• Description
• Application information
• Schedule information
• Travel information
• Community information

The Department of Mathematics and C.S. at Eastern Illinois University will host a Conference Board of the Mathematical Sciences Regional Conference during the week of June 22 through June 28, 2008. The topic of the conference will be: Ergodic Ramsey Theory- A Dynamical Approach to Static Theorems ( see flier).

Vitaly Bergelson, of the Ohio State University, will give a series of lectures on the history, present state and future outlook of ergodic Ramsey theory. These lectures will be published by the Conference Board of the Mathematical Sciences.

A funding application form is available. The form may be downloaded using your browser. You may copy the form into your email text processor and complete the form and send as email or you may down load the form, print and fill in by hand and send the form by mail. You may also request a hard copy form through the mail. Due April 21, 2008 and thereafter until funding is exhausted.

Or for more information write or email:prcoulton@eiu.edu

Patrick Coulton/CBMS Conference
Department of Mathematics and Computer Science
Eastern Illinois University
600 Lincoln Ave.
Charleston IL, 61920-3099

Conference organizers: Patrick Coulton, David Boyd,
Evgeny Gordon, Gregory Galperin

Tentative Schedule

• Sunday June 22, .................. Registration and check in - 1 pm -
  Andrews Hall-

• Monday June 23,
  • Breakfast - 7 am
  • Lecture I - 10 am - The early results of Ramsey theory
    
    We will give Hilbert's irreducibility theorem and discuss the Dickson-Schur work on Fermat's equation over finite fields. We introduce van der Waerden's theorem and Ramsey's theorem and its rediscovery by Erdos and Szekeres.
    
    
  • Lunch -12 pm
  • Lecture II - 2 pm - Three main principles of Ramsey theory
    
    First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of this result. Third principle: The sought-after configurations which are always to be found in large sets are abundant. Examples will be given.
    
    
  • Informal talks - 3:30 pm
  • Dinner

• Tuesday June 24,
  • Breakfast - 7 am
  • Lecture III- 10 am - A Dynamical approach to static results
    
    We will begin with a discussion of Furstenberg's approach to Ramsey theory. We include preliminaries on topological and measure preserving systems.
    
    
  • Lunch -12 pm
  • Lecture IV - 2 pm - Partition Ramsey theory and topological dynamics
    
    We will give a proof of van der Waerden's theorem, Hindman's theorem and the Graham-Rothchilde-Spencer's geometric Ramsey theorem by means of topological dynamics.
    
    
  • Informal talks - 3:30 pm
  • Dinner

• Wednesday June 25,
  • Breakfast - 7 am
  • Lecture V - 10 am - Density Ramsey theory and Furstenberg's correspondence principle
    
    We will discuss Furstenberg's correspondence principle and sketch the ergodic proof of Szemeredi's theorem. We will also discuss the polynomial Szemeredi theorem and the density version of the Hales-Jewett theorem.
    
    
  • Lunch -12 pm
  • Lecture VI - 2 pm - Stone-Cech compactifications and Hindman's theorem
    
    We will discuss the topological algebra in Stone-Cech compactifications and give an ultrafilter proof of Hindman's theorem. We will also consider central sets and their applications.
    
    
  • Informal talks - 3:30 pm
  • Dinner

• Thursday June 26,
  • Breakfast - 7 am
  • Lecture VII- 10 am - IP sets and ergodic Ramsey theory
    
    We will discuss the application of IP sets and idempotent ultrafilters to ergodic-theoretical multiple recurrence and to density Ramsey theory. We will give the polynomial Szemeredi theorem and its IP version. Some recent generalizations will be reviewed.
    
    
  • Lunch -12 pm
  • Lecture VIII- 2 pm - The nilpotent connection
    
    We will discuss Leibman's nilpotent Szemeredi theorem as well as Host-Kra and Ziegler's results on convergence. Finally, we will consider the nilpotent version of the Hales-Jewett theorem.
    
    
  • Informal talks - 3:30 pm
  • Dinner

• Friday June 27,
  • Breakfast - 7 am
  • Lecture IX - 10 am - Ergodic Ramsey theory and amenable groups
    
    We will give the general form of Furstenberg's correspondence principle and discuss topological and measure-theoretical results on multiple recurrence for amenable group actions and their combinatorial corollaries.
    
    
  • Lunch -12 pm
  • Lecture X - 2 pm - What next? Open problems and conjectures
    
    This lecture will focus on the formulation and discussion of diverse open problems, including those stemming from the material presented at the preceding lectures as well as those related to recent Green-Tao and Tao-Ziegler results on progressions in primes.
    
    
  • Informal talks - 3:30 pm
  • Dinner

• Saturday June 28 ........... Checkout by 12 pm

Travel Options

• Intersate 70 (East or West) to Interstate 57 North to Charleston exit. Exit going east 10 miles on Route 16

• Interstate 80 (East or West) to Interstate 57 South to Charleston exit. Exit going east 10 miles on Route 16

• Amtrack from Chicago to Mattoon (10 miles from Charleston). There is some taxi service, but if you let us know we may be able to pick you up.

• Champaign, IL (Willard Airport - 45 miles from Charleston). If you need transportation let us know ahead of time and we will try to arrange it.

• Chicago airports are about a three hour drive. (Amtrak service available from Chicago, see above)

• Indianapolis, IN airport is about a two hour drive from Charleston.

• St. Louis, MO airport is about a two hour drive from Charleston.

The EIU Campus is located in Charleston, a pleasant community of 20,000 residents. The University is only eight miles from Interstate 57, three hours south of Chicago, two hours east of St. Louis, and two hours west of Indianapolis. Nearby cities include Champaign, Illinois and Terre Haute, Indiana. Eastern Illinois University is a traditional, residential university in a beautiful campus setting. It has many academic and social organizations and a full athletic program.

The university sponsors many cultural activities throughout the year. The cost of living in Charleston is somewhat less than in most metropolitan areas. There are many choices of homes, apartments, and condominiums. Charleston has many parks and recreational facilities. Bike trails and state parks are nearby.