MCS 595 Graduate Seminar, Spring 2008

This semester, we meet weekly in 1227 SEO on Thursdays at 9AM. The topic of this seminar continues to be Tropical Geometry.
  1. Thu 17 Jan: After organizational issues, we resumed our discussions about tropical version of Bernstein 2nd theorem in the plane and how it relates to symbolic-numerical techniques to factor polynomials. We ended with an interesting class of 3 dimensional systems.
  2. Thu 24 Jan: discussed gift wrapping and reverse search ideas to enumerate all edges of a polytype, motivated by extending from planar to spatial case, via recursion.
  3. Thu 31 Jan: Mina Khan presented an overview of her Master's thesis on the application of Smale's alpha theory to certify solutions of polynomial systems.
  4. Thu 7 Feb: Danko Adrovic presented a connection between Puiseux series and tropical geometry, following Bernd Sturmfels lectures at TU Berlin, 12-16 September 2007.
  5. Thu 14 Feb: Dimitris Diochnos presented giftwrapping to compute convex hulls.
  6. Thu 21 Feb: formal power series, following Algebraic Curves by Robert Walker.
  7. Thu 28 Feb: fractional power series, following Algebraic Curves by Robert Walker.
  8. Thu 6 Mar: extrapolation and fractional power series.
  9. Thu 13 Mar: Danko Adrovic presented the sequel of the connection between Puiseux series and tropical geometry.
  10. Thu 20 Mar: no meeting, we went to the colloquium instead, which is an event of the SIAM Student Chapter.
  11. Thu 27 Mar: Spring break.
  12. Thu 3 Apr: following the paper of Joseph Maurer on "Puiseux expansion for space curves" (Manuscripta Math. 32, 91-100, 1980) we outline a generalization of the method described in the book of Robert Walker. Joseph Maurer starts by defining tropisms of ideals...
  13. Thu 10 Apr: we continued our exploration of the algorithm described by Maurer and computed the tropisms for a space curve defined by two trinomials in three variables.
  14. Thu 17 Apr: we elaborated Maurer's algorithm on cyclic 4-roots.
  15. Thu 24 Apr: Kathy Piret presented a Python interface to PHCpack.
  16. Thu 30 Apr: no meeting because of MICA'08.

Seminars organized in previous semesters: