Entrance hall of the ICMS Workshop

Higher Dimensional Algebraic Geometry: Classification, Minimal Models, Fano Varieties and Stacks

Sep 22, 2008 - Sep 26, 2008

ICMS, 14 India Street, Edinburgh

Organisers

Name Institution
Cheltsov, Ivan University of Edinburgh
Corti, Alessio Imperial College London
Reid, Miles University of Warwick

Short Report

The two main objectives of this workshop were to put into focus rapid recent developments in the higher dimensional minimal model program (HD MMP), and to consolidate advances in the geometry of Fano and Calabi-Yau 3-folds that have arisen over the last decade. In addition, the meeting helped plan how to exploit new results, methods and problems arising from these developments.

The last few years have seen dramatic advances in HD MMP, with the proof of the existence of minimal models under appropriate conditions, and the prospect within a few years of having a complete generalisation of the minimal model program and the classification of varieties in all dimensions, comparable to the known foundational framework of the theory or surfaces and 3-folds. At the same time, other topics in algebraic geometry are enjoying prominent advances; these include birational geometry (especially the geometry of Fano varieties), the geometry of moduli spaces, resolution of singularities, orbifold cohomology, etc.

These topics feature in several international programs and conferences, including the 2007-08 Warwick EPSRC algebraic geometry symposium and the MSRI half-year program on Algebraic geometry Jan-May 2009. Some of the problem areas we covered are fast moving, but we also considered a number of more established questions.

Link to full report

Arrangements

Participation
Participation is by invitation only. The workshop will begin with registration at on Monday 22 September and finish on Friday 26 September 2008.

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 provide a signed invitation letter.

Venue
The workshop will take place at the head-quarters of ICMS, 14 India Street, Edinburgh. This house is the birthplace of James Clerk Maxwell and is situated in the historic New Town of Edinburgh, near the city centre.

The ICMS travel pages contain advice on how to travel to Edinburgh. For local information the finding ICMS page shows the location of ICMS and contains useful maps of the city centre.

The seminar room at ICMS has whiteboards, 2 overhead projectors, a data projector and laptop.

Wireless access is available throughout the ICMS building. There are also five public PCs which may be used at any time for internet access and to check email.

Accommodation
ICMS will arrange single en-suite rooms in local guest houses for those who require it. Accommodation is typically about 15 to 30 minutes walk from ICMS. Participants are also free to make their own arrangements and may claim back the cost, with receipts, up to a maximum of £45.00 per night bed and breakfast. A list of Edinburgh accommodation of various sorts and prices is available here . Sections 1-3 are particularly relevant.

Meals and Refreshments
Buffet lunches will be provided on Monday 22 September and Friday 26 September only. 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.

Morning and afternoon refreshments will be provided throughout the workshop.

There will be an informal wine reception after the close of lectures on Monday 22 September.

On Tuesday 23 September there will be an informal dinner at a local restaurant.

The workshop dinner will take place on the evening of Thursday 25 September.

Registration
Registration will take place on Monday 22 September from 9.00 to 10.00.

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 and Friday, the wine reception, the informal supper on Tuesday and the Workshop Dinner on Thursday evening.

If we have agreed to pay some of your travel costs, you will be informed in the 'final information' email. Reimbursement will take place after the workshop. At Registration you will be given an expenses claim form and this should be submitted to ICMS, with receipts. Please note that we cannot reimburse any item without a receipt. 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 should supply their IBAN and SWIFT/BIC code.

Under the terms of our EPSRC funding we are required to charge a 30.00 GBP registration fee to cover costs not admissible under the grant. The fee will be payable on arrival at the workshop payment may be by cash, sterling cheque or credit/debit card. If you anticipate any difficulty covering the fee, please let me know.

Programme

PROVISIONAL (subject to change)

Monday 22 September

09.00 - 10.00

Registration

10.00 - 11.00

Jim Bryan (University of British Columbia)
The crepant resolution conjecture for Donaldson-Thomas theory and the orbifold topological vertex

11.00 - 11.30

Tea/Coffee

11.30 - 12.30

Frances Kirwan (University of Oxford)
Quotients by non-reductive group actions

12.30 - 14.00

Buffet lunch

14.00 - 15.00

Aleksandr Pukhlikov (University of Liverpool)
Birationally rigid Fano varieties

15.00 - 15.30

Tea/Coffee

15.30 - 16.30

Caucher Birkar (University of Cambridge)
Boundedness vs thresholds and flips

16.30 - 17.30

Nikos Tziolas (University of Cyprus)
Smoothings of schemes with non-isolated singularities

17.30 - 18.30

Wine reception at ICMS, 14 India Street

 

Tuesday 23 September

09.30 - 10.30

Hiroshi Iritani (Imperial College London)
Fourier-Mukai transformations and toric quantum cohomology
(Coates, Corti, Iritani and Tseng I)

10.30 - 11.00

Tea/Coffee

11.00 - 12.00

Tom Coates (Imperial College London / Royal Society)
Higher genus Gromov-Witten invariants and crepant resolutions
(Coates, Corti, Iritani and Tseng II)

12.00 - 13.00

Misha Verbitsky (Institute of Theoretical and Experimental Physics)
Nef classes on hyperkaehler manifolds

13.00 - 14.30

Lunch

14.30 - 15.30

Lawrence Ein (University of Illinois at Chicago)
Regularities of projective varieties

15.30 - 16.00

Tea/Coffee

16.00 - 17.00

Paolo Cascini (Imperial College London)
On the minimal model program

19.00 -

Informal evening meal at Nargile Turkish Restaurant, 73 Hanover Street

 

Wednesday 24 September

09.30 - 10.30

Valery Alexeev (University of Georgia)
Weighted hyperplane arrangements

10.30 - 11.00

Tea/Coffee

11.00 - 12.00

Gavin Brown (University of Kent)
Tom and Jerry and Sarkisov links on Fano 3-folds

12.00 - 13.00

Alexey Bondal (Aberdeen University)
Mirror symmetry for toric orbifolds

13.00 -

Free afternoon

 

Thursday 25 September

09.30 - 10.30

Vasily Iskovskikh (Steklov Mathematical Insitute)
On elements of prime order in the Cremona group of the plane over a perfect field

10.30 - 11.00

Tea/Coffee

11.00 - 12.00

Frederic Campana (Institut Élie Cartan Nancy)
Special orbifolds and classification

12.00 - 13.00

Dmitry Orlov (Steklov Mathematical Insitute)
Generators and dimensions of triangulated categories

13.00 - 14.30

Lunch

14.30 - 15.30

Jun-Muk Hwang (Korea Institute for Advanced Study)
Base manifolds for fibrations of projective irreducible symplectic manifolds

15.30 - 16.00

Tea/Coffee

16.00 - 17.00

Yuri Prokhorov (Moscow State University)
On Q-Fano threefolds

19.00 -

Workshop dinner at First Coast Restaurant, 99-101 Dalry Road, Edinburgh

 

Friday 26 September

09.30 - 10.30

Alessio Corti (Imperial College London)
Towards finite generation without the MMP

10.30 - 11.00

Tea/Coffee

11.00 - 12.00

Ludmil Katzarkov (University of Miami)
Generalized HMS and rationality questions

12.00 - 13.00

Dimitry Kaledin (Steklov Mathematical Insitute)
Motivic structures in non-commutative geometry

13.00 - 14.30

Buffet lunch

14.30 - 15.30

Mircea Mustata (University of Michigan)
An inductive approach to singularities of pairs

15.30 - 16.00

Tea/Coffee

16.00 - 17.00

TBA



Presentations:

Presentation Details
Alexeev, Valery
Weighted hyperplane arrangements
View Abstract Down
Birkar, Caucher
Boundedness vs thresholds and flips
View Abstract Down
Bondal, Alexei
Mirror symmetry for toric orbifolds
View Abstract Down
Brown, Gavin
Tom and Jerry and Sarkisov links on Fano 3-folds
View Abstract Down
Bryan, Jim
The crepant resolution conjecture for Donaldson-Thomas theory and the orbifold topological vertex
View Abstract Down
Campana, Frédéric
Special orbifolds and classification (subject to change)
View Abstract Down
Cascini, Paolo
On the minimal model program
View Abstract Down
Coates, Tom
Higher genus Gromov-Witten invariants and crepant resolutions
View Abstract Down
Corti, Alessio
Towards finite generation without the MMP
View Abstract Down
Ein, Lawrence
Regularities of projective varieties
View Abstract Down
Hwang, Jun-Muk
Base manifolds for fibrations of projective irreducible symplectic manifolds
View Abstract Down
Iritani, Hiroshi
Fourier-Mukai transformations and toric quantum cohomology
View Abstract Down
Iskovskikh, Vasily
On elements of prime order in the Cremona group of the plane over a perfect field
View Abstract Down
Kaledin, Dmitry
Motivic structures in non-commutative geometry
View Abstract Down
Katzarkov, Ludmil
Generalized HMS and rationality questions
View Abstract Down
Kirwan, Frances
Quotients by non-reductive group actions
View Abstract Down
Mustata, Mircea
An inductive approach to singularities of pairs
View Abstract Down
Orlov, Dmitry
Generators and dimensions of triangulated categories
View Abstract Down
Prokhorov, Yuri
On Q-Fano threefolds
View Abstract Down
Pukhlikov, Aleksandr
Birationally rigid Fano varieties
View Abstract Down
Tziolas, Nikolaos (Nikos)
Smoothings of schemes with non-isolated singularities
View Abstract Down
Verbitsky, Misha
Nef classes on hyperkaehler manifolds
View Abstract Down

Participants

Name Institution
Alexeev, Valery University of Georgia
Andreatta, Marco University of Trento
Birkar, Caucher University of Cambridge
Bondal, Alexei Steklov Mathematical Institute/Higher School of Economics
Brown, Gavin University of Kent
Bryan, Jim University of British Columbia
Campana, Frédéric Université de Lorraine
Cascini, Paolo Imperial College London
Cheltsov, Ivan University of Edinburgh
Ciliberto, Circo University of Rome Tor Vergata
Coates, Tom Imperial College London
Corti, Alessio Imperial College London
Craw, Alastair University of Bath
de Fernex, Tommaso University of Utah
Ein, Lawrence University of Illinois at Chicago
Galkin, Sergey Steklov Institute of Mathematics
Gasparim, Elizabeth University of Edinburgh
Hwang, Jun-Muk Korea Institute for Advanced Study
Iritani, Hiroshi Imperial College London
Iskovskikh, Vasily Steklov Mathematical Insitute
Kaledin, Dmitry Independent University of Moscow
Kaloghiros, Anne-Sophie Brunel University London
Katzarkov, Ludmil University of Miami
Kirwan, Frances University of Oxford
Kovalev, Alexei University of Cambridge
Lamy, Stéphane University of Warwick
Lazić, Vladimir Universität Bonn
Logvinenko, Timothy University of Liverpool
Lopez, Angelo University of Roma Tre
Lorenzo, Dibiagio University of Rome, La Sapienza
Mustata, Mircea University of Michigan
Orlov, Dmitry Steklov Mathematical Insitute
Panov, Dmitri King's College London
Park, Jihun Pohang University of Science and Technology
Prokhorov, Yuri Moscow State University
Pukhlikov, Aleksandr University of Liverpool
Reid, Miles University of Warwick
Ryder, Daniel University of Bristol
Sankaran, Gregory University of Bath
Tziolas, Nikolaos (Nikos) University of Cyprus
Verbitsky, Misha Institute of Theoretical and Experimental Physics
Wilson, Pelham University of Cambridge
Wisniewski, Jaroslaw University of Warsaw