Algebraic Geometry in Applications and Algorithms

Scope of the special session

In recent years applications of algebraic geometry to various other disciplines have flourished. This has been a consequence both of the theory provided by algebraic geometry and of the development of computational tools and algorithmic versions of the results established in this theory. This phenomenon has produced a clear synergy from these two research areas. In one direction, results from algebraic geometry are being applied in fields as computer aided design, computer graphics, computer vision, geometric modeling, computer numerical control or pattern recognition, modeling lens for cameras, solving differential equations, or in the automatic determination of geometric loci in dynamical geometry. On the other direction, the development of applications yields to problems of algebraic-geometric-computational type that turn to be a source of theoretical challenges for mathematics.

The proposal of this session is framed in this context and plans to focus on two different, but complementary, directions: the development of algorithms for solving problems of applied interest, and the treatment of the algebraic geometry aspects of some applications. More precisely, we want to focus on:

  • Applications of curves in geometric codes
  • Applications of curves and surfaces to the solving differential equations
  • Applications of algebraic geometry in computational biology
  • Solving problems derived from computer aided geometric design
  • Algorithms for parametrizing optimally curves and surfaces
  • Applications of algebraic geometry to algebraic statistic
  • Applications of algebraic geometry to computer vision
  • Solving sets of polynomial equations.

Organisers

  • A. Alzati (University of Milan, Italy)
  • M. Bertolini (University of Milan, Italy)
  • J.R. Sendra (University of Alcalá, Spain) - rafael.sendra@uah.es
  • C. Turrini (University of Milan, Italy)

Abstracts and schedule

Below you can download the schedule and the abstracts of all talks of this special session.

Speakers

  • GianMario Besana (De Paul University, USA)

          Critical loci for projective reconstruction from multiple views: a class of determinantal varieties arising  in Computer Vision

  • Cristiano Bocci (University of Siena, Italy)

          Advances in model identifiability: Bernoulli, tensors and beyond

  • Marta Casanellas Rius (Polytechnic University of Catalonia, Spain)

          Applying algebraic geometry to phylogenetics

  • Laureano González Vega (University of Cantabria, Spain)

          Polynomial Algebra by Values: Geometric Problems involving Curves and Surfaces

  • Chris Peterson* (Colorado State University, USA), Bruce Draper, Michael Kirby, Tim Marrinan

           Flags, Grassmannians, and Schubert Varieties in Computer Vision and Signal Detection

  • Tony Shaska (Oakland University, USA)

          Families of genus two curves with many elliptic subcovers

  • Carlos Villarino Cabellos*, J. R. Sendra (University of Alcalá, Spain)

          Hypercircles and ultraquadrics: a tool for simplifying coefficients in rational parametrizations

  • Franz Winkler (Johanner Kepler University Linz, Austria)

          Algebro-Geometric Methods for Solving Differential Equations

Support

Partially supported by the Department of Mathematics of the University of Milan.

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