There will be a dinner in honour of Sasha Premet's 60th birthday,on Tuesday 5 April, at 19:00at the St Trinnean’s Room, St Leonard’s Hall, Pollock Halls of Residence, University of Edinburgh.

 

Wireless Access

Access to wifi via Eduroam is available throughout the building. If you are not registered with Eduroam you will be given instructions and a code for accessing the wireless network. For those without laptops, there will also be a couple of computers available for you to check your emails.

 

Edinburgh International Science Festival

Delegates may wish to know that the workshop will take place during the Edinburgh International Science Festival. Details of the ICMS event on Sunday 3 April are on our Public Events page. See the Festival's website for the full programme.

 


Programme

The most up to date workshop timetable is available here.

The titles and abstracts are available here.

 

 

Participants

Name Institution
Ademehin, Ibukun University of Manchester
Amicone, Floriana University of Manchester
Andersen, Henning Haahr Aarhus University
Arakawa, Tomoyuki Kyoto University
Bach, Tran University of Edinburgh
Bavula, Vladimir University of Sheffield
Bazlov, Yuri University of Manchester
Benkart, Georgia University of Wisconsin-Madison
Brion, Michel Institut Fourier, Université de Grenoble
Chen, Cong University of Manchester
De Concini, Corrado Univeristà Sapienza "Roma"
Dolce, Salvatore The University of Edinburgh & University of Rome "La Sapienza"
Donkin, Steve University of York
Farnsteiner, Rolf Universität Kiel
Friedlander, Eric University of Southern California
Geranios, Harry University of York
Ginzburg, Viktor University of California, Santa Cruz
Goodwin, Simon University of Birmingham
Gordon, Iain University of Edinburgh
Gruson, Caroline Université de Lorraine
Jordan, David University of Edinburgh
Kleshchev,, Alexander University of Oregon
Lanini, Martina University of Edinburgh
Lenagan, Tom University of Edinburgh
Lenells, Jonatan Baylor University
Levy, Paul Lancaster University
Loseu, Ivan Northeastern University
Lu, Tao University of Sheffield
Malev, Sergey Univeristy of Edinburgh
Malle, Gunter TU Kaiserslautern
Moreau, Anne University of Poitiers
Nolan, Brendan University of Kent
Petukhov, Alexey University of Manchester
Premet, Alexander The University of Manchester
Procesi, Claudio universita di Roma La Sapienza
Przezdziecki, Tomasz University of Glasgow
Purslow, Thomas University of Manchester
Rumynin, Dmitriy University of Warwick
Serganova, Vera UC Berkeley
Sevastyanov, Alexey University of Aberdeen
Skryabin, Serge Kazan Federal University
Spenko, Spela Vrije Universiteit Brussels
Stafford, Toby University of Manchester
Stewart, David University of Newcastle
Strade, Helmut University of Hamburg/Germany (emeriti)
Tange, Rudolf University of Leeds
Testerman, Donna EPFL
Thiel, Ulrich University of Stuttgart
Topley, Lewis University of Padova
Vignoli, Veronica
Weelinck, Tim University of Edinburgh
White, Noah University of Edinburgh
Yakimova, Oksana University of Jena