TBD —  2008
    Professor Jacob Lurie

  Oct 4—Oct 6, 2005
    David Vogan

 
  Mar 28—Apr 1, 2005
    Stuart Antman

  Sep 28—Oct 1, 2004
    Pierre-Louis Lions

 
  Apr 17–23, 2004
    Maxim Kontsevich

  Feb 24–26, 2004
    Hillel Furstenberg

Ordway Visitors

  2008–09
  2007–08
  2006–07
  2005–06
  2004–05
  2003–04
  2002–03
  2001–02
  2000–01

Lecture 1: Patterns in the Stars, Recurrence in Dynamical Systems, and the Combinatorial Background for Non-Conventional Ergodic Theorems

Ramsey Theory - a branch of combinatorics - treats the phenomenon that rich structures often must contain certain patterns.  This can be regarded as a form of "recurrence", and often can be tied to the phenomenon of recurrence in dynamical systems. We shall give examples of this and show how the investigation of recurrence phenomena has motivated the the study of non-conventional ergodic averages.

3:30 pm, Tuesday, February 24, 2004, Vincent Hall 16

Lecture 2: Ergodicity, Mixing and the Long-Term Memory of Dynamical Systems

We discuss briefly the historical background for Ergodic Theory and the notion of ergodic systems which form the building blocks for this theory.  Ergodic systems can be classified by the degree of forgetfulness - or randomness - which they display. We'll discuss notions of mixing and higher order mixing which will culminate in Bergelson's "polynomial ergodic theorem" for weakly mixing systems. We will begin our analysis of non-weakly-mixing systems.

3:30 pm, Wednesday, February 25, 2004, Vincent Hall 16

Lecture 3: Ergodic Geometry and the Role of Nilpotent Groups and Nilmanifolds

We will describe the basic ideas underlying the recent work of B. Host and B. Kra in which they were able to establish a very general non-conventional ergodic theorem.  "Ergodic Geometry" enables one to isolate "geometrically meaningful" objects in the context of ergodic (rather than transitive) group actions,and the rudimentary study of these leads to a "completion" of the acting group.  The fact that this completion is nilpotent for certain cases will play a crucial role.

3:30 pm, Thursday, February 26, 2004, Vincent Hall 16

furstenberg1.pdf

furstenberg2.pdf

furstenberg3.pdf

Prof. Scot Adams lecture on Furstenberg's proof of Szemeredi's Theorem 404kB, 28 pages