This two-semester seminar will focus on the physics and mathematics underlying gauged linear sigma models, with the goal of understanding the monomial-divisor mirror map for Calabi-Yau hypersurfaces. Broadly speaking, we will cover:

  • Toric Geometry
    • Crash-course on toric varieties
    • Sheaves & Sheaf cohomology on toric varieties
    • Toric Residues (alg-geom/9410017) and mirror symmetry (math/0203216)
  • GLSMs

Students from both the mathematics and physics departments are encouraged to participate. The student-given talks will aim to develop a healthy mix of the abstract (sheaf cohomology & residues) and the concrete (computing correlators in twisted theories) in a way that is accessible to beginning graduate students and useful for older students as well.

Meeting Information

Meeting Time Fridays at 10am
Meeting Location DRL 2C8

Content

This semester we will concentrate on developing a thorough knowledge of toric varieties, with the goal (coming to fruition next semester) of understanding the toric residue mirror conjecture in math/0203216. We will use Cox, Little, Schenck's book on toric varieties as an introductory reference. The initial plan is to spend the first week introducing projective varieties and thereafter one or two lectures on each of chapters 4,5,7,8, and 9 in CLS.

Participants

  • Matt Ballard
  • Patrick Clarke
  • Ron Donagi
  • Josh Guffin
  • Jim Halverson
  • Victor Lu
  • Pooya Ronagh
  • Charlie Siegel
  • Jeffrey Teo

Date Speaker Topic
25 September, 2009 Victor Lu Projective Toric Varieties I
2 October, 2009 Victor Lu Projective Toric Varieties II
9 October, 2009 Josh Guffin Abstract Varieties
16 October, 2009 Josh Guffin Abstract Varieties
23 October, 2009 Pooya Ronagh Toric Divisors, Part I
30 October, 2009 Josh Guffin Toric Divisors, Part II
12 November, 2009 Josh Guffin Toric Divisors, III
18 November, 2009 Jim Halverson Homogeneous Coordinates I