We have agreed to meet certain

    Fridays 10-12 @ the Villa.

Below is a tentative schedule for us to learn the necessary background to unterstand this article:

https://arxiv.org/abs/1711.09512

And we will have breakfast.

We have agreed to give out "homework" after each talk and to discuss these assignments in between talks.

 

Nov 12

 Ehrhart theory, generating functions, h* [BR], [HNP] Sofía

Nov 26

 Ehrhart theory, "irrational" decomposition, h* ≥ 0 [BR], [HNP] Sofía

Dec 10

 Ehrhart theory, reciprocity, degree, codegree [BR], [HNP] Sofía

Jan 07

 IDP and all that [AIM09], [MFO07], [MFO17] Christian

Jan 14

 recitation session [AIM09], [MFO07], [MFO17] Christian

Jan 21

 semigroup rings, toric ideals and their Gröbner bases [GBCP], [AIM09], [MFO07], [MFO17] Kyle

Jan 28

 recitation session   Christian

Feb 4

 linear systems of parameters, regular sequences, Cohen Macaulay rings, Hilbert functions [MS], [S] Dante

Feb 11

 recitation session   Christian

Feb 18

 linear systems of parameters, regular sequences, Cohen Macaulay rings, Hilbert functions [MS], [S] Dante

Feb 25

 Lefschetz elements, Kähler package   Christian??

Mar 3 & 4

Mini-Symposium on Lattice Polytopes

The talks will be given on Zoom:
 
Meeting ID: 672 2864 2911
Password: 359878
 
During the morning and afternoon breaks you are invited to join us on gather.town:
 
 
(No password needed.)
 https://sites.google.com/view/mini-symposium-lattice-poly-22  

Mar 18

 uniform position principle https://arxiv.org/abs/1711.09512 Kyle & Sofía

Mar 18

 spanning lattice polytopes, no-gaps-theorem, uniform position principle https://arxiv.org/abs/1711.09512 Sofía & Kyle

References

[AIM09] American Institute of Mathematics workshop Combinatorial challenges in toric varieties https://www.aimath.org/ARCC/workshops/toricvarieties.html

[BR] Matthias Beck, Sinai Robins: Computing the Continuous Discretely: Integer-Point Enumeration in Polyhedra; Springer 2015.

[GBCP] Bernd Sturmfels: Gröbner Bases and Convex Polytopes. A.M.S. University Lecture Series 8 (1996).

[HNP] Christian Haase, Benjamin Nill, Andreas Paffenholz: Lattice Polytopes (lecture notes) [pdf (2012)] [pdf(2019)]

[MFO07] Mini-Workshop: Projective normality of smooth toric varieties. Oberwolfach Reports 4(3): 2283-2320 (2007).

[MFO17] Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications. Oberwolfach Reports 14(3): 2659--2701 (2017).

[MS] Ezra Miller, Bernd Sturmfels: Combinatorial Commutative Algebra, Springer GTM 227 (2005).

[S] Richard Stanley: Combinatorics and Commutative Algebra. Birkhäuser (1996).