Informal Dynamics Seminar Schedule

Fall 2014

Oct 8: Bena Tshishiku
Examples of Julia sets
McMullen 1.2 and page 2, Milnor 5, first page of 3

Oct 15: Wouter van Limbeek
Basic Properties of Julia sets
McMullen 5.1 and 5.2, Milnor 3, 11

Oct 22: Simion Filip
Conjugacies near periodic points, basins of attraction: Part 1
McMullen 5.4, 5.5, Milnor 6, 7

Oct 29: Alex Wright
Conjugacies near periodic points, basins of attraction: Part 2

Nov 5: Ian Le
The moduli space of Rational and Polynomial maps, connectivity of the Mandelbrot set
Paper and notes of Douady-Hubbard below, and talking to Ronen (who knows the material well)

Nov 12: Alden Walker
Postcritical set, (post)critically finite rational maps and intro to expanding maps
McMullen 5.6, 5.7, 5.8, Minor 14

Nov 19: Alden Walker
Intro to expanding maps continued

Nov 26: Simion Filip
Solving polynomials using dynamics
McMullen (Algebra and Dynamics, Chapter 1), Geometry of the Quintic.

Dec 3: Ian Frankel
Invariant Laminations on the Disk
Complex Dynamics: Families and Friends, Section "Polynomials and the Riemann Mapping Near Infinity" by Thurston, and the start of the appendix by Schleicher.

Here are some resources for complex dynamics in one variable:

Riemann surfaces, dynamics and geometry. Course notes by McMullen, also covering other topics.
Dynamics in one complex variable. Standard book by Milnor. Ronen has a hard copy.
The dynamics of rational transforms: the topological picture. A very nice 1986 survey by Lyubich, with proofs.
A first course in complex dynamics systems. This very short survey by Sindelarova is a great way to get an overview of the subject in only 10 pages, of course with no proofs.
Frontiers in complex dynamics. A more in depth survey by McMullen.
Iteration des polynomes quadratiques complexes. The 1982 paper by Douady and Hubbard, in which the Mandelbrot set is shown to be connected.
Algebra and Dynamics. More course notes by McMullen.
Geometry of the Quintic. Book by Jerry Shurman.
Complex Dynamics: Families and Friends. Book edited by Dierk Schleicher.

The Mandelbrot/Julia Set Applet. Very easy to use!
Fractal Stream. A more sophisticated program to explore dynamics systems. Ronen can teach you how to use it.

Spring 2013

Apr 2: Regis Varao.
Absolute continuity of the center foliation for partially hyperbolic diffeomorphisms.

Apr 9: Simion Filip.
Gromov's polynomial growth theorem following Shalom-Tao.

Apr 15: Simion Filip.
Gromov's polynomial growth theorem following Shalom-Tao, continued.

Starting Apr 22, the seminar will be a reading group of the work of Einsiedler-Katok-Lindenstrauss on diagonal actions. Here is a preliminary schedule of topics and speakers.

Apr 23: Intro following Venkatesh notes. Sebastian Hensel.
Apr 30: Section 3 of Pisa notes (Entropy, 5p). Amie Wilkinson.
May 7: Section 4 and 5 of Pisa Notes (Conditional Measures, 6p). Clark Butler.
May 14: Section 6 (Leafwise Measures, 15p). Regis Varao.
May 21: Section 7 (Leafwise Measures and Entropy, 20p). Jon Chaika.
May 28: Section 8 (The Product Measure, 5p). David Aulicino.
June 4: Section 9 (High Entropy Method, 10p). Wouter van Limbeek.
June 11: Section 10 and 11 (Low Entropy Method, Combining High and Low Entropy Methods, 7p). Alex Wright. Notes.

Here are some resources for EKL:
The work of Einsiedler, Katok and Lindenstrauss on the Littlewood Conjecture (Introduction), by Venkatesh.
Diagonal actions on locally homogeneous spaces (Pisa notes), by Einsiedler and Lindenstrauss.
Rigidity of multiparameter actions (Survey), by Lindenstrauss.
Diagonalizable flows on locally homogeneous spaces and number theory (ICM address), by Einsiedler and Lindenstrauss.
Entropy in dynamics (Book), by Einsiedler, Lindenstrauss and Ward. Chapter 2 has the basics, and Chapter 5 is a great reference for Section 7 of the Pisa notes.
Invariant measures and the set of exceptions to Littlewood's Conjecture (Paper), by Einsiedler, Katok and Lindenstrauss.
On measures invariant under diagonilizable actions - the rank one case and the general low entropy method (Paper), by by Einsiedler and Lindenstrauss.
Ratner's Theorem on Unipotent Flows (Book), by Witte Morris. Section 1.6 is a good reference for direction of divergence under unipotent flows.
Ratner's Theorem on SL(2,R)-invariant measures (Short Paper), by Einsiedler.
Invariant measures of actions of higher rank abelian groups (Paper), by Kalinin and Katok.

Wouter has also found some talks that may be of interest.
Lindenstrauss on Equidistribution in Homogeneous Spaces: Video, Notes.
Furstenberg on the work of Lindenstrauss: Video, Notes.
Soundararajan on Quantum Unique Ergodicity: Video, Notes.
Einsiedler's invited lecture in the dynamics section in 2010: Notes.

Winter 2013

Feb 5: Carlos Matheus.
On the regularity conjecture of Eskin-Kontsevich-Zorich.

Feb 12: Alex Wright.
Furstenberg's times 2 times 3 problem.
See Matheus' blog post on this topic.

Feb 19: Ilya Gekhtman.
Weyl's equidistribution theorem.

Feb 26: Vincent Delacroix.
The wind-tree model.

Mar 5: Alex Wright.
Stationary measures on the torus after Benoist-Quint, part 1.
See the notes and the paper. Preliminary notes from the first talk are here.

Mar 12: Alex Wright.
Stationary measures on the torus after Benoist-Quint, part 2.

Monday Mar 18, 1pm (in E312): Alex Wright.
Stationary measures on the torus after Benoist-Quint, part 3.