Lie algebras, vertex algebras and automorphic forms
Aug 31, 2009 - Sep 04, 2009
15 South College Street, Edinburgh EH8 9AA
Organisers
Name | Institution |
---|---|
Höhn, Gerald | Kansas State University |
Nikulin, Viacheslav | University of Liverpool |
Scheithauer, Nils | Technische Universität Darmstadt |
Group photograph taken outside ICMS at 15 South College Street is available here.
In 1968, Kac and Moody introduced a new class of infinite dimensional Lie algebras, called Kac-Moody algebras, which generalize the finite dimensional simple Lie algebras in a natural way. These Lie algebras became very important in many areas of mathematics. In 1986, Borcherds defined vertex algebras as an axiomatic framework for conformal field theories. Certain subquotients of these algebras have a Lie algebra structure. The Lie algebras obtained in this way are very similar to Kac-Moody algebras but might have imaginary simple roots. These generalized Kac-Moody algebras describe symmetries in string theory. The most interesting generalized Kac-Moody algebras have denominator identities which are automorphic forms on orthogonal groups.
The relations between generalized Kac-Moody algebras, vertex algebras and automorphic forms have led to fascinating results e.g. Borcherds' proof of Conway and Norton's moonshine conjecture for the monster. However, many important problems are still open including:
- Generalized Moonshine
- Moonshine for other groups
- Classification of vertex algebras and generalized Kac-Moody algebras
- Construction of vertex algebras and generalized Kac-Moody algebras
- Automorphic forms related to vertex algebras and generalized Kac-Moody algebras
- Related areas as hyperbolic reflection groups and moduli spaces
In this workshop we present the recent achievements in these problems. We also want to discuss possible new approaches to them.
PDF file of full report.
Arrangements
Venue
The workshop will be held at 15 South College Street, Edinburgh. All lectures will be held in the Newhaven Lecture Theatre. To view this room and a list of the visual equipment available click here. In addition, an overhead projector will be available to use and two blackboards have recently been installed. Follow this link for a map showing the location of 15 South College Street.
Computer Access
The workshop venue, 15 South College Street, has wireless access throughout. On arrival at Registration you will be given instructions and a code for accessing the wireless network. If you wish to use a computer while in 15 South College Street please ask a member of the ICMS staff.
Travel
Information about travel to the UK and Edinburgh is available here. You may find this map useful.
Lothian buses charge 1.20 GBP for a single journey and 3.00 GBP for a day ticket. Please note that the exact fare is required and no change is given.
A taxi directly from the airport will cost approximately 15.00 to 20.00 GBP to the city centre for a one-way journey.
From the airport, you can take the airport bus Airlink to the city centre. It will cost you 3.50 GBP for a single ticket, or 6.00 GBP return. More details on the airport bus Airlink is available here. The bus will take you to Waverley Bridge (next to Waverley Railway Station).
If travelling by train, please note that Edinburgh has two railway stations - Waverley Railway Station being the main station and closest to the workshop venue at 15 South College Street. If you alight the train at Edinburgh Waverley, the workshop venue is an easy 10 minute walk over North and South Bridge map.
Accommodation
ICMS has arranged accommodation for participants who require it. En-suite rooms have been booked in two locations (unless otherwise requested): The Kenneth MacKenzie Suite in the city centre, and Chancellor's Court in the Pollock Halls area. A map of the location of the two accommodation venues and the location of the workshop venue can be found here.
Participants are also free to make their own arrangements. 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. September is busy in Edinburgh and early booking is recommended.
Meals and Refreshments
Morning and afternoon refreshments will be provided on each day of the workshop.
On Monday 31 August, the first day of the workshop, a light buffet lunch will be provided free of charge to participants in the in the Chapterhouse on the ground floor of 15 South College Street. For the remainder of the days, participants are free to go out for lunch and explore the many cafes, restaurants, sandwich shops and bars in the surrounding area. On arrival we will provide you with a ‘welcome’ pack which will contain information about eating places nearby.
Following the last talk on Tuesday 1 September, an informal wine reception, to which all all participants are invited, will take place in the Chapterhouse on the ground floor of 15 South College Street. The workshop dinner will take place at 19.30 at Blonde, 75 St. Leonards's Street, Edinburgh, EH8 9QR, on the evening of Thursday 3 September. The workshop grant will cover the cost of this catering.
Registration
Registration will take place on Monday 31 August from 9.00 to 10.00 in the Chapterhouse on the ground floor of 15 South College Street.
Financial Arrangements
Unless otherwise specified in your invitation letter, the workshop grant will cover the cost of your bed and breakfast accommodation, tea/coffee throughout the workshop, lunch on Monday only, the wine reception, and the Workshop Dinner on Thursday evening.
If we have agreed to pay some of your travel costs, you will be informed by email. Reimbursement will take place after the workshop and will involve payment directly into your bank account. At Registration you will be given an expenses claim form and this should be submitted to ICMS, with original receipts. It would be helpful if you could bring your bank details to the workshop. In addition to the bank account number, participants from the USA and Canada will require their bank’s routing number, those from the UK will be asked for the bank sort code, and those from Europe and the rest of the world, their IBAN and SWIFT/BIC code. We cannot reimburse any item without a signed claim form and original receipts.
Unless otherwise stated in your invitation or further correspondence, there will be a registration fee of 40.00 GBP for the workshop. We ask that this is paid in advance by using this credit or debit card payment form. The form should be printed out, completed and faxed back (as email is not a secure way of sending credit card information). The fax number is on the form. If it is not possible for you pay in advance, you may print out the credit/debit card form above and bring the completed form along to Registration. We prefer not to handle cash at Registration. Please note we do not accept American Express or Discover Card. Alternatively, we can accept sterling cheques. The cheque should be made payable to Heriot-Watt University and can be handed over at Registration.
Knowledge transfer event
Date 1 September
Time 16.45 to 20.00 (See the below programme)
As part of the workshop, Victor Kac (MIT) will deliver a lecture on Tuesday 1 September from 17.30 to 18.30 in the Newhaven lecture theatre of the e-Science building, 15 South College Street, Edinburgh. This talk will be opened up to mathematicians and mathematical physicists from all Scottish Universities.
Those interested in attending only the lecture (and not the rest of the workshop) should register their interest by emailing Johanna Kytöharju at ICMS, giving the following information:
- your name and institution
A wine reception for all attendees will follow the lecture.
Please note the workshop participants have been automatically registered for this talk.
Programme
Monday 31 August
09.00 - 10.00 | Registration and coffee, Ground Floor, 15 South College Street |
10.00 - 10.15 | Welcome |
10.15 - 11.00 | Viacheslav Nikulin (University of Liverpool) PDF of Presentation On the classification of arithmetic hyperbolic reflection groups |
11.15 - 12.00 | Rudolf Scharlau (Technische Universität Dortmund) PDF of Presentation On the explicit construction of arithmetic hyperbolic reflection groups |
12.00 - 14.00 | Lunch provided in the Chapterhouse, Ground Floor, 15 South College Street |
14.00 - 14.45 | Daniel Allcock (University of Texas at Austin) On the classification of reflective Lorentzian lattices |
15.00 - 15.45 | Tathagata Basak (University of Chicago) PDF of Presentation A complex hyperbolic reflection group and the bimonster |
15.45 - 16.15 | Tea/Coffee |
16.15 - 17.00 | Robert Griess (University of Michigan) Automorphism groups of VOAs |
Tuesday 1 September
09.00 - 09.45 | Gerald Höhn (Kansas State University) PDF of Presentation Vertex algebra constructions of generalized Kac-Moody algebras |
09.45 - 10.15 | Tea/Coffee |
10.15 - 11.00 | Scott Carnahan (Massachusetts Institute of Technology) PDF of Presentation Singular commutative rings in a braided category |
11.15 - 12.00 | Antun Milas (University at Albany, SUNY) W-algebra extensions of minimal models |
12.00 - 14.00 | Lunch break |
14.00 - 14.45 | Masahiko Miyamoto (University of Tsukuba) PDF of presentation Semirigidity and flatness of C_2-cofinite VOAs |
15.00 - 15.45 | Ching Hung Lam (Academia Sinica, Taipei) PDF of Presentation Virasoro frames and structure codes of the moonshine vertex operator algebra |
16.00 - 16.45 | John McKay (Concordia University) Absorbing sporadics |
Knowledge Transfer event | |
16.45 - 17.30 | Tea/Coffee |
17.30 - 18.30 | Victor Kac (MIT) PDF of Presentation Quantization and chiralization |
18.30 - 20.00 | Wine Reception in the Chapterhouse, 15 South College Street, Edinburgh |
Wednesday 2 September
09.00 - 09.45 | Nils Scheithauer (Technische Universität Darmstadt) PDF of Presentation On the classification of automorphic products and generalized Kac-Moody algebras |
10.00 - 10.45 | Valery Gritsenko (Laboratoire Paul Painlevé) The baby functions of the Borcherds form Phi_12 |
10.45 - 11.15 | Tea/Coffee |
11.15 - 12.00 | Shigeyuki Kondo (Nagoya University) PDF of Presentation The moduli spaces of Enriques, Coble surfaces and automorphic forms |
12.15 - 13.00 | Nils-Peter Skoruppa (Universität Siegen) Weil representations of finite quadratic modules and automorphic forms of critical weight |
13.00 - | Free afternoon |
Thursday 3 September
09.00 - 09.45 | Urmie Ray (Université de Reims) On Cartan subalgebras |
09.45 - 10.15 | Tea/Coffee |
10.15 - 11.00 | Chris Cummins (Concordia University) Torsion free, genus one congruence subgroups, eta products and monstrous moonshine |
11.15 - 12.00 | John Duncan (Harvard University) Rademacher sums, monstrous moonshine and black holes |
12.00 - 14.00 | Lunch break |
14.00 - 14.45 | Miranda Cheng (Harvard University) PDF of Presentation Wall-crossing, black holes and generalized Kac-Moody algebras |
15.00 - 15.45 | Christoph Schweigert (Universität Hamburg) PDF of Presentation Mapping class group representations and conformal boundary conditions |
15.45 - 16.15 | Tea/Coffee |
16.15 - 17.00 | Shrawan Kumar (University of North Carolina) PDF of Presentation The Cachazo-Douglas-Seiberg-Witten conjecture for simple Lie algebras and its generalization to symmetric spaces |
19.30 - | Workshop Dinner at Blonde Restaurant, 75 St Leonard's Street, Edinburgh |
Friday 4 September
09.00 - 09.45 | Peter Bantay (Eötvös Loránd University) PDF of Presentation Vector-valued modular forms |
09.45 - 10.15 | Tea/Coffee |
10.15 - 11.00 | Terry Gannon (University of Alberta) Mostly moonshine and vector-valued modular forms |
11.15 - 12.00 | Michael Tuite (National University of Ireland, Galway) PDF of Presentation Vertex operator superalgebras on a genus two Riemann surface |
12.00 - 14.00 | Lunch break |
14.00 - 14.45 | Hiroshi Yamauchi (Aichi University of Education) PDF of Presentation n-transposition groups and vertex operator algebras |
15.00 - 15.45 | Chongying Dong (University of California, Santa Cruz) PDF of Presentation A characterization of the vertex operator algebra L(1/2,0) otimes L(1/2,0) |
15.45 - 16.15 | Tea/Coffee |
16.15 - 17.00 | Geoffrey Mason (University of California, Santa Cruz) PDF of Presentation Vector-valued modular forms and logarithmic field theories |
Presentations:
Presentation Details | |
---|---|
Allcock, Daniel | |
On the classification of reflective Lorentzian lattices | |
View Abstract | |
Bantay, Peter | |
Vector-valued modular forms | |
View Abstract | |
Basak, Tathagata | |
A complex hyperbolic reflection group and the bimonster | |
View Abstract | |
Carnahan, Scott | |
Singular commutative rings in a braided category | |
View Abstract | |
Cheng, Miranda C.N. | |
Wall-crossing, black holes and generalized Kac-Moody algebras | |
View Abstract | |
Cummins, Chris | |
Torsion free, genus one congruence subgroups, eta products and monstrous moonshine | |
View Abstract | |
Dong, Chongying | |
A characterization of the vertex operator algebra L(1/2,0) otimes L(1/2,0) | |
View Abstract | |
Duncan, John | |
Rademacher sums, monstrous moonshine and black holes | |
View Abstract | |
Gannon, Terry | |
Mostly moonshine and vector-valued modular forms | |
View Abstract | |
Griess, Robert | |
Automorphism groups of VOAs | |
View Abstract | |
Gritsenko, Valery | |
The baby functions of the Borcherds form Phi_12 | |
View Abstract | |
Höhn, Gerald | |
Vertex algebra constructions of generalized Kac-Moody algebras | |
View Abstract | |
Hung Lam, Ching | |
Virasoro frames and structure codes of the moonshine vertex operator algebra | |
View Abstract | |
Kac, Victor | |
Quantization and chiralization | |
View Abstract | |
Kondo, Shigeyuki | |
The moduli spaces of Enriques, Coble surfaces and automorphic forms | |
View Abstract | |
Kumar, Shrawan | |
The Cachazo-Douglas-Seiberg-Witten conjecture for simple Lie algebras and its generalization to symmetric spaces | |
View Abstract | |
Mason, Geoffrey | |
Vector-valued modular forms and logarithmic field theories | |
View Abstract | |
McKay, John | |
Absorbing sporadics | |
View Abstract | |
Milas, Antun | |
W-algebra extensions of minimal models | |
View Abstract | |
Miyamoto, Masahiko | |
Semirigidity and flatness of C_2-cofinite VOAs | |
View Abstract | |
Nikulin, Viacheslav | |
On the classification of arithmetic hyperbolic reflection groups | |
View Abstract | |
Ray, Urmie | |
On Cartan subalgebras | |
View Abstract | |
Scharlau, Rudolf | |
On the explicit construction of arithmetic hyperbolic reflection groups | |
View Abstract | |
Scheithauer, Nils | |
On the classification of automorphic products and generalized Kac-Moody algebras | |
View Abstract | |
Schweigert, Christoph | |
Mapping class group representations and conformal boundary conditions | |
View Abstract | |
Skoruppa, Nils-Peter | |
Weil representations of finite quadratic modules and automorphic forms of critical weight | |
View Abstract | |
Tuite, Michael | |
Vertex operator superalgebras on a genus two Riemann surface | |
View Abstract | |
Yamauchi, Hiroshi | |
n-transposition groups and vertex operator algebras | |
View Abstract |
Participants
Name | Institution |
---|---|
Allcock, Daniel | University of Texas at Austin |
Bantay, Peter | Eötvös Loránd University |
Barraclough, Richard | Goldsmiths' College, University of London |
Basak, Tathagata | University of Chicago |
Carnahan, Scott | Massachusetts Institute of Technology |
Cheng, Miranda C.N. | Harvard University |
Cooney, Nicholas | University of Oxford |
Cummins, Chris | Concordia University |
Docherty, Pamela | University of Edinburgh |
Dong, Chongying | University of California, Santa Cruz |
Duncan, John | Harvard University |
Gannon, Terry | University of Alberta |
Griess, Robert | University of Michigan |
Gritsenko, Valery | Universite Lille 1 |
Höhn, Gerald | Kansas State University |
Hung Lam, Ching | Academia Sinica, Taipei |
Hurley, Donny | National University of Ireland, Galway |
Kac, Victor | MIT |
Kohnen, Winfried | Universität Heidelberg |
Kondo, Shigeyuki | Nagoya University |
Konechny, Anatoly | Heriot-Watt University |
Krauel, Matthew | University of California, Santa Cruz |
Kühn, Ulf | Universität Hamburg |
Kumar, Shrawan | University of North Carolina |
Lentner, Simon | Ludwig-Maximillians-Universität München |
Mason, Geoffrey | University of California, Santa Cruz |
McKay, John | Concordia University |
Milas, Antun | University at Albany, SUNY |
Miyamoto, Masahiko | University of Tsukuba |
Nikulin, Viacheslav | University of Liverpool |
Norton, Simon | Cambridge University |
Raulf, Nicole | Université des Sciences et Technologies de Lille |
Ray, Urmie | Université de Reims |
Scharlau, Rudolf | Technische Universität Dortmund |
Scheithauer, Nils | Technische Universität Darmstadt |
Schulze-Pillot, Rainer | Universität des Saarlandes |
Schweigert, Christoph | Universität Hamburg |
Skoruppa, Nils-Peter | Universität Siegen |
Spencer, Christopher | University of Edinburgh |
Tuite, Michael | National University of Ireland, Galway |
Yamauchi, Hiroshi | Aichi University of Education |
Zuevsky, Alexander | National University of Ireland, Galway |