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

minimal surface Institut Henri Poincare

Dates and Location. June 18–22, 2018, at Institut Henri Poincaré (IHP), in the center of Paris (access map). The amphitheater can accomodate 150 persons.

Presentation. This is a one-week school devoted to low-dimensional geometry and topology, from both the viewpoints of mathematicians and computer scientists. The expected participants are graduate students and researchers in mathematics and computer science interested in geometric or topological aspects. This includes, not exhaustively, mathematicians working in differential, Riemannian, or topological geometry; and computer scientists working in computational geometry or topology. The goal is to foster interactions between these various communities.

Speakers. The two main speakers, each giving about 90 minutes of lectures each of the five days of the week, are:

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

Tentative title: Two-dimensional computational topology

Tentative abstract (see here for a more detailed tentative plan of the lectures). 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.

Joel Hass
Joel Hass (University of California at Davis, USA)

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

Abstract (see here for a more detailed tentative plan of the lectures). 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.

The following researchers will also give a presentation:

Registration. Registration is free but mandatory, before March 15, 2018. Registration is not open yet.

Student support. We expect to be able to provide accommodation for about 20 students. The application webpage is not open yet. We expect that the deadline for applying will be on March 1st, 2018.

Related events.

Organizing committee. It consists of a team of mathematicians and computer scientists in the East of Paris who all belong to the Bézout Labex:

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