MCS 595 Graduate Seminar, Fall 2005

This semester, we plan to meet again weekly in 712 SEO on Thursdays at 11AM. The theme of this year will be loosely centered on "polyhedral methods in algebraic geometry", attempting to understand how to exploit sparsity in polynomial system solving.
  1. Thu 25 Aug: organizational meeting. We showed that a "sparse" witness set of a space curve defined by a binomial system is again a binomial system.
  2. Thu 1 Sep: we defined a sparse witness set for a binomial hypsurface, extending the result of last week.
  3. Thu 8 Sep: Anton Leykin on parallel monodromy factorization.
  4. Thu 15 Sep: we discussed an example of a 2D surface in 4-space defined by a binomial system for which a sparse witness set is more challenging and outlined the general research plan looking at the cyclic 4-roots problem.
  5. Thu 22 Sep: a polyhedral compactification leads to conditions for a positive dimensional solution set to exist.
  6. Thu 29 Sep, no meeting at 11AM, but we all attend the AG/NT seminar of Bernd Ulrich at 3PM.
  7. Thu 6 Oct: Frank Sottile (Texas A&M) on "Bounds for real solutions to structured polynomial systems", also scheduled as AG/NT seminar.
  8. Thu 13 Oct, we did not meet in compensation for our attendance to MAGIC'05 in Notre Dame.
  9. Thu 20 Oct: "Toward accurate polynomial evaluation in rounded arithmetic", following a recent preprint of Demmel, Dimitriu, and Holtz.
  10. Thu 27 Oct: Olga Kashcheyeva on "Toroidal structure of the map between generating sequences in dimension 2 function fields".
  11. Thu 3 Nov: Mathias Drton (University of Chicago), scheduled as a Mathematics and Its Applications seminar, on "Algebraic Factor Analysis: Tetrads, Pentads and Beyond"
  12. Thu 10 Nov: Yan Zhuang on "polyhedral methods to compute sparse witness sets using face systems"
  13. Thu 17 Nov: Kathy Piret on "solving polynomial systems with parameters"
  14. Thu 24 Nov, no meeting because of Thanksgiving.
  15. Thu 1 Dec: Amir Niknejad

Seminars organized in previous semesters: