NSF-CBMS Ergodic Ramsey Theory Conference

• Description
• Campus information
• Schedule information
• List of Participants
• 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.

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.

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 and following
  Andrews Hall desk open until midnight-
  Andrews Hall-yes it is air conditioned

• 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 - Inger Knutson - 3:30 pm
    
    TITLE: Examples of averaging sets of recurrence.
    ABSTRACT: It is known that large families of generalized polynomials give rise to sets of recurrence and that there is a Szemeredi theorem for classes of them. We will discuss the notion of averaging set of recurrence and give a criteria for when a generalized polynomial is an averaging set of recurrence.
  • 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 - Grigory Polotovsky -3:30 pm
    
    TITLE: Topology of Real Algebraic Curves: History and Results. ABSTRACT: A brief review of the history of algebraic curves.Algebraic curves included in David Hilbert's 16th problem will be discussed.
    
    Max Alekseyev - 4:30 pm
    TITLE: Solving the Tower of Hanoi with Random Moves
    ABSTRACT: What is the expected number of moves to solve the tower of Hanoi assuming random moves?
  • 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 - Micheal Boshernitzan - 3:30 pm
    
    Bogdan Petrenko -4:30 pm
    TITLE: On the smallest number of generators of finite direct sums of matrix algebras
    ABSTRACT: This talk will be based on my joint work with Said Sidki (arXiv:math/0512186) and Rostyslav Kravchenko (arXiv:math/0611674). In particular I'll discuss the formulas for the smallest number of generators for finite direct sums of the following: 1. The ring of 2-by-2 integer matrices. 2. The ring 3-by-3 integer matrices provided the number of copies as at least 769. (We conjecture that the ring M_3(\mathbb{Z})^k for k < 769 admits 2 generators.) 3. Matrix algebras over finite fields (exact and asymptotic formulas).
  • Dinner
    805 6th St. Cookout. Walk north on 6 th Street for 2 long blocks.
    805 is on the right hand side the second from the end of the second block next to the old brick 'church'.

• 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 - Alex Iosevich - 3:30 pm
    TITLE: Geometric configurations in Euclidean, integer and finite field geometries
    ABSTRACT: We study the question of how large a subset of a vector space needs to be to contain a suitable copy of a given geometric configuration. Arithmetic considerations play an important role.
    
    Mel Nathanson (CUNY) 4:30 pm
    TITLE: Sums and products of finite set integers
    ABSTRACT: Erdos conjectured that a finite set of positive integers can not have simultaneously few sums and few produxts. More precisely, for A a subset of the natural numbers, define the set summation A+A and the set product A · A, then for every &epsilon > o there exist a k_o(&epsilon) such that if |A| >= k_o(&epsilon), then
    
    max{ |A+A|, |A · A|} >= |A|^(2 - &epsilon)
    
    This talk will describe the follwing recent result of Solymos:
    
    max{|A+A|, |A · A|} >= |A|^(4/3 - &epsilon)
    
    This is the best result so far on Erdos' conjecture.
    
  • 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.
    
    
  • Dinner

    Final Reception after dinner at 805 6th St.

• 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.

Please let me know of your air travel plans as soon as possible. I have detailed some information below that you should take into account.

If you you be traveling by air to the CBMS conference at Eastern Illinois University June 22-28, plan to arrive on June 22 and to depart on June 28.

We will attempt to pick attendees up if they arrive at

Mattoon train station.

Champaign-Urbana Airport

Indianapolis Airport.

Indianapolis- It is probably easiest to fly into Indianapolis. The drive from Charleston is only about 1 hr and 40 min. So it is not difficult for us to pick you up there.

Chicago- If your destination is Chicago you should take the train from Union station to Mattoon. Otherwise try to get a flight from Chicago into Champaign (but this is usually more expensive).

Champaign- If you fly into Champaign then we will try to pick you up. The distance is too far for a taxi (about 45-50 miles). It is approximately an hour's drive each way.

Mattoon- If you take the train into Mattoon on Sunday June 22, we will try to pick you up. It is only about 10 miles from Charleston. The train arrivals are limited to once or twice a day and you should book ahead. Also there is a significant taxi fare from O'Hare to Union Station. It may also be difficult to arrange an air departure with the train schedule.

We will also try to get you to the appropriate station or air terminal for your flight out. This of course may mean that you will need to leave early on Sat. Morning. If possible try to arrange times for airport departure that are not too early in the day.

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.