Fields Institute Summer School & Conference

Valuation Theory and Integral Closures in Commutative Algebra

July 3-22, 2006
University of Ottawa, Ottawa, Canada

Steven Dale Cutkosky
University of Missouri-Columbia
CutkoskyS at

Sara Faridi
Dalhousie University
faridi at

Franz-Viktor Kuhlmann
University of Saskatchewan
fvk at

Irena Swanson
Reed College
iswanson at

Manoj Kummini's photos (More coming soon!)

Lab files and Lecture notes

Feb 1: application for funding
NOTE: you do not need to pay the registration fee to apply for financial support!
Feb 1: submission of abstracts to be considered for conference
Mar 1: notification of funding
Mar 30: application for summer school (no funding)
May 15: conference registration

Funding provided by:
Fields Institute
University of Ottawa

In recent years, valuation theory has witnessed a rapid increase of interest and many new applications in various areas of mathematics, including algebraic geometry. A main open problem in algebraic geometry is resolution of singularities in positive characteristic, solved in low dimensions by Abhyankar using methods of valuation theoretic nature. Closely related is the use of Rees valuations to study the integral closures of ideals in a polynomial ring. Integral closures of ideals arise in resolutions of singularities, in combinatorics, and in analysis. The structure of integrally closed ideals in a given ring encodes the birational geometry of the ring. As such the structure is well understood by the work of Zariski in dimension two, and is difficult to unravel in higher dimensions.

Our goal in the school is to introduce students to various branches of this vibrant area of research. We will have introductory courses on valuation theory and integral closures of ideals covering various related topics, such as geometrical aspects, combinatorial methods, and computational techniques. We plan to have extra discussion sessions that focus on open problems in the field and methods of approach, as well as additional introductory lectures given during the courses by the people invited for the subsequent conference.

The last week will be devoted to a conference. The conference shall familiarize the students and young researchers with several directions of this active area of research, not necessarily restricted to the topics covered by the courses. At the same time, it shall bring together researchers working on integral closures with others who develop and use valuation theory for related applications in algebraic geometry. The aim is to exchange knowledge about the various valuation theoretical tools used in cutting edge research, as well as to introduce the participants to the most recent results of research on integral closures.


NEW! The three-week program is now available for download here. You can find a program of the conference only here.

All lectures will be held in SITE C0136 at the south end of campus for the first two weeks, and in SITE B0138 for the third week.

Week 1: School

  1. Introduction to Valuations, Franz-Viktor Kuhlmann and Hagen Knaf (Kaiserslautern, Germany)
  2. Rees Valuations and Integral Closure of Ideals, Irena Swanson

Week 2: School

  1. Combinatorial and Computational Techniques for Computing Integral Closures, Irena Swanson, Amelia Taylor (St. Olaf's College) and Winfried Bruns (University of Osnabrück)
  2. Further Developments and Applications of Valuation Theory, Dale Cutkosky, Franz-Viktor Kuhlmann, Hagen Knaf (Kaiserslautern, Germany), Bernard Teissier (ENS, Paris) and Michel Vaquié (Toulouse)

Week 3: Conference (July 17 -- 22)

Invited Speakers

Shreeram Abhyankar (Purdue University, USA)
Holger Brenner (University of Sheffield, UK)
Antonio Campillo (Universidad de Valladolid, Spain)
Vincent Cossart (Université de Versailles, France)
Terence Gaffney (Northeastern University, USA)
Laura Ghezzi (Florida International University, USA)
Shiro Goto (Meiji University, Japan)
Reinhold Hübel (Universität Regensburg, Germany)
Craig Huneke (University of Kansas, USA)
Dan Katz (University of Kansas, USA)
Hagen Knaf (Kaiserslautern, Germany)
Monique Lejeune (Université de Versailles, France)
Olivier Piltant (CNRS et Université de Versailles, France)
Bernard Teissier (Institut de Mathématique de Jussieu, France)
Mark Spivakovsky (Toulouse, France)
Hans Schoutens (CUNY, USA)
Michel Vaquié (Toulouse, France)
Wolmer Vasconcelos (Rutgers University, USA)
Marie Vitulli (University of Oregon , USA)
Rafael Villarreal (CINVESTAV-IPN, Mexico)

List of participants

Registration, financial support and contributed talks

There is funding available through the Fields Institute, in particular for students and young researchers to attend the event. To apply for funding, please submit your application by February 1, 2006 using the Fields Institute form. NOTE: you do not need to pay the registration fee to apply for financial support!
We also welcome contributed talks for the conference. If you are interested in giving a talk, please submit an abstract by February 1, 2006 through this link.

Fees: (All sums are in Canadian Dollars)

$50 a week (students)
$75 a week (postdocs and mathematicians without grants)
$150 a week (other)

Application Procedure:
To apply for financial support, please fill in the application form at the Fields Institute website. Graduate students are additionally asked to provide a letter from their supervisor. Letters can be sent to via email by the supervisor.
The deadline for application for financial support is February 1, 2006 , and for general attendance in school, the registration deadline is March 30, 2006. The deadline for conference registration is May 15, 2006.

Local information

Click here for a map of campus.

A block of 2 bedroom suites (click here for more information) has been reserved for the participants. These are air-conditioned suites which include two separate bedrooms with a double bed in each, a kitchenette (with a fridge & microwave) and a private three-piece bathroom. There is a common kitchen area with an oven and stove and a large laundry room located on the main floor. There is also a $10.00 parking fee per day.
Pricing information and instructions for making reservations:

Event name & reservation #: Fields Summer School 2006, #125042
Deadline for reservation: 2006-05-15
Arrival: 16h and Departure: 10h
Single: $89.95 + taxes(12%)=$100.74
Double: +$10.00 per additional person for a maximum of 4 people per unit

Address: 90 University St (marked "residential complex" on the campus map .

For reservations:
Tel: (613) 562-5885
Fax: (613) 562-5109

A cheaper option would be to stay in the Conventional Residences. The rooms are furnished with single beds, desk, bookshelf and armoire. The bathrooms are shared on the floor. Linen and bathroom amenities are provided. The 2005 nightly rate was $40.00 for a single room and $60.00 for a double room. They have a special rate of $23 per person/per night for groups reserving 10 rooms or more.
There are also many hotels and B&Bs nearby. You can find these through the official Ottawa Tourism Site or various other web resources. A useful piece of information: University of Ottawa is located in a neighborhood called "Sandy Hill".

Travel to Ottawa:
Most US and Canadian airlines have flights to Ottawa. Air Canada has a daily direct flight to London, and the budget airline Zoom also offers direct flights to London and Glasgow.

Ottawa is about 2 hours by train or bus from Montreal, and about 4 hours from Toronto.

From the airport: Bus 97 goes between the airport and campus. There is a bus stop as you walk out of the terminal. The ride takes approximately 30 minutes and costs about $3. This is the cheapest way to get to the university, and is quite convenient. Please check the OC Transpo website for details and maps.
A taxi from the airport to campus should cost about $25, and will take about 20 minutes. There are also various shuttles outside the terminal.

The housing provided by the conference is marked "residential complex" on the map of campus . The check in counter is located close to the parking lot.