Entrance hall of the ICMS

Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry

May 12, 2008 - May 17, 2008

ICMS, 14, India Street, Edinburgh

Organisers

Name Institution
Cluckers, Raf Université Lille 1/University of Leuven
Macintyre, Angus Queen Mary University of London
Nicaise, Johannes Université Lille 1
Sebag, Julien Université Bordeaux 1

Short Report

 

The objective of this workshop was to realize progress on Motivic Integration by gathering some of the leading specialists active in and around this domain and neighbouring domains such as Rigid Geometry and Model Theory. Since its creation by M. Kontsevich in 1995, Motivic Integration has been a rapidly developing subject connected to Algebraic Geometry, Singularity Theory, Model Theory and Number Theory. Because of the many challenges related to the development of the theory and its applications and the rapid evolution of the subject, this meeting should yield substantial new developments and open up many new challenges.

The talks were divided into two parts:

  • Short courses. Their aim was to give an introduction to the following subjects: Non-Archimedean Geometry (Bosch (2×1h), Berkovich (2×1h), Huber (2×1h)), Model Theory (Macintyre (1h), Chatzidakis (1h), Cluckers (1h)), Motivic Integration (Denef (1h), Nicaise (2×1h), Scanlon (1h), Loeser (1h));
  • Specialized talks (50 minutes), with a special emphasis on applications in singularity theory (Merle, Temkin, Veys) and the Langlands program (Fargues, Hales, Kaletha).

The short courses were of particular importance because they offered a survey of some recent developments in domains in full expansion. In particular, it was to our knowledge the first time that all major approaches to non-Archimedean geometry (rigid varieties, formal schemes, analytic spaces, adic spaces, Zariski-Riemann spaces) were presented and explained at the same conference; the short course on motivic integration covered the various formalisms developed since Kontsevich’ original work (geometric motivic integration on algebraic varieties, formal schemes and non-Archimedean spaces; model-theoretic framework of Cluckers-Loeser and Hrushovski-Kazhdan). Since these developments are not cumulative and each of the theories presents its own merits in particular applications, it was quite fruitful to introduce them all and to allow for a comparison of their specific characteristics.

 Download the pdf file of the full report

Arrangements

Participation
Participation is by invitation only. The workshop will begin with registration at 09.00 on Monday 12 May and finish on the morning of Saturday 17 May 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 7 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
A sandwich lunch will be provided on the first day of the workshop, Monday 12 May. 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 12 May.

On Tuesday 13 May you are invited to attend an informal supper at Nargile Turkish Restaurant. The workshop dinner will take place on the evening of Thursday 15 May.

Registration
Registration will take place between 10.30 and 12.00 on Monday 12 May. The talks will start at 12.00.

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 the first day, 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 by 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.

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

Mini courses:

A. Non-archimedean Geometry (6h): Bosch (2h), Berkovich (2h), Huber (2h)

B. Model Theory (3h): Macintyre, Chatzidakis, Cluckers

C. Motivic integration (5h): Denef, Nicaise (2h), Scanlon, Loeser

 

Monday 12 May

09.00 - 10.00

Registration

10.00 - 11.00

Siegfried Bosch (Westfälische Wilhelms - Universität Münster)
Introduction to formal and rigid geometry (A 1) Link to pdf file of slides

11.00 - 11.30

Coffee/Tea

11.30 - 12.30

Siegfried Bosch (Westfälische Wilhelms - Universität Münster)
Introduction to formal and rigid geometry (A 2) Link to pdf file of slides

12.30 - 14.30

Lunch

14.30 - 15.30

Zoé Chatzidakis (CNRS - Université Paris 7)
The basic model theory of valued fields (B 1) Link to pdf file of slides

15.40 - 16.40

Angus Macintyre (University of London)
Quantifier elimination in the p-adics and their algebraic closure, and issues of uniformity (B 2)

16.40 - 17.10

Coffee/Tea

17.10 - 18.00

Françoise Delon (CNRS - Université Paris 7)
C-minimal structures

18.00 - 19.00

Wine reception at ICMS, 14 India Street

 

Tuesday 13 May

09.00 - 09.50

Emmanuel Kowalski (ETH Zürich)
Algebraic exponential sums and their uses in analytic number theory

10.00 - 11.00

Vladimir Berkovich (Weizmann Institute of Science)
Non-Archimedean analytic spaces (A 3)

11.00 - 11.30

Coffee/Tea

11.30 - 12.30

Vladimir Berkovich (Weizmann Institute of Science)
Non-Archimedean analytic spaces (A 4)

12.30 - 14.30

Lunch

14.30 - 15.30

Raf Cluckers (École Normale Supérieure, Paris)
Integration through cell decomposition and b-minimality (B 3)

15.40 - 16.30

Immanuel Halupczok (École Normale Supérieure, Paris)
Trees of definable sets in Z_p Link to pdf file of related slides - Link to related preprint

16.30 - 17.00

Coffee/Tea

17.00 - 17.50

Yan Soibelman (Kansas State University)
Motivic Donaldson-Thomas invariants

19.00

Informal group supper at Nargile Turkish Restaurant, 73 Hanover Street

 

Wednesday 14 May

09.00 - 10.00

Jan Denef (University of Leuven)
Course on motivic integration I (C 1)

10.10 - 11.10

Roland Huber (Bergische Universität Wuppertal)
Analytic adic spaces (A 5)

11.10 - 11.30

Coffee/Tea

11.30 - 12.30

Roland Huber (Bergische Universität Wuppertal)
Analytic adic spaces (A 6)

12.30

Lunch
Free afternoon

 

Thursday 15 May

09.00 - 09.50

Fumiharu Kato (Kyoto University)
Topological rings in rigid geometry Link to pdf file of slides

10.00 - 11.00

Johannes Nicaise (Université Lille 1)
Non-archimedean geometry and complex singularities (C 2) Link to pdf file of slides

11.00 - 11.30

Coffee/Tea

11.30 - 12.30

Johannes Nicaise (Université Lille 1)
Non-archimedean geometry and complex singularities (C 3) Link to pdf file of slides

12.30 - 14.30

Lunch

14.30 - 15.30

Thomas Scanlon (University of California, Berkeley)
Integration in valued fields (after Hrushovski and Kazhdan) (C 4)

15.40 - 16.30

Willem Veys (Katholieke Universiteit Leuven)
Smallest poles of motivic zeta functions Link to related paper

16.30 - 17.00

Coffee/Tea

17.00 – 18:00

Problem Session

19.00

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

 

Friday 16 May

09.00 - 10.00

François Loeser (École Normale Supérieure)
Motivic integration via cell decomposition and applications (C 5)

10.10 - 11.00

Michael Temkin (University of Pennsylvania)
Desingularization of quasi-excellent schemes over Q Link to pdf file of slides

11.00 - 11.30

Coffee/Tea

11.30 - 12.20

Antoine Chambert-Loir (Université Rennes 1)
Igusa zeta functions in Diophantine geometry Link to pdf file of slides

12.30 - 14.30

Lunch

14.30 - 15.20

Tasho Statev Kaletha (University of Chicago)
The stabilization of the trace formula and the fundamental lemma

15.30 - 16.20

Laurent Fargues (CNRS - Université Paris-Sud)
On some results about the étale cohomology of rigid analytic spaces linked to the local Langlands correspondence

16.20 - 17.00

Coffee/Tea

17.00 - 17.50

Thomas Hales (University of Pittsburgh)
Transfer principle for the fundamental lemma Link to pdf file of slides

 

Saturday 17 May

09.00 - 09.50

Antoine Ducros (Université de Nice – Sophia Antipolis)
The image of a flat map in non-Archimedean geometry: description via the quantifyers elimination for algebraically closed valued fields

10.00 - 10.50

Michel Merle (Université de Nice – Sophia Antipolis)
Nearby cycles, convolution and composition with a two variable function Link to pdf file of slides

10.50 - 11.30

Coffee/Tea

11.30 - 12.20

Karl Rökaeus (Stockholm University)
A version of geometric motivic integration that specializes to p-adic integration Link to pdf file of related slides

 

Presentations:

Presentation Details
Berkovich, Vladimir
Non-Archimedean analytic spaces
View Abstract Down
Bosch, Siegfried
Introduction to formal and rigid geometry
View Abstract Down
Chambert-Loir, Antoine
Igusa zeta functions in Diophantine geometry
View Abstract Down
Chatzidakis, Zoé
The basic model theory of valued fields
View Abstract Down
Cluckers, Raf
Integration through cell decomposition and b-minimality
View Abstract Down
Delon, Françoise
C-minimal structures
View Abstract Down
Denef, Jan
Course on motivic integration I
View Abstract Down
Ducros, Antoine
The image of a flat map in non-Archimedean geometry: description via the quantifyers elimination for algebraically closed valued fields
View Abstract Down
Fargues, Laurent
On some results about the étale cohomology of rigid analytic spaces linked to the local Langlands correspondence
View Abstract Down
Hales, Thomas
Transfer principle for the fundamental lemma
View Abstract Down
Halupczok, Immanuel
Trees of definable sets in Z_p
View Abstract Down
Huber, Roland
Analytic adic spaces
View Abstract Down
Kaletha, Tasho Statev
The stabilization of the trace formula and the fundamental lemma
View Abstract Down
Kato, Fumiharu
Topological rings in rigid geometry
View Abstract Down
Kowalski, Emmanuel
Algebraic exponential sums and their uses in analytic number theory
View Abstract Down
Loeser, François
Motivic integration via cell decomposition and applications
View Abstract Down
Macintyre, Angus
Quantifier elimination in the p-adics and their algebraic closure, and issues of uniformity
View Abstract Down
Merle, Michel
Nearby cycles, convolution and composition with a two variable function
View Abstract Down
Nicaise, Johannes
Non-archimedean geometry and complex singularities
View Abstract Down
Rökaeus, Karl
A version of geometric motivic integration that specializes to p-adic integration
View Abstract Down
Scanlon, Thomas
Integration in valued fields (after Hrushovski and Kazhdan)
View Abstract Down
Soibelman, Yan
Motivic Donaldson-Thomas invariants
View Abstract Down
Temkin, Michael
Desingularization of quasi-excellent schemes over Q
View Abstract Down
Veys, Willem
Smallest poles of motivic zeta functions
View Abstract Down

Participants

Name Institution
Aschenbrenner, Matthias University of California, Los Angeles
Balwe, Chetan University of Pittsburgh
Berkovich, Vladimir Weizmann Institute of Science
Blickle, Manuel University of Essen
Bosch, Siegfried Westfälische Wilhelms - Universität Münster
Chambert-Loir, Antoine Université Rennes 1
Chatzidakis, Zoé CNRS/Université Paris Diderot - Paris 7
Cluckers, Raf Université Lille 1/University of Leuven
Comte, Georges Université de Nice - Sophia Antipolis
Delon, Françoise CNRS/Université Paris 7
Denef, Jan University of Leuven
Ducros, Antoine Université de Nice – Sophia Antipolis
Fargues, Laurent CNRS - Université Paris-Sud
Fichou, Goulwen Université Rennes 1, France
Hales, Thomas University of Pittsburgh
Halupczok, Immanuel Universtiy of Leeds
Huber, Roland Bergische Universität Wuppertal
Kaletha, Tasho Statev University of Chicago
Kappen, Christian Westfälische Wilhelms - Universität Münster
Kato, Fumiharu Kyoto University
Kowalski, Emmanuel ETH Zürich
Loeser, François École Normale Supérieure
Macintyre, Angus Queen Mary University of London
Macpherson, Dugald University of Leeds
Merle, Michel Université de Nice - Sophia Antipolis
Morrow, Matthew University of Nottingham
Nicaise, Johannes Université Lille 1
Pillay, Anand University of Leeds
Raibaut, Michel Université de Nice - Sophia Antipolis
Rökaeus, Karl Stockholm University
Scanlon, Thomas University of California, Berkeley
Sebag, Julien Université Bordeaux 1
Soibelman, Yan Kansas State University
Temkin, Michael University of Pennsylvania
van den Dries, Lou University of Illinois
Veys, Willem Katholieke Universiteit Leuven
Wahle, Christian Westfälische Wilhelms - Universität Münster