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 |
- Group Photograph (left click to view, right click to save)
- Links to copies of slides or relevant web resources now available within the timetable
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) |
11.00 - 11.30 | Coffee/Tea |
11.30 - 12.30 | Siegfried Bosch (Westfälische Wilhelms - Universität Münster) |
12.30 - 14.30 | Lunch |
14.30 - 15.30 | Zoé Chatzidakis (CNRS - Université Paris 7) |
15.40 - 16.40 | Angus Macintyre (University of London) |
16.40 - 17.10 | Coffee/Tea |
17.10 - 18.00 | Françoise Delon (CNRS - Université Paris 7) |
18.00 - 19.00 | Wine reception at ICMS, 14 India Street |
Tuesday 13 May
09.00 - 09.50 | Emmanuel Kowalski (ETH Zürich) |
10.00 - 11.00 | Vladimir Berkovich (Weizmann Institute of Science) |
11.00 - 11.30 | Coffee/Tea |
11.30 - 12.30 | Vladimir Berkovich (Weizmann Institute of Science) |
12.30 - 14.30 | Lunch |
14.30 - 15.30 | Raf Cluckers (École Normale Supérieure, Paris) |
15.40 - 16.30 | Immanuel Halupczok (École Normale Supérieure, Paris) |
16.30 - 17.00 | Coffee/Tea |
17.00 - 17.50 | Yan Soibelman (Kansas State University) |
19.00 | Informal group supper at Nargile Turkish Restaurant, 73 Hanover Street |
Wednesday 14 May
09.00 - 10.00 | Jan Denef (University of Leuven) |
10.10 - 11.10 | Roland Huber (Bergische Universität Wuppertal) |
11.10 - 11.30 | Coffee/Tea |
11.30 - 12.30 | Roland Huber (Bergische Universität Wuppertal) |
12.30 | Lunch |
Thursday 15 May
09.00 - 09.50 | Fumiharu Kato (Kyoto University) |
10.00 - 11.00 | Johannes Nicaise (Université Lille 1) |
11.00 - 11.30 | Coffee/Tea |
11.30 - 12.30 | Johannes Nicaise (Université Lille 1) |
12.30 - 14.30 | Lunch |
14.30 - 15.30 | Thomas Scanlon (University of California, Berkeley) |
15.40 - 16.30 | Willem Veys (Katholieke Universiteit Leuven) |
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) |
10.10 - 11.00 | Michael Temkin (University of Pennsylvania) |
11.00 - 11.30 | Coffee/Tea |
11.30 - 12.20 | Antoine Chambert-Loir (Université Rennes 1) |
12.30 - 14.30 | Lunch |
14.30 - 15.20 | Tasho Statev Kaletha (University of Chicago) |
15.30 - 16.20 | Laurent Fargues (CNRS - Université Paris-Sud) |
16.20 - 17.00 | Coffee/Tea |
17.00 - 17.50 | Thomas Hales (University of Pittsburgh) |
Saturday 17 May
09.00 - 09.50 | Antoine Ducros (Université de Nice – Sophia Antipolis) |
10.00 - 10.50 | Michel Merle (Université de Nice – Sophia Antipolis) |
10.50 - 11.30 | Coffee/Tea |
11.30 - 12.20 | Karl Rökaeus (Stockholm University) |
Presentations:
Presentation Details | |
---|---|
Berkovich, Vladimir | |
Non-Archimedean analytic spaces | |
View Abstract | |
Bosch, Siegfried | |
Introduction to formal and rigid geometry | |
View Abstract | |
Chambert-Loir, Antoine | |
Igusa zeta functions in Diophantine geometry | |
View Abstract | |
Chatzidakis, Zoé | |
The basic model theory of valued fields | |
View Abstract | |
Cluckers, Raf | |
Integration through cell decomposition and b-minimality | |
View Abstract | |
Delon, Françoise | |
C-minimal structures | |
View Abstract | |
Denef, Jan | |
Course on motivic integration I | |
View Abstract | |
Ducros, Antoine | |
The image of a flat map in non-Archimedean geometry: description via the quantifyers elimination for algebraically closed valued fields | |
View Abstract | |
Fargues, Laurent | |
On some results about the étale cohomology of rigid analytic spaces linked to the local Langlands correspondence | |
View Abstract | |
Hales, Thomas | |
Transfer principle for the fundamental lemma | |
View Abstract | |
Halupczok, Immanuel | |
Trees of definable sets in Z_p | |
View Abstract | |
Huber, Roland | |
Analytic adic spaces | |
View Abstract | |
Kaletha, Tasho Statev | |
The stabilization of the trace formula and the fundamental lemma | |
View Abstract | |
Kato, Fumiharu | |
Topological rings in rigid geometry | |
View Abstract | |
Kowalski, Emmanuel | |
Algebraic exponential sums and their uses in analytic number theory | |
View Abstract | |
Loeser, François | |
Motivic integration via cell decomposition and applications | |
View Abstract | |
Macintyre, Angus | |
Quantifier elimination in the p-adics and their algebraic closure, and issues of uniformity | |
View Abstract | |
Merle, Michel | |
Nearby cycles, convolution and composition with a two variable function | |
View Abstract | |
Nicaise, Johannes | |
Non-archimedean geometry and complex singularities | |
View Abstract | |
Rökaeus, Karl | |
A version of geometric motivic integration that specializes to p-adic integration | |
View Abstract | |
Scanlon, Thomas | |
Integration in valued fields (after Hrushovski and Kazhdan) | |
View Abstract | |
Soibelman, Yan | |
Motivic Donaldson-Thomas invariants | |
View Abstract | |
Temkin, Michael | |
Desingularization of quasi-excellent schemes over Q | |
View Abstract | |
Veys, Willem | |
Smallest poles of motivic zeta functions | |
View Abstract |
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 |