Blogs about: 254a Ergodic Theory

Featured Blog

254A, Lecture 17: A Ratner-type theorem for SL_2(R) orbits

In this final lecture, we establish a Ratner-type theorem for actions of the special linear group on homogeneous spaces. More precisely, we show: Theorem 1. Let G be a Lie group, let be a discret… more →

What's new

254A, Lecture 17: A Ratner-type theorem for SL_2(R) orbits — 2 comments

Terence Tao wrote 8 months ago: In this final lecture, we establish a Ratner-type theorem for actions of the special linear group o … more →

Tags: math.DS, math.RT, Lie Algebras, Lie Groups, Mautner phenomenon, Ratner's theorem, unipotence

254A, Lecture 16: A Ratner-type theorem for nilmanifolds — 2 comments

Terence Tao wrote 8 months ago: The last two lectures of this course will be on Ratner’s theorems on equidistribution of orbit … more →

Tags: math.DS, math.GR, Dichotomy, ergodicity, nilmanifolds, nilpotent groups, Ratner's theorem, Structure

254A, Lecture 15: The Furstenberg-Zimmer structure theorem and the Furstenberg recurrence theorem — 2 comments

Terence Tao wrote 8 months ago: In this lecture - the final one on general measure-preserving dynamics - we put together the results … more →

Tags: math.DS, Furstenberg recurrence theorem, randomness, Structure, Zorn's lemma

254A, Lecture 14: Weakly mixing extensions — 6 comments

Terence Tao wrote 8 months ago: Having studied compact extensions in the previous lecture, we now consider the opposite type of exte … more →

Tags: math.DS, math.OA, almost periodicity, Hilbert-Schmidt operators, randomness, weak mixing

254A, Lecture 13: Compact extensions — 3 comments

Terence Tao wrote 8 months ago: In Lecture 11, we studied compact measure-preserving systems - those systems in which every functio … more →

Tags: math.DS, math.OA, almost periodicity, compact extensions, Hilbert modules, multiple recurrence, Structure, van der Waerden's theorem

254A, Lecture 12: Weakly mixing systems — 4 comments

Terence Tao wrote 9 months ago: In the previous lecture, we studied the recurrence properties of compact systems, which are systems … more →

Tags: math.DS, math.FA, randomness, Roth's theorem, compactness, weak mixing, strong mixing, van der Corput, cauchy-schwarz

254A, Lecture 11: Compact systems — 9 comments

Terence Tao wrote 9 months ago: The primary objective of this lecture and the next few will be to give a proof of the Furstenberg re … more →

Tags: math.CA, math.DS, almost periodicity, compact systems, Kronecker systems, multiple recurrence

254A, Lecture 10: The Furstenberg correspondence principle — 5 comments

Terence Tao wrote 9 months ago: In this lecture, we describe the simple but fundamental Furstenberg correspondence principle which c … more →

Tags: math.CO, math.DS, averaging argument, correspondence principle, density Hales-Jewett, multiple recurrence, polynomial recurrence, Szemeredi's theorem

254A, Lecture 9: Ergodicity — 12 comments

Terence Tao wrote 9 months ago: We continue our study of basic ergodic theorems, establishing the maximal and pointwise ergodic theo … more →

Tags: math.DS, disintegration, ergodic decomposition, ergodic theorem, ergodicity, maximal inequality, probability kernel

254A, Lecture 8: The mean ergodic theorem — 22 comments

Terence Tao wrote 9 months ago: We now begin our study of measure-preserving systems , i.e. a probability space together with a pro … more →

Tags: math.DS, mean ergodic theorem, von Neumann ergodic theorem, spectral theorem, dual functions, conditional expectation, Hilbert spaces

254A, Lecture 7: Structural theory of topological dynamical systems — 9 comments

Terence Tao wrote 9 months ago: In our final lecture on topological dynamics, we discuss a remarkable theorem of Furstenberg that cl … more →

Tags: math.DS, distal systems, Furstenberg structure theorem, Structure, weak mixing

254A, Lecture 6: Isometric systems and isometric extensions — 28 comments

Terence Tao wrote 9 months ago: In this lecture, we move away from recurrence, and instead focus on the structure of topological dyn … more →

Tags: math.AT, math.DS, math.GR, math.MG, Isometric extensions, Kronecker factor, polynomial sequences, Ratner's theorem, Structure

254A, Lecture 5: Other topological recurrence results — 19 comments

Terence Tao wrote 10 months ago: In this lecture, we use topological dynamics methods to prove some other Ramsey-type theorems, and m … more →

Tags: math.CO, math.DS, hypergraphs, Ramsey theory, Hales-Jewett theorem, polynomial van der Waerden theorem, Hindman's theorem, Ramsey's theorem, idempotents

254A, Lecture 4: Multiple recurrence — 17 comments

Terence Tao wrote 10 months ago: In the previous lecture, we established single recurrence properties for both open sets and for sequ … more →

Tags: math.CO, math.DS, van der Waerden's theorem, multiple recurrence

254A, Lecture 3: Minimal dynamical systems, recurrence, and the Stone-Čech compactification — 36 comments

Terence Tao wrote 10 months ago: We now begin the study of recurrence in topological dynamical systems - how often a non-empty open … more →

Tags: math.DS, math.LO, math.GN, lamplighter group, Recurrence, almost periodicity, syndetic sets, Stone-Cech compactification, ultrafilter

254A, Lecture 2: Three categories of dynamical systems — 22 comments

Terence Tao wrote 10 months ago: Before we begin or study of dynamical systems, topological dynamical systems, and measure-preserving … more →

Tags: math.CT, math.DS, minimal system, Morse sequence, topological dynamics, Zorn's lemma

254A, Lecture 1: Overview — 22 comments

Terence Tao wrote 10 months ago: In this lecture, I define the basic notion of a dynamical system (as well as the more structured not … more →

Tags: math.DS, ergodic theory, Ratner's theorem, course overview, recurrence theorem

254A: Topics in Ergodic Theory — 4 comments

Terence Tao wrote 11 months ago: Next quarter, starting on Wednesday January 9, I will be teaching a graduate course entitled “ … more →

Tags: math.DS, ergodic theory


Have your say. Start a blog.

See our free features →

Related Tags
All →

Follow this tag via RSS

Find other items tagged with “254a-ergodic-theory”:
Technorati Del.icio.us IceRocket