ICERM Semester Program on "Low-dimensional Topology,
Geometry, and Dynamics"
(September 9, 2013 - December 6, 2013)

 

CLICK HERE TO PARTICIPATE
Dec 1, 2012 (Early Consideration)
March 15, 2013 (Normal Deadline)
After March 15, 2013, applications will be reviewed on a rolling basis
Organizing Committee

Pappus
[Image courtesy of
Rich Schwartz, Brown University]



Introduction

The program focuses on the recent impact of computation and experiment on the study of the pure mathematics sides of topology, geometry, and dynamics. Specific areas include 3-dimensional topology, the study of locally symmetric spaces, low-dimensional dynamics, and geometric group theory. Included are areas where computation has not yet had an impact, but might do so in the near future.






 Workshops:

Exotic Geometric Structures (September 16-20, 2013)


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Review of applications will begin on May 15, 2013
Organizing Committee
  • Richard Schwartz (chair)
    (Brown University)
  • Bill Goldman
    (University of Maryland)
  • John Parker
    (University of Durham)
  • Caroline Series
    (Warwick University)
  • Genevieve Walsh
    (Tufts University)

Description

This workshop will focus on recent advances in the study of geometric structures and their associated group representations. As well as featuring hyperbolic structures, the workshop will also consider more exotic structures, such as projective structures, complex hyperbolic and spherical CR-structures and locally homogeneous space-times. A related focus includes aspects of coarse or non-positively curved geometry such as Gromov hyperbolic spaces and CAT(0) complexes. We will explore the interaction between experimental evidence and rigorous proof.



Topology, Geometry and Group Theory, Informed by Experiment (October 21-25, 2013)


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Review of applications will begin on June 15, 2013
Organizing Committee
  • Danny Calegari
    (Cambridge University)
  • Marc Culler
    (University of Illinois, Chicago)
  • David Gabai
    (Princeton University)
  • Joel Hass
    (UC Davis)
  • Robert Lipshitz
    (Columbia University)
  • Karen Vogtmann
    (Cornell University)
  • Genevieve Walsh
    (Tufts University)

Description

The mathematical focus of this workshop will include all aspects of the topology and geometry of low-dimensional manifolds and geometric group theory. It has been understood for over a century that these subjects are tightly connected, but the connections have become even deeper as the subjects have matured. Recent advances have given dramatic evidence of this. The workshop aims to further extend the interplay between these subjects.

Algorithms have been an important and consistent feature of all of these mathematical areas from the beginning. This includes both questions about the existence of algorithms and the development of practical algorithms for computing natural invariants. More recently, computer experiments and rigorous computer-assisted proofs have had a significant impact. It is natural to expect experimental and computational methods to play an expanding role in the theory of low dimensional spaces. Additional goals of the workshop are to explore the development of new computational tools and implementations of new algorithms, and to provide opportunities for researchers to become more familiar with existing tools and how they can be applied in research.


Geometric Structures in Low-Dimensional Dynamics (November 18-22, 2013)


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Review of applications will begin on July 15, 2013
Organizing Committee
  • Anton Zorich (chair)
    (IMJ, University Paris-7)
  • Moon Duchin
    (Tufts University)
  • Pascal Hubert
    (l'Université Paul Cézanne)
  • Richard Schwartz
    (Brown University)
  • Howard Masur
    (University of Chicago)

Description

This workshop will present topics in low-dimensional dynamics such as billiards, flows on flat surfaces, dynamics on moduli spaces, and piecewise isometric maps. One theme in the workshop will be the appearance of geometric structures such as hyperbolic space and Teichmüller space in connection with dynamical systems which are basically defined in terms of the Euclidean plane. Computer experiments are common in these areas, and will be discussed, but the emphasis will be on the mathematics that comes out of the experiments.