Polytopes and Discrete Geometry
About this Title
Gabriel Cunningham, University of Massachusetts Boston, Boston, MA, Mark Mixer, Wentworth Institute of Technology, Boston, MA and Egon Schulte, Northeastern University, Boston, MA, Editors
Publication: Contemporary Mathematics
Publication Year: 2021; Volume 764
ISBNs: 978-1-4704-4897-4 (print); 978-1-4704-6420-2 (online)
This volume contains the proceedings of the AMS Special Session on Polytopes and Discrete Geometry, held from April 21–22, 2018, at Northeastern University, Boston, Massachusetts.
The papers showcase the breadth of discrete geometry through many new methods and results in a variety of topics. Also included are survey articles on some important areas of active research. This volume is aimed at researchers in discrete and convex geometry and researchers who work with abstract polytopes or string $C$-groups. It is also aimed at early career mathematicians, including graduate students and postdoctoral fellows, to give them a glimpse of the variety and beauty of these research areas.
Topics covered in this volume include: the combinatorics, geometry, and symmetries of convex polytopes; tilings; discrete point sets; the combinatorics of Eulerian posets and interval posets; symmetries of surfaces and maps on surfaces; self-dual polytopes; string $C$-groups; hypertopes; and graph coloring.
Graduate students and research mathematicians interested in various aspects of discrete, combinatorial, and convex geometry.
Table of Contents
- Margaret M. Bayer – The $cd$-index: A survey
- Tibor Bisztriczky and Déborah Oliveros – $d$-dimensional self-dual polytopes and Meissner polytopes
- Peter A. Brooksbank – On the ranks of string C-group representations for symplectic and orthogonal groups
- Joseph Ray Clarence Damasco and Dirk Frettlöh – Perfect colorings of regular graphs
- J. A. De Loera, T. A. Hogan, F. Meunier and N. H. Mustafa – Tverberg theorems over discrete sets of points
- Antoine Deza, Lionel Pournin and Rado Rakotonarivo – The vertices of primitive zonotopes
- Michael Gene Dobbins and Florian Frick – Barycenters of points in polytope skeleta
- Maria Elisa Fernandes, Dimitri Leemans, Claudio Alexandre Piedade and Asia Ivić Weiss – Two families of locally toroidal regular 4-hypertopes arising from toroids
- Alathea Jensen – Self-polar polytopes
- Ken-ichi Kawarabayashi, Pavel Klavík, Bojan Mohar, Roman Nedela and Peter Zeman – Isomorphisms of maps on the sphere
- Jim Lawrence – Some enumeration relating to intervals in posets
- Dimitri Leemans – String C-group representations of almost simple groups: A survey
- Undine Leopold and Thomas W. Tucker – Orientation-reversing symmetry of closed surfaces immersed in euclidean 3-space
- Peter McMullen – Realizations of the $120$-cell
- Egon Schulte, Pablo Soberón and Gordon Ian Williams – Prescribing symmetries and automorphisms for polytopes
- Marjorie Senechal and Jean E. Taylor – The rhombic triacontahedron and crystallography
- Mark D. Tomenes and Ma. Louise Antonette N. De Las Peñas – Tilings with congruent edge coronae