Entrance hall of the ICMS Workshop

Torsors: theory and applications

Jan 10, 2011 - Jan 14, 2011

ICMS, 15 South College Street Edinburgh

Organisers

Name Institution
Batyrev, Victor Universität Tübingen
Skorobogatov, Alexei N Imperial College London

The aim of the workshop is to bring together those who work with torsors from different perspectives (geometric invariant theory, computational algebraic geometry, representation theory, non-abelian cohomology) and those who apply torsors in arithmetic geometry. 

Short report

The idea of the meeting was to bring together mathematicians who use torsors in their research. Two mini-courses presented recent achievements on the borderline between geometric invariant theory and representation theory. One morning session was devoted to new applications of étale homotopy; arithmetic applications of torsors featured in a number of other talks. On the whole, talks were accessible to a heterogeneous audience of experts, postdocs and PhD students coming from different backgrounds (algebra, algebraic geometry and arithmetic geometry). We had a good mix of speakers: well established influential researchers as well as brilliant younger people. Much discussion went on between the talks. One goal has already been achieved: mathematicians working in areas that are related but which had limited contact have become aware of the existing methods and techniques. We are confident that this cross-fertilisation of ideas will continue. There was sufficient enthusiasm to publish a volume of conference proceedings featuring lecture notes of the two mini-courses.

The full report can be found here.

 

Arrangements

Participation
Participation is by invitation only. The workshop will begin on Monday morning 10 January 2011 and finish on Friday afternoon 14 January 2011.

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. If you do require a visa, ICMS can (on request) provide a signed invitation letter.

Venue
The workshop will take place at 15 South College Street, ICMS headquarters. South College Street is a small side street of Nicolson Street and it is next to Old College which is a local landmark. If you need to ask for directions, most people should know these places.

Wireless Access
ICMS at 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.  For those without laptops, there are a number of computers available for you to check your emails. Delegates are welcome to make use of the public areas at 15 South College Street throughout the week.

Accommodation
Delegates who wish to have accommodation booked for them are asked to tick the appropriate box on the registration form. Accommodation is block booked for single occupancy. Delegates who plan to travel with partners and/or family should contact ICMS to discuss this. All booked accommodation is located in the Pollock Halls area (a map will be available here shortly). When arriving to the Pollock Halls campus please go to the Reception Centre to check in or for further instructions (during some hours check-in may be available in the respective accommodations). The Reception Centre is manned 24/7.

Wednesday 12 January - afternoon activity
We are very pleased to be able to offer a very interesting guided tour of Edinburgh's Historic Vaults during the free afternoon on Wednesday 12 January. More details will follow.

Map
This map shows the location of the Pollock Halls area where the accommodation is located, and the location of the workshop venue (ICMS, 15 South College Street).

Insurance
All delegates must ensure their travel insurance cover is adequate. ICMS cannot be held responsible for costs incurred in case of flight delays or similar.  

Programme

Programme published 14 December 2010. Last amendment 13 January 2011.

 

Monday 10 January

09.00 - 09.55

Registration and coffee/tea

09.55 - 10.00

Welcome & Health and Safety information

10.00 - 10.50

Victor Batyrev (Universität Tübingen)
Distribution of rational points and Mori program

10.50 - 11.20

Coffee and tea served in the Chapterhouse

11.20 - 12.20

Jürgen Hausen (Universität Tübingen)
Cox rings and geometric invariant theory (part I) Link to slides

12.20 - 14.30

Lunch served in the Chapterhouse

14.30 - 15.30

Vera Serganova (University of California at Berkley)
Representation theory, torsors and del Pezzo surfaces (part I) Link to slides

15.30 - 16.00

Coffee and tea served in the Chapterhouse

16.00 - 16.50

Jacob Stix (Universität Heidelberg)
On the section conjecture over finite fields

17.00 - 17.50

Felipe Voloch (University of Texas at Austin)
Finite descent obstructions for integral points on curves Link to slides

18.00 - 19.30

Wine reception


Tuesday 11 January

09.00 - 10.00

Jürgen Hausen (Universität Tübingen)
Cox rings and geometric invariant theory (part II) Link to slides

10.10 - 11.10

Vera Serganova (University of California at Berkley)
Representation theory, torsors and del Pezzo surfaces (part II) Link to slides

11.10 - 11.40

Coffee and tea served in the Chapterhouse

11.40 - 12.30

Phillipe Gille (Ecole Normale Supérieure)
Torsors and classification of multiloop Lie algebras

12.30 - 15.00

Lunch

15.00 - 15.50

Mathieu Florence (Université Paris 6)
Equivariant geometry of Grassmannians

15.50 - 16.20

Coffee and tea served in the Chapterhouse

16.20 - 17.10

Jenia Tevelev (University of Massachusetts at Amherst)
Geometric tropicalization and Cox coordinates


Wednesday 12 January

09.00 - 09.50

Ambrus Pál (Imperial College London)
Rational points and homotopy theory

10.00 - 10.50

Yonatan Harpaz (The Hebrew University in Jerusalem)
Homotopy obstructions to integral points

10.50 - 11.20

Coffee and tea served in the Chapterhouse

11.20 - 12.10

Tomer Shlank (The Hebrew University in Jerusalem)
The Brauer- Manin obstruction applied to ramified covers

12.10- 13.45

Lunch

13.45 - 15.00

Extracurricular activity: Guided tour of the Historic Vaults
(more details to follow)


Thursday 13 January

09.00 - 10.00

Jürgen Hausen (Universität Tübingen)
Cox rings and geometric invariant theory (part III) Link to slides

10.10 - 11.10

Vera Serganova (University of California at Berkley)
Representation theory, torsors and del Pezzo surfaces (part III) Link to slides

11.10 - 11.40

Coffee and tea served in the Chapterhouse

11.40 - 12.30

Ulrich Derenthal (Ludwig-Maximilians-Universität München)
Counting rational points via universal torsors

12.30 - 15.00

Lunch

15.00 - 15.50

Antonio Laface (Universidad de Concepción)
Techniques for calculating Cox rings

15.50 - 16.20

Coffee and tea served in the Chapterhouse

16.20 - 17.10

Ivan Arzhantsev (Lomonosov Moscow State University)
Two applications of Cox rings in affine geometry

19.00-

Workshop dinner at The Magnum Restaurant, 1 Albany Street


Friday 14 January

09.00 - 09.50

David Harari (Universite Paris-Sud)
Descent theory for open varieties

10.00 - 10.50

Cyril Demarche (Université Paris 6)
Strong approximation in homogeneous spaces over number fields

10.50 - 11.20

Coffee and tea served in the Chapterhouse

11.20 - 12.10

Mikhail Borovoi (Tel Aviv University)
Extended Picard complex of a homogeneous space

12.20 - 13.10

Sergey Gayfullin (Moscow State University)
Cox rings of S-varieties

 

End of workshop

 

Presentations:

Presentation Details
Arzhantsev, Ivan
Two applications of Cox rings in affine geometry
View Abstract Down
Batyrev, Victor
Distribution of rational points and Mori program
View Abstract Down
Borovoi, Mikhail
Extended Picard complex of a homogeneous space
View Abstract Down
Demarche, Cyril
Strong approximation in homogeneous spaces over number fields
View Abstract Down
Derenthal, Ulrich
Counting rational points via universal torsors
View Abstract Down
Gayfullin, Sergey
Cox rings of S-varieties
View Abstract Down
Gille, Philippe
Torsors and classification of multiloop Lie algebras
View Abstract Down
Harari, David
Descent theory for open varieties
View Abstract Down
Harpaz, Yonatan
Homotopy obstructions to integral points
View Abstract Down
Laface, Antonio
Techniques for calculating Cox rings
View Abstract Down
Pál, Ambrus
Rational points and homotopy theory
View Abstract Down
Shlank, Tomer
The Brauer- Manin obstruction applied to ramified covers
View Abstract Down
Stix, Jakob
On the section conjecture over finite fields
View Abstract Down
Tevelev, Jenia
Geometric tropicalization and Cox coordinates
View Abstract Down
Voloch, Felipe
Finite descent obstructions for integral points on curves
View Abstract Down

Participants

Name Institution
Arzhantsev, Ivan Lomonosov Moscow State University
Baeker, Hendrik University of Tuebingen
Batyrev, Victor Universität Tübingen
Borovoi, Mikhail Tel Aviv University
Colliot-Thélène, Jean-Louis CNRS et Université Paris-Sud
Demarche, Cyril Université Paris 6
Derenthal, Ulrich Ludwig-Maximilians-Universität München
Florence, Mathieu Université Paris 6
Gayfullin, Sergey Moscow State University
Gille, Philippe Ecole Normale Supérieure
Harari, David Universite Paris-Sud
Harpaz, Yonatan The Hebrew University in Jerusalem
Hausen, Jürgen Universität Tübingen
Herppich, Elaine University of Tübingen
Kuyumzhiyan, Karine Universite Grenoble I / Moscow State University
Laface, Antonio Universidad de Concepción
Lee, Ting-Yu DMA, ENS
Loughran, Daniel University of Bristol
Mendes da Costa, David University of Bristol
Mennecke, Susanne Universität Tübingen
Pál, Ambrus Imperial College London
Perepechko, Aleksandr Institut Fourier
Pirutka, Alena Universite Paris-Sud
Preu, Thomas Zurich Graduate School in Mathematics
Serganova, Vera UC Berkeley
Shlank, Tomer Hebrew University In Jerusalem
Skorobogatov, Alexei N Imperial College London
Stix, Jakob Universität Heidelberg
Stoll, Michael Universität Bayreuth
Testa, Damiano University of Oxford
Tevelev, Jenia University of Massachusetts at Amherst
Viray, Bianca Brown University
Voloch, Felipe University of Texas at Austin