March : Combinatorial Commutative Algebra


Organizers

Carlo Sircana und Isabel Stenger (Kaiserslautern)

Title

Combinatorial Commutative Algebra

Abstract

 

Literature

  • Lectures on Polytopes, Günter M. Ziegler, Springer
  • Combinatorial Commutative Algebra, Ezra Miller and Bernd Sturmfels, Springer

Date

Monday, March 12th, to Wednesday, March 14th

Location

Jugendherberge Bingen

Participants

Name
Ali Aslam
Rina Dong
Raul-Paul Epure
Daniel Gromada
Philipp Korell
Felix Leid
Lukas Ristau
Emil Rotilio
Simon Schmidt
Ricardo Schnur
Carlo Sircana
Christian Steinhart
Isabel Stenger
Jayantha Suranimalee
Andrea Thevis

Schedule

Monday, 12th March 
10:30-11:00Registration
11:00-12:00
Gröbner bases: monomial orderings, properties and algorithm (Suri)
12:00-13:30
Lunch break
13:30-15:00
Introduction to homological algebra and graded algebras: Hilbert function,
Betti numbers, Cohen-Macaulay rings and Tor functor (Andrea
and Daniel)
15:15-15:45
Coffee break
15:45-16:30
Polytopes: Definition and main properties (Raul)
16:45-17:30
Squarefree Monomial Ideals (Lukas)
17:45-18:30
Exercises
18:30
Dinner
Tuesday, 13th March 
9:30-11:303-Dimensional Staircases (Carlo and Ali)
11:30-12:00
Exercises
12:00-13:30
Lunch break
13:30-14:15
Borel-Fixed ideals (Christian)
14:30-15:15
Cellular resolutions I (Rina and Philipp)
15:45-16:30
Cellular resolutions II (Rina and Philipp)
16:45-18:30
Exercises
18:30
Dinner
Wednesday, 14th March 
9:30-10:30Semigroup rings (Ricardo)
10:30-11:30
Multigraded polynomial rings (Emil)
11:30-12:00
Exercises
12:00-13:15
Lunch break
13:15-15:00
Toric varieties (Felix and Simon)
15:15-16:00
Plücker coordinates (Isabel)

Some Impressions