Toric Varieties, Fall 2024.

Projects for the end-of-semester presentations


Suggestions (these are broad, we should discuss what one would actually do)

Arithmetic toric varieties                        Jordy Lopez and Somak Dutta    *9 AM Wednesday December 3
SAGBI (or Khovanskii) bases and toric varieties   Pooja Joshi and Zijin Xiao     Either day
Differential algebras on toric varieties          Michael Keeler and Yaoze Zou   *December 3
Stanley's g- Theorem                              Derek Wu and Abishek Hariharan Dec 3 ?
Multigraded Hilbert Scheme                        CJ Bott and Phil Speegle       *Dec 4 after John and Manasi
Divisors on Toric Varieties                       John Ajayi and Manasi Gore     *December 4
Toric Varieties Package in Macaulay2              Paul Dessauer and Daniel Dale

If 4 talks, every 40 minutes
if 3 talks, every 45 minutes

, and Ruzho Sagarayaj  


Toric varieties in algebraic statistics
A-Discriminant
Secondary fan of a point configuration and its toric variety
Vertically parametrized polynomial systems
fewnomial bounds via Gale duality
Complexity one T-varieties (rational)
Irrational toric varieties
[Ask your advisor for a suggestion]


Topics from past semesters:

 "The A-Discriminant Amoeba Structure"
 "Gale diagrams for codimension 2 lattice ideals"
 "Geometry of complete intersection toric varieties"
 "A Toric Degeneration of the Grassmannian"
 "Vector bundles over toric varieties"
 "Real structures on toric varieties"
 "Toric Varieties Associated to Graphs"
 "Three-Dimensional Staircases"
 "Buchberger's algorithm for Groebner bases"  (Not appropriate)