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:


SPECIAL COLLOQUIUM -- Some recent convergence results for nonconventional ergodic averages

by Tim Austin | UCLA
Time: 15:10  (Monday, Feb. 01, 2010)
Location: BA6183, Bahen Center, 40 St. George Street
The phenomenon of multiple recurrence in ergodic theory occurrs when several of the images of one fixed positive-measure set under some probability-preserving transformations, indexed by the points of some finite configuration in the acting group, all overlap in a set of positive measure.  Instances of this were first investigated very generally by Furstenberg, who related them to Szemeredi's Theorem in additive combinatorics and so gave a new proof of that theorem.  His analysis focuses on certain `nonconventional' ergodic averages, and these have gone on to attract considerable further interest.  In this talk I will discuss some recent progress in their analysis, showing how an extension of an initially-given system of commuting probability-preserving transformations can be used in a proof of the norm convergence of some such averages.

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)