Tim Austin - notes, chapters, teaching

Notes, book chapters and teaching materials

Materials from past teaching (unstable, not recommended for citation)

Notes and homeworks from Math 254A: Entropy and Ergodic Theory (UCLA fall quarter 2017). NOTE: I expect to retire this material over summer 2023. Please do not expect it to be available after June 30th.

Book contributions

The following 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. This pre-publication version is made available with the kind permission of Cambridge University Press.

"Multiple Recurrence and Finding Patterns in Dense Sets"

Slides and notes from talks

Concentration of measure

Sketch notes on concentration of measure for tutorial lectures at Quantitative Linear Algebra program at IPAM, UCLA, March 2018.

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.
- "Exchangeable random arrays"

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)

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).

Tim Austin,
Math Sciences Building, office 6232
UCLA Mathematics Department, Box 951555, Los Angeles CA 90095-1555, U.S.A.
timaustin AT g DOT ucla DOT edu