### 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.

**Look here for the detailed plan and recommended literature.**
**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.

**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).

The **registration** for the school is closed.

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

The school is supported by:

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