Vanderbilt University, Department of Mathematics
Nashville, Tennessee, USA

THE FOURTH ANNUAL SPRING INSTITUTE

ON

NONCOMMUTATIVE GEOMETRY AND OPERATOR ALGEBRAS

Noncommutative Geometry, Quantum Field Theory and Motives

May 8 to May 17, 2006

The Fourth Annual Spring Institute on Noncommutative Geometry and Operator Algebras is a combination of spring school and international conference. During the school part of the meeting several mini-courses on a variety of topics from noncommutative geometry, operator algebras and related topics will be given by leading experts. The conference will comprise a number of invited research talks and short contributions. We strongly encourage students and postdocs to attend this conference. Please read the section on financial aid below regarding information on how to apply for financial support.

For information on the Clay Mathematics Institute/Shanks international conference and spring school on Noncommutative Geometry and Applications in May 2003 (=the First Annual Spring Institute on NCGOA), please click here. For information on the Second Annual Spring Institute on NCGOA, please click here. For information on the Third Annual Spring Institute on NCGOA, please click here.

The home page of the research group in noncommutative geometry and operator algebras at Vanderbilt University can be found here.

Schedule

Talks will start at 9:20 am on Monday, May 8, 2006, and end at noon on Wednesday, May 17, 2006. Friday, May 12, 2006, will be a day off since commencement/graduation will take place at Vanderbilt on that day. From May 8 to May 10, 2006, all lectures will be held in Lecture Hall 4327, Stevenson Center (for short SC). From May 11 to May 17, 2006, all lectures will be held in Lecture Hall 4309, Stevenson Center . SC 4309 and SC 4327 are adjacent. The seminar room SC 5208 (right next to SC 4309) and the seminar rooms in the math building (e.g. SC 1312, SC 1320, SC 1403, SC 1404) are available for discussions. Limited computer access is available in the computer lab of the mathematics department (SC 1427). Moreover Vanderbilt campus has a wireless network which is accessible from many campus locations.

Directions to the lecture hall. The Stevenson Center consists of several buildings. The mathematics department is located in building 1 and the lecture hall in building 4, which are right next to each other. For more details, please consult the campus map (click on ``Building List'', then ``Mathematics Building, Stevenson Center'' to find the math department and on ``Building List'', then ``Lecture Halls/Stevenson Center'' to find the lecture hall. Note that the map is zoomable.).

Schedule. Click here to see the the schedule (pdf file) (or the schedule (ASCII file)).

List of participants and abstracts. Click here to see the list of participants (ASCII file). Click here to see the list of participants (pdf file). Click here to see the abstracts (pdf file) or abstracts (ASCII file).

Information sheet. Click here to see the information sheet (pdf file).

Invited Speakers

The following people have been invited to give mini-courses:

Alain Connes, Collège de France, IHES & Vanderbilt University
The following topics will be covered in the mini-course:

From Renormalization as Birkhoff Decomposition to the Riemann-Hilbert Correspondence
The Cosmic Galois group, the Group of Diffeographisms and Diffeomorphisms of Coupling Constants, the Role of Motivic Galois Theory
A Candidate Mental Picture of Space-Time, after Renormalization and Taking the Standard Model Seriously

Katia Consani, Johns Hopkins University
An Introduction to the Arithmetic of Motives
Herbert Gangl, University of Durham
From Polygons and Trees to Cycles and Motives
Li Guo, Rutgers University
Some Constructions and Applications of Rota-Baxter Algebras
Dirk Kreimer, IHES & Boston University
Renormalization and Hopf Algebras
Feynman Graphs
Birkhoff Decomposition and Dyson--Schwinger Equations
Towards Number Theory and Motives
Matilde Marcolli, Max-Planck-Institute Bonn
Noncommutative Geometry and Motives
Niranjan Ramachandran, University of Maryland
Introduction to Motives

Laura Reina, Florida State University
Introduction to Quantum Field Theory

The following people have been invited to give additional talks:

Prakash Belkale, University of North Carolina at Chapel Hill
Matroids, Motives and Conjecture of Kontsevich
Don Blasius, UCLA
Motives and Automorphic Forms: An Overview with Examples and Open Problems
Kurusch Ebrahimi-Fard, University of Bonn
Birkhoff Type Decompositions and the Baker-Campbell-Hausdorff Recursion
Bertfried Fauser, Universität Konstanz
Hopf algebras in Arithmetic and Renormalization
Frederic Fauvet, Universite Louis Pasteur (Strasbourg)
Alien Calculus in Quantum Field Theory
Alessandra Frabetti, Universite Lyon I
QED Hopf Algebras and Groups of Combinatorial Series
Eugene Ha, Max-Planck-Institute Bonn
The Connes-Moscovici Hopf Algebra and Representation Theory
Benoit Jacob, Universite Paris 6 (Pierre et Marie Curie)
Bost-Connes type Systems for Function Fields
Minhyong Kim, University of Arizona and Purdue University
Non-abelian Cohomology Varieties in Diophantine Geometry
Marcelo Laca, University of Victoria
Equilibrium and Symmetries of Hecke C*-algebras
Ralf Meyer, Georg-August-Universität Göttingen
Homological Algebra for Schwartz Algebras of Reductive p-adic Groups
Henri Moscovici, Ohio State University
Noncommutative Complex Geometry on the Moduli Space of Q-Lattices of Rank 2
Frederic Paugam, Universite Paris 6 (Pierre et Marie Curie)
Bost-Connes-Marcolli Systems for Shimura Varieties
Bahram Rangipour, Ohio State University
Bicrossed Product Hopf Algebras and their Hopf Cyclic Cohomology
Walter van Suijlekom, Max-Planck-Institute Bonn
The Hopf Algebra of Feynman Graphs in QED
Lucia Di Vizio, Universite Pierre et Marie Curie (Paris)
P-adic q-Difference Equations

Transparencies and other material related to the talks

Alain Connes (transparencies of talk 1, pdf file)

Alain Connes (transparencies of talk 2, pdf file)

Alain Connes (transparencies of talk 3, pdf file)

Alain Connes (link to home page which contains downloadable articles etc.)

Katia Consani (transparencies of talk 1, pdf file)

Kurusch Ebrahimi-Fard (transparencies of talk, pdf file)

K. Ebrahimi-Fard, L. Guo, D. Manchon, Birkhoff type decompositions and the Baker-Campbell-Hausdorff recursion

Kurusch Ebrahimi-Fard, Dirk Kreimer, Hopf algebra approach to Feynman diagram calculations

Bertfried Fauser (transparencies of talk, pdf file)

Bertfried Fauser (handout, pdf file)

Li Guo (mini-course, lecture 1, pdf file)

Li Guo (mini-course, lecture 2, pdf file)

Benoit Jacob (transparencies of talk, pdf file)

Benoit Jacob, Bost-Connes type systems for function fields

Dirk Kreimer, talk 1 (paper)

Dirk Kreimer, talk 2 (paper)

Dirk Kreimer, talk 3 (paper)

Dirk Kreimer, talk 4 (paper)

Matilde Marcolli (transparencies of mini-course, pdf file)

Ralf Meyer, Homological Algebra for Schwartz Algebras of Reductive p-adic Groups

Henri Moscovici (transparencies of talk, pdf file)

Frederic Paugam (transparencies of talk, pdf file)

Bahram Rangipour (transparencies of talk, pdf file)

Registration

All participants are asked to register. Please download the registration form here, fill it out and email it to the organizing committee at ncgoa06[at]math[dot]vanderbilt[dot]eduand to Lori Rafter at lori.rafter[at]vanderbilt[dot]edu (click on ``registration form here'', then save the registration form to a file (use your browser's ``Save page as'' feature), edit it and email the file as an attachment to the organizing committee). If you prefer an email version of the registration form, please request it by email from the organizing committee. There will be a registration fee of $40. If you intend to request support, please read the section ``Financial Aid'' before filling out the registration form.

Financial Aid

We hope that financial support will be available to (partially) fund graduate students, postdoctoral researchers and other participants without grant support. We encourage those of you who are asking for support to share accommodations. If you plan to apply for funding, please fill out the registration form (see section ``Registration'') at your earliest convenience and provide the information requested. Please submit your request for financial support by April 4, 2006. Late applications will be considered as long as financial support is available. Note that we are unable to provide any support in advance.

Reimbursement policy.

Please see Traveling to the United States (The National Academies), US State Department and US State Department Visa Waiver Program for information about visas.

Please be advised that according to U.S. immigration laws, individuals who enter the U.S. and wish to be reimbursed for travel related expenses should enter only on a B-1, WB or J-1 visa (WT and B-2 visa do not permit reimbursement of any expenses). See the web pages above for visitors entering from Canada and Mexico. Entering on a Visa Waiver is discouraged due to concerns as to how the new law will be interpreted. Please call your local US consulate or embassy and inquire what the rules are pertaining to your country.

NSF funds can be used for reimbursement of air fare only if a U.S. flag carrier (i.e. a U.S. airline) has been used.

Upon arriving, please see the staff person at the registration desk for the necessary forms to be filled out and returned prior to your departure. We will need all original receipts for any expenses for which reimbursement is claimed and copies of your visa if applicable.

Accommodation

Rooms have been reserved in the following hotels (in alphabetical order). The quoted rates below do not include a 14.25% state and city tax. When you make the reservation for your room, please mention the ``The Fourth Spring Institute on Noncommutative Geometry and Operator Algebras''. Many of the rooms are doubles and can be shared. Since we have reserved only a limited number of rooms in each hotel, we recommend that you make your reservations as soon as possible in the hotel of your choice. Click on the hotel name for a list of amenities.

Courtyard by Marriott, 1901 West End Ave., Nashville, TN 37203, $87 per night (single and double room rates are the same). Walking distance (10-15 minutes). For reservations please call Marriott Reservations at 800-245-1959 or the hotel directly at (615) 327-9900 (mention Fourth Spring Institute on Noncommutative Geometry & Operator Algebras for Vanderbilt Mathematics Department). Reserve by April 24, 2006.
Days Inn Vanderbilt-Music Row, 1800 West End Ave., Nashville, TN 37203, $65 per night (single and double room rates are the same). About 4 blocks away. Walking distance (15 minutes). Phone (615) 327-0922, fax (615) 327-0102. Reserve by April 8, 2006 (mention the room block for the Vanderbilt Mathematics Department).
Hampton Inn Nashville/Vanderbilt, 1919 West End Ave., Nashville, TN 37203, special rate of $91 per night for those staying a minimum of 10 nights. 1 or 2 blocks away. Walking distance (10 minutes). Phne (615) 329-1144 You can also call toll free 1-800-426-7866. The fax number is (615) 321-7282. See www.hamtponinnnashville.com for more information. Reserve by April 7, 2006. (Mention that you are with The Fourth Spring Institute on Noncommutatve Geometry and Operator Algebras.)
Holiday Inn Select Vanderbilt, 2613 West End Ave., Nashville, TN 37203, $91 per night (single and double room rates are the same). 6 or 7 blocks away. Walking distance (10-15 minutes). Phone (615) 327-4707, fax (615) 327-8034. For reservations you may also call (800) 633 4427. Reserve by April 7, 2006 (ask for the Fourth Spring Institute Conference Room block).

Other nearby hotels include:

Embassy Suites Hotel, 1811 Broadway, Nashville, TN 37203. Walking distance (10 minutes). Phone (615) 320-8899, fax (615) 320-8881. For reservations you may also call (800) EMBASSY.
Extended Stay America, (615) 383-7490. Walking distance, 15 minutes walk. Ask for the weekly rates.
Quality Inn Hall of Fame, (615) 242-1631.

Remark 1: Sometimes the best hotel room rates can be obtained by reserving a room via the internet.
Remark 2: The Extended Stay America has offered good rates in the past for longer stays (weekly rates). You may want to check it out first and compare rates.

Travel Information

Follow the links below for directions, maps, information regarding parking, airport, weather etc..

Getting to Vanderbilt. How to get to Nashville, and then how to get to the Vanderbilt area.
Directions to Vanderbilt University. Another page with directions to campus, directions to parking etc..
A zoomable campus map.
Another map , which shows the lecture hall and the math department.
Parking at Vanderbilt. A link to the office of traffic and parking at Vanderbilt University. Parking information for visitors.
Nashville International Airport . Flight information, airport guide, ground transportation.
Incare Shuttle Service (airport shuttle). Incare Shuttle Service, 1102 Buchanan St., Nashville, TN 37203, (615) 255-3519.
A virtual tour of campus.
Vanderbilt University, campus webcams.
Vanderbilt University home page.
Department of Mathematics at Vanderbilt University.
Restaurants. A list of restaurants close to campus.
More information on Nashville.
Current weather in Nashville.
The Nashville Scene.
The Tennessean.

Organizing Committee

Dietmar Bisch (Vanderbilt University), Alain Connes (Collège de France, IHES & Vanderbilt University; Director of the Fourth Annual Spring Institute), Bruce Hughes (Vanderbilt University), Gennadi Kasparov (Vanderbilt University), Matilde Marcolli (Max-Planck-Institute Bonn) and Guoliang Yu (Vanderbilt University).

Further Information

Further information may be obtained from the following sources.

Email:	ncgoa06[at]math[dot]vanderbilt[dot]edu or ncgoa06[at]vanderbilt[dot]edu
Web:	http://www.math.vanderbilt.edu/~bisch/ncgoa06/
Web (NCGOA at Vanderbilt):	http://www.math.vanderbilt.edu/~ncgoa/
Regular mail:	NCGOA 2006 Department of Mathematics, SC 1326 Vanderbilt University Nashville, TN 37240, USA
Phone:	(615) 322-6672 (Department of Mathematics)
Fax:	(615) 343-0215
Contact Person:	Lori Rafter (same email address as above), (615) 322-4163

Last update 1/7/07.

Vanderbilt University, Department of Mathematics Nashville, Tennessee, USA