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

The last two lectures of this course will be on Ratner’s theorems on equidistribution of orbits on homogeneous spaces. Due to lack of time, I will not be able to cover all the material here tha… more →

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

Terence Tao wrote 5 months ago: The last two lectures of this course will be on Ratner’s theorems on equidistribution of orbit … more →

Tags: 254A - ergodic theory, math.DS, Dichotomy, ergodicity, nilmanifolds, nilpotent groups, Ratner's theorem, Structure

Kleiner's proof of Gromov's theorem — 7 comments

Terence Tao wrote 6 months ago: This week there is a conference here at IPAM on expanders in pure and applied mathematics. I was an … more →

Tags: math.CA, talk, Cayley graphs, Gromov's theorem, Harmonic Functions, polynomial growth, virtually nilpotent, virtually solvable

Equivariant DeRham Cohomology — 1 comment

Greg Muller wrote 6 months ago:     My lectures on equivariant cohomology are spinning a bit out of control.  The questions and … more →

Tags: Greg, math.AT, math.GT

The Cohomology of Quotients — 8 comments

Greg Muller wrote 6 months ago:     We’ve organized a mostly informal Topics in Noncommutative Algebra seminar this semeste … more →

Tags: Greg, math.AT, math.GT

Puzzles, Groups, and Groupoids — 12 comments

Jim Belk wrote 6 months ago: Over at Good Math, Bad Math, MarkCC has a nice post introducing groupoids which uses the fifteen puz … more →

Tags: Basic Grad Student, High School, Jim, Undergraduate

254A, Lecture 6: Isometric systems and isometric extensions — 26 comments

Terence Tao wrote 6 months ago: In this lecture, we move away from recurrence, and instead focus on the structure of topological dyn … more →

Tags: 254A - ergodic theory, math.AT, math.DS, math.MG, Isometric extensions, Kronecker factor, polynomial sequences, Ratner's theorem, Structure

The quantitative behaviour of polynomial orbits on nilmanifolds — 43 comments

Terence Tao wrote 11 months ago: Ben Green and I have just uploaded our paper “The quantitative behaviour of polynomial orbits … more →

Tags: math.DS, paper, equidistribution, nilmanifolds, polynomial sequences, Ratner's theorem, Structure, symmetric spaces, Weyl's equidistribution theorem

Fields Medalist Symposium — 10 comments

Terence Tao wrote 1 year ago: On Thursday, UCLA hosted a “Fields Medalist Symposium“, in which four of the six Univers … more →

Tags: talk, math.NT, math.QA, Richard Borcherds, Efim Zelmanov, Vaughan Jones, Fields Medal

Open question: noncommutative Freiman theorem — 29 comments

Terence Tao wrote 1 year ago: This is another one of my favourite open problems, falling under the heading of inverse theorems in … more →

Tags: math.CO, Question, additive combinatorics, Freiman's theorem, Group Theory


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