Algebraic Geometry School 2017

40th Autumn School in Algebraic Geometry

Binomial Ideals

Lukecin, Poland, September 3 - September 9, 2017

Teachers: Takayuki Hibi (Osaka) and Thomas Kahle (Magdeburg)

Program of the school: Two lectures each morning, 90 min each, followed by two 60 min excercise sessions in the afternoon.

Takayuki Hibi, Binomial ideals arising from combinatorics
Current trends on binomial ideals arising from convex polytopes, finite partially ordered sets, root systems together with finite graphs will be surveyed. A tentative schedule of talks is as follows:

Monday: A quick introduction to Gröbner bases
Tuesday: Toric rings and toric ideals
Wednesday: Join-meet ideals of finite lattices
Thursday: Normal polytopes and regular unimodular triangulations
Friday: Order polytopes of finite partially ordered sets

No special knowledge will be required to understand the talks. However, it is desirable for the participant to be familiar with fundamental materials on ideals of the polynomial ring as well as on partially ordered sets.
Look here for a detailed plan and reading suggestions.
Filip Rupniewski prepared notes from the lectures.

Thomas Kahle, Composing and decomposing binomial ideals
In these lectures and projects we study binomial ideals with a particular focus on intersection (de)compositions. Topics for the lectures include

basics of binomial ideals and their applicability in the sciences
efficient tests of binomiality of an ideal
primary, mesoprimary, and irreducible decomposition of binomial ideals
composition of binomial ideals: intersections of ideals that result in a binomial ideal

Along with the lectures we will have exercises and projects in which we will explore, for example, algorithmic aspects of the topics of the lectures using Macaulay2 and Singular.
Look here for tasks to do before the school.

Organizers: Maria Donten-Bury (University of Warsaw) and Mateusz Michałek (Polish Academy of Sciences and Max Planck Institute for Mathematics in the Sciences).

Venue: The school will take place in a Warsaw University pension in Lukecin, on Western part of Polish Baltic sea shore, see the map. The accommodation (full board, shared double room) will cost about 130 zloty (PLN) a day (1 Euro is approx. 4.3 PLN, but the exchange rate is not fixed).

Registration: Please register by filling in the form before May 1st, 2017.

Financial support: Graduate students and young researchers with inadequate support from their home institutions are encouraged to apply for accommodation cost waiver.
Please apply in the registration form and provide the year of graduation (or expected year of graduation) and the name of your scientific advisor (we may ask you to provide an additional letter of recommendation). The organizers will not pay for participants' travel.

All inquiries should be directed to Maria Donten-Bury, marysia [at] mimuw [dot] edu [dot] pl.

The school is supported by:

September Schools Homepage