Workshop
Cherednik Algebras
Jun 18, 2007 - Jun 22, 2007
Kings Buildings, University of Edinburgh
Organisers
Name | Institution |
---|---|
Gordon, Iain | University of Edinburgh |
Scientific Organisers
Dr Karin Baur, University of Leicester
Professor Pavel Etingof, Massachusetts Institute of Technology
Professor Victor Ginzburg, University of Chicago
Professor Iain Gordon, University of Edinburgh
Dr Alison Parker, University of Leicester
Dr Catharina Stroppel, University of Glasgow
Short Report
The workshop was attended by around seventy mathematicians, a mixture of PhD students and postdocs, UK based researchers working in related topics and international leaders in the field of Cherednik Algebras. There were twenty six talks during the week, the majority of which reported on research in Cherednik algebras that had been carried out in the last six months. These talks represented many different points of view on the subject - algebraic, geometric, combinatorial and analytic - and featured several significant breakthroughs from the last couple of months. The week included a special lecture on Open Problems designed for non-experts. There was a great deal of interaction throughout the workshop, and one of the great bonuses was the chance for on-the-spot discussion with people with intellectually and geographically diverse backgrounds. An immediate outcome of the workshop will be a special issue of Selecta Math devoted to Cherednik Algebras: this will feature mostly the ICMS participants, writing either research or survey articles.
Participants list and links to available presentations are further down this page.
Download the pdf file of the full report
Original Details
Cherednik algebras were first introduced in 1994 in the guise of double affine Hecke algebras to solve the Macdonald inner product conjectures. Since then, these algebras and their offshoots have become increasingly influential in a growing number of fields. Their representation theory has significant connections with algebraic geometry, combinatorics, finite dimensional algebra, homological algebra, integrable systems, Lie theory, noncommutative algebra and q–calculus: they have been used to confirm conjectures and answer questions in all of these subjects.
The first goal of this workshop is to bring together the international figures working on Cherednik algebras. There are many different strands to the field, and it is vital that as much discussion as possible takes place between researchers. The workshop to act as a primer for future research. To achieve this the meeting will address the following general areas (as well as others that prove to be important or that arise in the meantime):
- quantisation of symplectic algebraic varieties;
- representation theory of cyclotomic Hecke algebras;
- generalised Calogero–Moser systems;
- geometric representation theory through quantum Hamiltonian reduction;
- Lie theoretic combinatorics (Kazhdan–Lusztig theory, orthogonal polynomials).
A second aim is to widen interest amongst the UK representation theory community in Cherednik algebras and their applications, and to found new collaborations between UK mathematicians.
A third aim is to give young mathematicians access to established, international researchers in this field. This will be achieved through our objective of having a series of six short talks in the workshop, through the relatively small number of participants, and through the timetabling of long afternoon discussion breaks in our programme.
The Organisers would like to thank the Glasgow Mathematical Journal Research Support Fund, the Edinburgh Mathematical Society Research Support Fund and the London Mathematical Society for their support for this workshop.
Arrangements
Venue
The Workshop will be held in the James Clerk Maxwell Building (JCMB), King's Buildings, University of Edinburgh . The lectures will be held n Room 6301, with registration, teas, coffees and break-out space in Rooms 5326 and 5327.
Registration
There will be a combined Registration and Welcome Buffet from 18.30 to 21.00 on Sunday 17 June, in the St Trinnean's Room, St Leonard's Hall, Pollock Halls. Food will be available throughout that period and you may register at any time between 18.30 and 21.00.
Those who cannot register on Sunday evening may do so at King's Buildings from 08.30-09.00 before the talks start on Monday morning.
Accommodation
ICMS has arranged en suite rooms in university accommodation in Pollock Halls for those who require it. Participants who are being funded are also free to make their own arrangements and may claim back the cost, with receipts, up to a maximum of £35 per night for bed and breakfast. A list of Edinburgh accommodation of various sorts and prices can be found on the Accommodation Page on the ICMS web site. Section 4 is particularly relevant. June is very busy in Edinburgh and early booking is recommended.
Meals and Refreshments
There will be a Registration buffet in the St Trinneans Room in St Leonards, Pollock Halls, (near the Reception Centre – see map) on Sunday evening and a Workshop dinner on Thursday evening in the St Trinnean's Room. Morning and afternoon refreshments and lunch will be provided at the workshop venue. You will be given vouchers for lunch in the first floor restaurant in King’s Buildings House (No 10 on the map). There will be a reception with wine and nibbles at 17.30 on Wednesday 20 June at ICMS, 14 India Street.
Programme
Sunday 17 June18.30-21.00 | Registration & buffet, St Trinnean's Room, St Leonard's, Pollock Halls |
Monday 18 June
08.30-09.00 | Registration - Room 5326, JCMB |
09.00-10.00 | Iain Gordon (University of Edinburgh) What is a Cherednik algebra |
10.00-11.00 | Raphael Rouquier (University of Oxford) Introduction to Cherednik algebras, I |
11.00-11.30 | Coffee break |
11.30-12.30 | Victor Ginzburg (University of Chicago) Character sheaves and Cherednik algebras I |
12.30-14.30 | Lunch, KB House |
14.30-15.30 | Raphael Rouquier (University of Oxford) Introduction to Cherednik algebras, II |
15.30-16.30 | Will Turner (University of Oxford) Cubist algebras |
16.30-17.00 | Coffee break |
17.00-18.00 | Monica Vazirani (University of California at Davis) The combinatorics of tableaux for the double affine Hecke algebra |
Tuesday 19 June
09.00-10.00 | Yuri Bazlov (University of Warwick) Braided doubles and rational Cherednik algebras |
10.00-11.00 | Victor Ginzburg (University of Chicago) Character sheaves and Cherednik algebras II |
11.00-11.30 | Coffee break |
11.30-12.30 | Arkady Berenstein (University of Oregon) Quasiharmonic polynomials for Coxeter groups and rational Cherednik algebras |
12.30-14.30 | Lunch, KB House |
14.30-15.30 | Takeshi Suzuki (Okayama University) Cylindrical combinatorics and the representation theory of Cherednik algebras |
15.30-16.30 | Maurizio Martino (Universität Bonn) Restricted rational Cherednik algebras and two-sided cells |
16.30-17.00 | Coffee break |
17.00-18.00 | Raphael Rouquier (University of Oxford) Microlocalization of rational Cherednik algebras |
Wednesday 20 June
09.00-10.00 | Alexander Premet (University of Manchester) Primitive ideals and finite W-algebras |
10.00-11.00 | Pavel Etingof (Massachusetts Institute of Technology) Geometry of rational Cherednik algebras, I |
11.00-11.30 | Coffee break |
11.30-12.30 | Eric Opdam (University of Amsterdam) Classification and structure of discrete representations of affine Hecke algebras |
12.30-13.00 | Pavel Etingof (Massachusetts Institute of Technology) Open problems |
13.00-14.30 | Lunch, KB House |
14.30 onwards | Free afternoon |
17.30-19.00 | Reception with wine & nibbles, ICMS, 14 India Street |
Thursday 21 June
09.00-10.00 | Nicholas Guay (Université de Versailles) Quantum algebras associated to quivers and symplectic reflection algebras |
10.00-11.00 | David Hernandez (Université de Versailles) Double affine quantum algebras and their representations |
11.00-11.30 | Coffee break |
11.30-12.30 | Pavel Etingof (Massachusetts Institute of Technology) Geometry of rational Cherednik algebras, II |
12.30-14.30 | Lunch, KB House |
14.30-15.30 | Eric Rains (University of California at Davis) New deformations of Coxeter groups |
15.30-16.30 | Michela Varagnolo (Université de Cergy-Pontoise) Representation theory of double affine Hecke algebras, I |
16.30-17.00 | Coffee break |
17.00-18.00 | Eric Vasserot (Université Paris 7) Representation theory of double affine Hecke algebras, II |
19.30 | Workshop Dinner, St Trinnean's Room, St Leonard's, Pollock Halls |
Friday 22 June
09.30-10.30 | Maxim Nazarov (University of York) Extremal cocycles on Weyl groups and the reflection equation |
10.30-11.00 | Coffee break |
11.00-12.00 | Silvia Montarani (Massachusetts Institute of Technology) Finite dimensional representations of symplectic reflection algebras associated to wreath products |
12.00-13.00 | Pavel Etingof (Massachusetts Institute of Technology) Surprise |
13.00-14.00 | Lunch, KB House |
14.00-15.00 | Yuri Berest (Cornell University) The generalised Calogero-Moser spaces |
Background Lecture Notes:
Here are some notes from a graduate school on Cherednik Algebras in Luminy from 2/4-6/4 2007 . They are from 4 series of introductory lectures.
- Category O and finite dimensional representations of rational Cherednik algebras by Nicolas Guay (1, 2, 3, 4)
- Rational Cherednik algebras, category O and shift operators by Eric Opdam
- Representations of double affine Hecke algebras by Eric Vasserot
- Rational Cherednik algebras and Hilbert schemes by Iain Gordon
A further paper has also been received: Open problems by Pavel Etingof and Victor Ginzburg.
Presentations:
Presentation Details | |
---|---|
Bazlov, Yuri | |
Braided doubles and rational Cherednik algebras | |
View Abstract | |
Berenstein, Arkady | |
Quasiharmonic polynomials for Coxeter groups and rational Cherednik algebras | |
View Abstract | |
Etingof, Pavel | |
Geometry of rational Cherednik algebras | |
View Abstract | |
Ginzburg, Viktor | |
Character sheaves and Cherednik algebras | |
View Abstract | |
Hernandez, David | |
Double affine quantum algebras and their representations | |
View Abstract | |
Martino, Maurizio | |
Restricted rational Cherednik algebras and two-sided cells | |
View Abstract | |
Montarani, Silvia | |
Finite dimensional representations of symplectic reflection algebras associated to wreath products | |
View Abstract | |
Nazarov, Maxim | |
Extremal cocycles on Weyl groups and the reflection equation | |
View Abstract | |
Opdam, Eric | |
Classification and structure of discrete representations of affine Hecke algebras | |
View Abstract | |
Premet, Alexander | |
Primitive ideals and finite W-algebras | |
View Abstract | |
Suzuki, Takeshi | |
Cylindric combinatorics and the representation theory of Cherednik algebras | |
View Abstract | |
Turner, Will | |
Cubist algebras | |
View Abstract | |
Vasserot, Eric | |
Representation theory of double affine Hecke algebras | |
View Abstract | |
Vazirani, Monica | |
The combinatorics of tableaux for the double affine Hecke algebra | |
View Abstract |
Participants
Name | Institution |
---|---|
Alev, Jacques | University of Reims |
Ardakov, Konstantin | University of Oxford |
Baur, Karin | University of Graz |
Bazlov, Yuri | University of Manchester |
Bellamy, Gwyn | University of Glasgow |
Berenstein, Arkady | University of Oregon |
Berest, Yuri | Cornell University |
Berger, Roland | University of Saint-Etienne |
Braden, Harry | University of Edinburgh |
Brown, Ken A | University of Glasgow |
Chalykh, Oleg | University of Leeds |
Chervov, Alexander | ITEP Moscow |
Cox, Anton | City University London |
Dotsenko, Vladimir | Trinity College Dublin |
Etingof, Pavel | Massachusetts Institute of Technology |
Eu, Ching-Hwa | MIT |
Feigin, Misha | University of Glasgow |
Geck, Meinolf | University of Aberdeen |
Ginzburg, Viktor | University of California, Santa Cruz |
Gordon, Iain | University of Edinburgh |
Grabowski, Jan | University of Oxford |
Grime, Matthew | University of Bristol |
Grojnowski, Ian | University of Cambridge |
Guay, Nicholas | Université de Versailles |
Gupta, Neha | University of Warwick |
Hernandez, David | CNRS - Université de Versailles |
Hinchcliffe, Victoria | University of Sheffield |
Iancu, Lacrimioara | University of Aberdeen |
Ion, Bogdan | Universities of Pittsburgh & Bonn |
Jacon, Nicolas | Université de Franche-Comté |
Kolb, Stefan | Newcastle University |
Krähmer, Ulrich | Technische Universität Dresden |
Kremnizer, Kobi | Massachusetts Institution of Technology |
Kuwabara, Toshiro | Kyoto University |
Launois, Stéphane | University of Kent |
Lenagan, Tom | University of Edinburgh |
Loktev, Sergey | Institute for Theoretical and Experimental Physics |
Ma, Xiaoguang | MIT |
Macauley, Monica | University of Glasgow |
Macleod, Marjory | University of Glasgow |
Martin, Paul | University of Leeds |
Martino, Maurizio | University of Bonn |
McGerty, Kevin | University of Oxford |
Montarani, Silvia | Massachusetts Institute of Technology |
Nazarov, Maxim | University of York |
Opdam, Eric | Korteweg de Vries Institute/University of Amsterdam |
Parashar, Deepak | University of Warwick |
Parker, Alison | University of Leeds |
Premet, Alexander | University of Manchester |
Rains, Eric | University of California at Davis |
Richard, Lionel | University of Edinburgh |
Rigal, Laurent | Université Jean-Monnet |
Rouquier, Raphaël | University of Oxford |
Russell, Euan | University of Edinburgh |
Rybnikov, Leonid | Institute for Theoretical and Experimental Physics (ITEP) |
Sahi, Siddhartha | Rutgers University |
Schedler, Travis | Massachusetts Institute of Technology |
Sergeev, Alexander | Loughborough University |
Sevastyanov, Alexey | University of Aberdeen |
Sierra, Susan | University of Edinburgh |
Smith, Paul | University of Washington |
Stafford, Toby | University of Manchester |
Stokman, Jasper | University of Amsterdam |
Stroppel, Catharina | University of Bonn |
Suzuki, Takeshi | Math. Department, Faculty of Science, Okayama University |
Turner, Will | University of Aberdeen |
Ubly, Glenn | University of Southampton |
Vale, Richard | Universities of Glasgow & Freiburg |
Varagnolo, Michela | Université de Cergy-Pontoise |
Vasserot, Eric | Université Paris 7 |
Vazirani, Monica | University of California at Davis |
Yvonne, Xavier | Université Lyon I |