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.
- 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.
- 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.
- 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.
- 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.
- Thu 14 Feb: Dimitris Diochnos presented giftwrapping
to compute convex hulls.
- Thu 21 Feb: formal power series, following
Algebraic Curves by Robert Walker.
- Thu 28 Feb: fractional power series, following
Algebraic Curves by Robert Walker.
- Thu 6 Mar: extrapolation and fractional power series.
- Thu 13 Mar: Danko Adrovic presented the sequel of
the connection between Puiseux series and tropical geometry.
- Thu 20 Mar: no meeting, we went to the colloquium instead,
which is an event of the SIAM Student Chapter.
- Thu 27 Mar: Spring break.
- 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...
- 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.
- Thu 17 Apr: we elaborated Maurer's algorithm on
cyclic 4-roots.
- Thu 24 Apr: Kathy Piret presented a Python interface
to PHCpack.
- Thu 30 Apr: no meeting because of MICA'08.
Seminars organized in previous semesters: