Departmental Colloquium

The departmental colloquium meets regularly on Wednesdays, 4:10 - 5:00 pm, in room 6183 in the Bahen Centre (40 St. George Street).

Refreshments are served before the colloquium in the Math Lounge (6th floor) at 3:30 pm.

Additional information and previous colloquia can be found at the following link:


Measure rigidity for dynamical systems on (very) non-compact spaces

by Omri Sarig | Penn State University and the Weizmann Institute of Science
Time: 16:10 — 17:00  (Wednesday, Mar. 24, 2010)
Location: BA6183, Bahen Center, 40 St George St
The long term statistical behavior of the orbits of a dynamical system T:X --> X can be studied by analyzing the invariant measures of T. Different measures correspond to different statistics of meandering in space. Usually, there are many different invariant measures, and listing all possible types of statistical behavior is intractable. But sometimes there are few invariant measures and this is possible. In such a case we speak of "measure rigidity".

There are many classical examples of measure rigidity where X is compact.The phenomenology is by now understood. But the situation in the non-compact case is not clear. I will survey some examples (mostly horocycle flows on infinite genus hyperbolic surfaces) which indicate the exotic phenomena which may appear in seriously non-compact situations.

Dates in this series

· Wednesday, Jan. 13, 2010: A tale of two spaces: locally symmetric spaces and moduli space of curves (Lizhen Ji)
· Wednesday, Jan. 20, 2010: Bernstein-Kushnirenko theorem and its generalizations  (Askold Khovanskii)
· Wednesday, Jan. 27, 2010: The Dynamical Mordell-Lang Conjecture (Dragos Ghioca)
· Monday, Feb. 01, 2010: SPECIAL COLLOQUIUM -- Some recent convergence results for nonconventional ergodic averages (Tim Austin)
· Wednesday, Feb. 10, 2010: Higher-order filling inequalities and nilpotent groups (Robert Young)
· Monday, Feb. 22, 2010: SPECIAL COLLOQUIUM -- Group Representation Patterns in Digital Signal Processing (Shamgar Gurevich)
· Wednesday, Feb. 24, 2010: Interval Exchange Transformations (Jon Chaika)
· Thursday, Mar. 04, 2010: Boundary rigidity, volume minimality, and minimal surfaces in L: a survey (Dima Burago)
· Wednesday, Mar. 10, 2010: Einstein Metrics, Complex Surfaces, and Symplectic 4-Manifolds (Claude LeBrun)
· Wednesday, Mar. 24, 2010: Measure rigidity for dynamical systems on (very) non-compact spaces (Omri Sarig)
· Wednesday, Mar. 31, 2010: Large scale behaviour of the continuum random polymer and KPZ (Jeremy Quastel)
· Wednesday, Jul. 07, 2010: Zeroes of Gaussian entire functions. (Fedor Nazarov)
· Wednesday, Sep. 29, 2010: On bounded-depth Boolean circuits (Mark Braverman)
· Wednesday, Oct. 06, 2010: New Invariants on Algebraic Cycles (James Lewis)
· Wednesday, Oct. 13, 2010: Optimality of Hopf fibrations and Hopf vector fields (Herman Gluck)
· Wednesday, Oct. 27, 2010: Pentagonal Tilings and Other Partition Problems (Frank Morgan)
· Wednesday, Nov. 03, 2010: Particle systems and Landau damping (Cédric Villani)
· Wednesday, Nov. 10, 2010: Poisson varieties and D-modules (Travis Schedler)
· Wednesday, Nov. 17, 2010: Non-archimedean integrals over algebraic varieties and their applications (Victor Batyrev)
· Wednesday, Nov. 24, 2010: Singular numbers of random matrices: the asymptotic non-limiting theory (Nicole Tomczak-Jaegermann)
· Wednesday, Dec. 01, 2010: Quantum information as asymptotic geometry (Patrick Hayden)
· Monday, Jan. 17, 2011: SPECIAL COLLOQUIUM -- Counting Representations of Arithmetic Groups (Nir Avni)
· Tuesday, Jan. 18, 2011: Classical algebraic geometry in the tropical limit (Grisha Mikhalkin)
· Wednesday, Jan. 19, 2011: Topological solitons and dispersion (David Stuart)
· Wednesday, Jan. 19, 2011: SPECIAL COLLOQUIUM -- Spectral gaps for lattices in Lie groups (Dubi Kelmer )
· Wednesday, Jan. 26, 2011: Surface operators in 3d topological field theory (Natalia Saulina)
· Monday, Jan. 31, 2011: Boundedness of algebraic varieties (Chenyang Xu)
· Wednesday, Feb. 02, 2011: Statistical Mechanics on Sparse Random Graphs (Amir Dembo)
· Wednesday, Feb. 09, 2011: Systems of quadratic inequalities (Antonio Lerario)
· Wednesday, Mar. 02, 2011: Integrable systems and geometry of Riemann surfaces (Igor Krichever)
· Wednesday, Mar. 09, 2011: On the stability of filament flows and Schrodinger maps (Didier Smets)
· Wednesday, Mar. 23, 2011: Dunkl operators: from analysis to algebra and back (Raphaël Rouquier)
· Wednesday, Mar. 30, 2011: The Erdos distinct distance problem (Larry Guth)
· Wednesday, Apr. 06, 2011: On the formation of singularities in geometric evolution equations (Igor Rodnianski)
· Wednesday, Apr. 13, 2011: Banach-valued Holomorphic Functions on the Maximal Ideal Space of H^\infty and a Problem of Sz. Nagy (Alex Brudnyi)
· Wednesday, Oct. 12, 2011: Eigenvalues, interlacing inequalities and tropical calculus (Anton Alekseev)
· Wednesday, Oct. 19, 2011: Fusion categories and subfactors (Scott Morrison)
· Wednesday, Nov. 09, 2011: Lieb-Thirring Inequalities at Positive Density (Robert Seiringer)
· Wednesday, Nov. 23, 2011: Convex bodies in algebraic geometry and representation theory (Kiumars Kaveh)
· Monday, Nov. 28, 2011: What is K-theory and what is it good for? (Paul Baum)
· Wednesday, Nov. 30, 2011: Bilipschitz embeddings of metric spaces in Banach spaces (Bruce Kleiner)
· Wednesday, Dec. 07, 2011: Quantifying simple connectivity: an introduction to the Dehn function (Robert Young)
· Monday, Jan. 16, 2012: SPECIAL COLLOQUIUM -- Interval exchange transformations (Jon Chaika)
· Wednesday, Jan. 18, 2012: Partial Frobenius integrability and its applications (Yum-Tong Siu)
· Friday, Jan. 20, 2012: SPECIAL COLLOQUIUM -- Arnold diffusion: a combined geometrical and variational approach  (Ke Zhang)
· Monday, Jan. 23, 2012: SPECIAL COLLOQUIUM -- Probabilistic Techniques in Mathematical Phylogenetics: Relating Combinatorial and Variational Distances Between Trees (Sebastien Roch)
· Wednesday, Jan. 25, 2012: SPECIAL COLLOQUIUM -- Counting closed loops in a stratum of quadratic differentials (Kasra Rafi)
· Friday, Jan. 27, 2012: SPECIAL COLLOQUIUM -- Equivariant Schroedinger Maps in 2D with large data (Ioan Bejenaru)
· Monday, Jan. 30, 2012: SPECIAL COLLOQUIUM -- Symplectic resolutions and Poisson-de Rham homology (Travis Schedler)
· Wednesday, Feb. 01, 2012: SPECIAL COLLOQUIUM -- Semisimple algebras and subfactors (Noah Snyder)
· Wednesday, Feb. 15, 2012: Monotonicity formulas revisited and applications (Toby Colding)
· Wednesday, Mar. 07, 2012: Martin's Maximum (Justin Moore)
· Wednesday, Mar. 14, 2012: Perfectoid Spaces (Peter Scholze)
· Wednesday, Mar. 28, 2012: Beyond the Künneth formula (Jan Nekovář)
· Wednesday, Sep. 05, 2012: The Kollár Problem (Charles Fefferman)
· Thursday, Sep. 20, 2012: PUBLIC LECTURE: Counting stationary modes: a discrete view of geometry and dynamics (Stéphane Nonnenmacher)
· Wednesday, Sep. 26, 2012: Microlocal analysis: some old results and new trends (Gilles Lebeau)
· Wednesday, Oct. 03, 2012: The Hilbert 16th problem and its infinitesimal version (Gal Binyamini)
· Wednesday, Oct. 10, 2012: On the bounded $L^2$ curvature conjecture (Sergiu Klainerman)
· Wednesday, Oct. 17, 2012: Animation, Teeth and Skeletons (Ingrid Daubechies)
· Wednesday, Oct. 24, 2012: Integral Apollonian Gaskets (Alex Kontorovich)
· Wednesday, Nov. 07, 2012: Integrable Probability (Ivan Corwin)
· Wednesday, Nov. 14, 2012: Controlled Active Vision/Image Processing with Applications to Medical Image Computing (Allen Tannenbaum)
· Wednesday, Nov. 21, 2012: Billiards and curves in moduli space (Curtis McMullen)
· Wednesday, Nov. 28, 2012: Rotation of invariant tensors and geometric representation theory (Joel Kamnitzer)
· Wednesday, Dec. 05, 2012: Winning sets for Schmidt games, badly approximable real numbers, and rational billiards (Howard Masur)
· Wednesday, Jan. 23, 2013: Unexpected applications of polynomials in combinatorics (Larry Guth)
· Wednesday, Jan. 30, 2013: Operator limits of random matrices (Balint Virag)
· Tuesday, Feb. 05, 2013: SPECIAL DEPARTMENTAL COLLOQUIUM -- An introduction to unlikely intersections (Jacob Tsimerman)
· Wednesday, Feb. 06, 2013: Universal spaces for birational invariants (Yuri Tschinkel)
· Wednesday, Feb. 27, 2013: From Nash to Onsager: funny coincidences across differential geometry and the theory of turbulence (Camillo De Lellis)