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11/12/2007, 14:30 — 15:30 — Room P9, Mathematics Building
, Instituto de Matemática Pura e Aplicada (IMPA)

Dynamics and geometry of flat surfaces

Flat surfaces carry a metric whose curvature vanishes identically, outside a finite set of conical singularities. Geodesics correspond to straight lines, in appropriate local coordinates, and so the local picture is completely trivial. However, the global behavior of geodesics is suprisingly rich! I'll discuss some main notions, and two results in this field: the Masur-Veech unique ergodicity theorem, and the Zorich-Kontsevich asymptotic flag conjecture, proved by Avila and myself, following important partial results by Forni.

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The Mathematics Colloquium is a series of monthly talks organized by the Department of Mathematics of IST, aiming to be a forum for the presentation of mathematical ideas or ideas about Mathematics. The Colloquium welcomes the participation of faculty, researchers and undergraduate or graduate students, of IST or other institutions, and is seen as an opportunity of bringing together and fostering the building up of ideas in an informal atmosphere.

Organizers: Conceição Amado, Lina Oliveira e Maria João Borges.