Location: in Klagenfurt. www.hotel-sille.com Time: From Wed(12:00), 03.05.2017 to Sat(12:00), 06.05.2017.
Unlike previous years, we are going to focus on one particular topic. The proposed topic is “Puiseux series”, and the idea is to roughly divide the meeting in two parts, a first one where the main results about Puiseux series are established, and the second, where some applications of the theory of Puiseux series are presented.
The main reference for the first part is the book “Plane Algebraic Curves” by Gerd Fisher. in particular Chapters 6 and 7.
Coordinators: Matteo Gallet (firstname.lastname@example.org).
Participants: Jose Capco, Giancarlo Castellano, Christopher Chiu, Matteo Gallet, Herwig Hauser, Lin Jiu, Christoph Koutschan, Hana Kovacova, Jan Legersky, Zijia Li, Niels Lubbes, Stefan Perlega, Lukas Prader, Josef Schicho.
|Wednesday afternoon||Niels Lubbes||(Convergent) power series|
|Wednesday afternoon||Christopher Chiu||Decomposition into local branches|
|Thursday morning||Hana Kovacova||(Formal) parametrization by Puiseux series|
|Thursday afternoon||Matteo Gallet||(Convergent) parametrization by Puiseux series|
|Thursday afternoon||Zijia Li||An example of the Puiseux-Newton algorithm|
|Friday morning||Christoph Koutschan||Puiseux series and integral bases of rational functions|
|Friday afternoon||Jan Legersky||Puiseux series and Laman graphs|
|Friday afternoon||Josef Schicho||The complexity of the Newton-Puiseux algorithm|
Here is the proposed path through the theory of Puiseux series. Here we denote by [F] the book “Plane Algebraic Curves” by Fisher and by [SWP] the book “Rational Algebraic Curves: A Computer Algebra Approach” by Sendra, Winkler and Perez-Diaz.
Short description: This talk will introduce the basic concepts for power series, and will state the Weierstrass Preparation and Division Theorem. The material that could be covered is
Short description: This talk will introduce the decomposition of a germ of a curve into local branches.
Short description: This talk will prove that local branches can be parametrize by formal Puiseux series.
Short description: This talk will prove that local branches can be parametrize by convergent Puiseux series.
Short description: This talk will show an example of the Puiseux-Newton algorithm.
Short description: Two questions arise and will be treated in this talk: