Knotting Mathematics and Art : International Conference in Low Dimensional Topology and Mathematical Art

Nagle Lecture, Opening Talk) John H. Conway (Princeton University) From Topology to Symmetry (This talk will be the Nagle Lecture, http://www.math.usf.edu/Nagle/index.html, scheduled on November 1, 7:30–8:30PM, also regarded as an opening lecture of the conference.) It is well known that the symmetries of repeating patterns in the Euclidean plane belong to just one of 17 groups. Less well-known are the corresponding enumerations for frieze patterns (7 types) and patterns on the sphere (7 particular groups + 7 infinite series) and the hyperbolic plane, which supports a multiple infinity of groups. I shall describe some of these, and perhaps say something about the corresponding enumerations in 3 and more dimensions. Abstract (Plenary Talks) (In alphabetical order of the author’s last name)Plenary Talks) (In alphabetical order of the author’s last name) Thomas Banchoff (Brown University) The Fourth Dimension and Salvador Dali Salvador Dali was fascinated by geometric objects in the fourth dimension, including hypercubes and catastrophe surfaces. Where did he get his inspirations and how did he represent fourdimensional phenomena in his paintings? This talk will describe contacts with the artist over a ten-year period starting in 1975 as well as some new information about his sources. J. Scott Carter (University of South Alabama), Tony Robbin (Artist and author) Collaboration across the the two cultures Starting from a mathematically simple idea — that the sum of cubes can be written as the square of a triangle — we begin investigating the aesthetics of the product of two isosoles right triangles from our respective disciplines. The investigation is simultaneuosly enhanced and obstructed by computer systems and electronic communications. In this talk we will demonstrate the mathematical encryption of the figures, a 3 dimensional animation, some 2-dimensional projections, and rough sketches that indicate meaning of the figures. We also will show slides of some of Mr. Robbin’s recent works. In the process, we will also discuss the importance of communication between us and how this on-going work has influenced our own points of view of our work.