PORTO, Portugal, June 10–13, 2015 00 ! General 1111-00-22 Dirk R. H. Schlingmann* ([email protected]), 800 University Way, Contr.Session Spartanburg, SC 29303. Mathematics and Music. In this paper, I will present my work on how I use mathematics and the technical computing software Math- ematica to analyze, manipulate, and create music. Musical pieces are available as Musical Instrument Digital Interface (MIDI) files. I will compare the work of well-known composers through statistical analysis, and will present variations of their compositions by performing geometrical transformations on their musical data. Fur- thermore, I will play musical creations that are entirely based on mathematical functions. (Received December 31, 2014) 1111-00-77 Anne Mendes Burns* ([email protected]), Mathematics Department, Long Island Session 39 University, Brookville, NY 11548. Variation of Parameters: Visual Proof in Complex Analysis. Preliminary report. Complex analysis, taking place in two dimensions, is ideally suited for visualization. In addition to providing insight into the mathematics of complex variable theory, visualization produces beautiful works of art that awe even non-mathematicians. Topics taken from complex variable theory such as complex vector fields, circle inversions, Mobius Transformations and Dynamical Systems provide a variety of ways to assign color, value and transparency to a two-dimensional space. Interpreting a complex function as a vector field, stunning works of art can be produced. Vector fields can be plotted over one or more paths defined by complex functions; singularities and their multiplicities are easily discerned by the assignment of hue, value and transparency as functions of magnitude, direction and time. Transformations acting on circles provides a limitless source for mathematically inspired art. Mobius Transformations are ideal for use in iterated functon systems where circles are mapped to circles. ”Continuously” varying the parameters in the Unit Circle Group leads to fascinating and sometimes surprising animations. The complexity of a dynamical system involving rational functions produces amazing pictures suggesting truths that can later be proved analytically. (Received January 19, 2015) 1111-00-89 Marcus du Sautoy* ([email protected]), Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, United Kingdom. The Secret Evening Public Lecture Mathematicians. From composers to painters, writers to choreographers, the mathematician’s palette of shapes, patterns and numbers has proved a powerful inspiration. Artists can be subconsciously drawn to the same structures that fascinate mathematicians as they hunt for interesting new structures to frame their creative process. Professor du Sautoy will explore the hidden mathematical ideas that underpin the creative output of well- known artists and reveal that the work of the mathematician is also driven by strong aesthetic values. (Received January 21, 2015) 1111-00-197 Bren Cavallo and Delaram Kahrobaei* ([email protected]), New York, NY Session 1 10016. Afamilyofpolycyclicgroupsoverwhichtheuniformconjugacyproblemis NP-complete. Our main result is that we construct polycyclic groups Gn whose conjugacy problem is at least as hard as the subset sum problem with n indeterminates. As such, the conjugacy problem over the groups Gn is NP-complete where the parameters of the problem are taken in terms of n and the length of the elements given on input. (Received February 02, 2015) 1111-00-280 Carolyn A Yackel* ([email protected]), 1501 Mercer University Dr., Macon, GA Session 39 31207. An Analysis of Fair Isle Knitting. Preliminary report. During this talk we will discuss Fair Isle knitting. Fair Isle knitting is a type of stranded knitting employing two strands on any given row with floats of limited length.Thecombinatorialanalysisofasinglerowdefines the variety of potential row patterns, yet further investigation is required to discover how the row patterns can be assembled together to create two-dimensional patterns displaying specific crystallographic symmetries. (Received February 04, 2015) 1 200 GENERAL [email protected] Session 1 1111-00-284 Bren Cavallo, Jonathan Gryak* ( ), Delaram Kahrobaei and Conchita Martinez-Perez. Conjugacy Problem in Polycyclic and Metabelian Groups: Algorithms and Complexity. Preliminary report. In this talk we present a couple of algorithms for solving the conjugacy problem in various polycyclic and metabelian groups. We analyze the complexity of such algorithms, and present experimental results of the algorithms’ performance. (Received February 04, 2015) 1111-00-386 Jos´eTenreiroMachado*([email protected]), Rua Dr. Ant´onio Bernardino Session 21 de Almeida, 431, 4200-07 Porto, Portugal, and Ant´onio M Lopes ([email protected]), Rua Dr. Roberto Frias, 4200-465 Porto, Portugal. Analysis of complex phenomena by means of signal processing and fractional calculus. Complex systems (CS) emerge from the relationships between multiple objects that contribute to a collective behaviour often revealing surprisingdynamicalphenomena.ThemodellingofCScanadoptsophisticatedmath- ematical tools, but often we verify that those are still far from capturing the overall richness of the involved dynamics. A common property to CS is the absence of a characteristic length-scale, meaning that CS reveal frequency-size power-law (PL) behaviour. PL distributions have been associated to systems with memory, as is the case of fractional-order systems. We study several natural and man-made CS in the perspective of dynamical systems. From such a viewpoint, a CS has an output that results from stimuli, being that signal interpreted as amanifestationoftheglobalsystemdynamics.ThesystemoutputisanalysedbymeansoftheFouriertrans- form (FT). The amplitude spectrum is approximated by a PL function and the parameters are interpreted as a signature of the CS characteristics. In a complementary approach, we compare and visualize similarities among several cases studied. Our approach contributes to better understand CS dynamics and their ruling principles, as well as to expose hidden correlations between systems from very distinct areas. (Received February 06, 2015) 1111-00-397 Radmila Sazdanovic* ([email protected]), Department of Mathematics, Session 39 North Carolina State University, SAS Hall PO Box 8205, Raleigh, NC 27695, and Andrew Cooper. Visual thinking in mathematics. Preliminary report. Visualizations and visual thinking are essential to progress in many areas of mathematics. Visual representations of mathematical objects, structures or relations among them often provide a simple, natural description, useful for communicating complex ideas. But visual methods in mathematics are used for more than just presenting information. Visualization also advances understanding by distilling essential information and building intuition. When there is an equivalence between mathematical objects and their visual descriptions, both can be used exclusively, simultaneously, or interchangeably in constructing proofs. In addition to visualization as a tool, several fields of research study the mathematics of the visual, regarding visual objects as the primitives on which mathematical structures are built. (Received February 06, 2015) 1111-00-468 Susan Goldstine* ([email protected]), Dept of Mathematics and Computer Science, Session 39 St. Mary’s College of Maryland, 18952 E Fisher Road, St. Mary’s City, MD 20686. Thinking Outside the Torus: New directions in bead crochet. Preliminary report. For the past six years, Ellie Baker and I have studied the mathematics of bead crochet rope bracelets. The traditional form for such a bracelet is an apparently seamless torus of beads arranged in a single spiral. This spiral structure introduces fascinating constraints on pattern design, and we have spoken about our discoveries at various conferences and published them in several papers and a book. The underlying crochet in a standard bead crochet bracelet is very simple, with the same stitch repeated throughout the piece; the intricate patterns and textures in a bracelet stem entirely from the choice and ar- rangement of beads. Incorporating different crochet stitches such as increases, decreases, and chain stitches can produce bead crochet with more complicated geometry and topology. This talk will cover some of these new explorations into the mathematical possibilities of the art form. (Received February 08, 2015) 1111-00-772 Luke Wolcott* ([email protected]). The phenomenology of mathematical Contr.Session understanding: an experiential investigation. What is it like to understand mathematics? We have investigated the lived experience of understanding the notion of groups in mathematics, and extracted a generic structure of it as a series of mental cognitive gestures and embodiments. We use the first-person methodology of theinterviewofelicitation(entretiend’explication in French), developed by Pierre Vermersch and Francisco Varela and now used extensively for investigating the microdynamics of lived experience. This work is a collaboration between Luke Wolcott, a mathematics professor from Lawrence University, and Alexandra Van-Quynh, a philosopher of mathematics from Universidade de Lisboa. (Received February 10, 2015) 01 HISTORY AND BIOGRAPHY 3 1111-00-781 Luke Wolcott* ([email protected])andElizabeth McTernan Contr.Session ([email protected]). Aclassificationofmath-artwork. We present a rough classification