Talk at the International Conference on Algebraic Informatics 2017
July 3, 2017
I wouldn’t miss a chance to visit Greece during the summer, so when the opportunity presented itself for me to give a talk about my MSc thesis there, I was more than happy to seize it. The manifestation of this opportunity was the International Conference on Algebraic Informatics 2017, or CAI 2017.
This year, CAI was held in Kalamata; a perfect conference location if you enjoy attending lectures while being one minute away from an alternate reality in which you are reading the book of your choice  half submerged at the point where sea meets land, slowly and softly being hypnotized by the rythmic white noise of waves and distant seagulls.
Back in the conference reality, the variety of the tracks allowed for a valuable exchange of interesting ideas. The five tracks ranging from Natural and Quantum Computing to Design Theory stimulated interdisciplinary discussions among the participants.
My talk was part of the Computer Algebra track and was based on part of my MSc thesis. It is joint work with Ioannis Emiris and Christos Konaxis in which we present a method for constructing an implicit matrix representation of a rational curve or a rational triangular surface when the only input is a sufficient set of points for which the parameter value of the underlying parametrization is also known.
There are certain scenarios where this can be useful. At this point we are only interested in the method itself, which is based on interpolating the syzygies of the parametrization, and not the applications. You can read more about this work here, and more on implicit matrix representations here.
When I started my PhD, the focus of my research shifted from computational algebra to computational design and applied geometry, apart from other areas. This led to ideas for new application areas for this method. One of those is to use this method to develop a design tool for curves where the user defines a set of points, each equipped with a parameter value, to be interpolated by a rational parametrization. The difference with traditional interpolation is that here we care about the “time” at which the rational parametric curve passes through the given point.
Early afternoon of the third conference day, we had a chance to visit Ancient Messene, a well preserved and beautifully presented archaeological site, about 35km outside Kalamata. While extremely hot and sunny at that time of day, exploring this historic city-state was an enjoyable experience. Just be prepared for the heat if you intend to visit under similar circumstances.
Overall, the conference was great and I would like to thank Ilias Kotsireas for the successful organization, as well as Rafael Sendra and Franz Winkler for chairing the Computer Algebra track and for the nice discussions we had.