SF2716: Valda ämnen i matematik:
TORIC GEOMETRY

In recent years toric geometry has become increasingly visible in mathematics. Its importance comes from the bridge that the toric action provides between a discrete setting (polytopes) and an algebraic setting (complex algebraic varieties). The aim of this course is to give an introduction to toric geometry with a view towards applications.

FACTS about the course:

This course is for both undergraduates and PhD students. The PhD students will present a "research" topic in toric geometry at the end of the course, as part of the course requirement.

  • Teacher: Sandra Di Rocco, contact.
  • Secretary: Rose-Marie Jansson, rom 3527, tel: 7907201, contact.
  • Book: Notes from the upcoming book on "toric geometry" by Cox-Little-Schenck, to be handed out in class.
  • Prerequisite: Basic algebra ( like SF2703) and discrete mathematics (like SF1630).
  • Exam: take-home assignments + presentation.
  • Good reference to check out the subject: Toric Tutorial by David Cox.
  • Additional references: Introduction to toric varieties (by W. Fulton), Combinatorial convexity and Algebraic geometry (G. Ewald)
    		•  ANNOUNCEMENTS:
  • The course will be given during period 3 and 4. There will be one two-hour lecture every week on mondays in room 3733.
  • The oral presentations are scheduled on May 12.

    • NOTES from lectures:

    January 21 | January 29 | February 4 | February 11 |
    February 18 | March 3 | March 10 | March 17 |
    March 31 | April 7| April 14 | 21 April | 28 April

    Mini-Symposium on toric geometry
    May 12, rum 3721

    10:00-10:30
    		 D. Eklund The BKK-theorem
    10:45-11:15
    		 M. Björklund The Beginning of Algebraic Statistics
    11:30-12:00
    		 K. Vorwerk A glimpse of phylogenetic algebraic geometry
     
    LUNCH
    BREAK
    13:30-13:45
    		 T. Westerbäck Toric codes
    14:00-14:30
    		 M. Tavakol Equations for Chow and Hilbert quotients

     

     

     

     

    ASSIGNMENTS:

    Assignment I (due March 10)

    Assignment II (due May 10)

     

     

     

     
    PRESENTATIONS:

    Preliminarly scheduled on May 5,12.
    Suggestions for topics:

    -BKK bound:Notes(Cox), Article (Li)

    - Phylogenetics: Article (Sturmfels), Article(Erksosson)

    -Dinamical Systems: Article( JAR-LAUB)

    -Codes: Article(Hansen)