Exchangeable random variables and related extremal combinatorics, spin glasses

- For the `Conference on Graphs and Analysis', Institute for Advanced Study, June 2012:
- "Exchangeable random arrays". Supplementary notes, corrected version of June 11th, 2012
- "Mean field models for spin glasses". Supplementary notes, corrected version of June 11th, 2012

- For the `Workshop on Limit Theorems in Probability', January 2013. These were originally labelled as being for ISI, Bangalore. That was a typo: they were actually delivered at the Indian Institute of Science.

Ergodic theory: multiple recurrence and related arithmetic combinatorics

- Slides for `Trends in Dynamics', Northwestern, May 2011:
- "Multiple recurrence and joining rigidity" (Slides from Trends in Dynamics, Northwestern, May 2011)

- The following notes will appear as a chapter in the proceedings of the Easter School on `Dynamics and Analytic Number Theory', held at Durham University, U.K., in April 2014. The version here is made available with the kind permission of Cambridge University Press. It is very provisional!

Cohomology of groups, topological algebra

- Slides for `Ergodic Theory with Connections to Arithmetic', University of Heraklion, June 2013:
- "Partial difference equations over compact Abelian groups" (Notes slightly modified to reflect subsequent development)

Miscellaneous old notes

- "On the geometry of a class of invariant measures and a problem of Aldous" (2008)
- "Razborov flag algebras as algebras of measurable functions" (2008)
- "A counterexample in von Neumann algebra dynamics" (2008): pdf.
- "Entropy and Probability Theory" (2007): pdf. These notes were written to accompany a talk to sixth-form students at Winchester College (UK).
- "Entropy and Sinai's Theorem" (2006): pdf. These notes were written loosely to accompany a pair of graduate seminars at UCLA.
- "Phase transitions" (2005): pdf
- "Spectral measures without the spectrum" (2004): pdf
- "On coordinate-permutation-invariant signed Radon measures on Cartesian powers of compact Hausdorff spaces: a look at de Finetti's theorem" (2003): pdf

Tim Austin,

Courant Institute of Mathematical Sciences, New York University

New York, NY 10012, U.S.A.

tim AT cims DOT nyu DOT edu