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School on
Low-Dimensional Geometry and Topology:
Discrete and Algorithmic Aspects

minimal surface Institut Henri Poincare

List of abstracts

Main lectures

Jeff Erickson (University of Illinois at Urbana-Champaign, USA)

Tentative title: Two-dimensional computational topology

Tentative abstract: This series of lectures will describe recent and not-so-recent works in computational topology of curves in the plane and on surfaces. Combinatorial and algorithmic aspects will be discussed.

Tentative lecture plan:

  1. Historical roots of computational topology
  2. Homotopy testing
  3. Shortest paths and cycles
  4. Maximum flows and minimum cuts
  5. Curve simplification

Joel Hass (University of California at Davis, USA)

Title: Algorithms and complexity in the theory of knots and manifolds

Abstract: These lectures will introduce algorithmic procedures to study Knots and 3-dimensional manifolds. Algorithmic questions have been part of the study of manifolds since the time of Dehn, and are finding increasing practicality as algorithms and hardware improve. The study of algorithmic procedures often points the way to interesting directions in the theoretical study of manifolds. We’ll begin by reviewing an easy algorithm to classify 2-manifolds, and then outline Markov's argument for the undecidability of 4-manifold recognition. We’ll then turn to 3-dimensions and and study the Unknotting Problem. Using Haken’s ideas on normal surfaces, we’ll describe algorithms that resolve this and related 3-manifold problems. Normal surfaces turn out to have many similarities to minimal surfaces, and we’ll see how this connection leads to an algorithm to recognize the 3-sphere. Finally we’ll discuss the complexity of topological algorithms, allowing us to connect their difficulty to that of problems in numerous other areas, and to get an idea of which problems are compuationally feasible.

Tentative lecture plan:

Other invited presentations

(titles and abstracts to be determined later)

Acknowledgments. This school is funded by the Bézout Labex. We also gratefully acknowledge support from Institut Henri Poincaré. The image at the top of this page is a Chen Gackstatter surface created with 3D-Xplormath.

Contact. geomschool2018sep2listessep1univ-mlvsep1fr.

Labex Bezout    Institut Henri Poincare