13-17th August 2018
Hyperplane arrangements and computations with CoCoA
Sapporo, Japan

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We are happy to announce the summer course Hyperplane arrangements and computations with CoCoA which will take place on 13-17th August 2018 at Sapporo, Japan within the Hokkaido Summer Institute (HSI) program.

John Abbott (Università degli Studi di Genova)
Anna Maria Bigatti (Università degli Studi di Genova)
Elisa Palezzato (Hokkaido University)
Michele Torielli (Hokkaido University)
Masahiko Yoshinaga (Hokkaido University)

The course will introduce the basic theory of hyperplane arrangements and it will teach how to compute some of their invariants using the computer algebra system CoCoA. The goal of this course is to teach students both the theoretical aspects of hyperplane arrangements and how to perform related computations on a computer. This will be realized via traditional lecture and computer sessions using CoCoA.

The course is designed for Master and PhD students in Mathematics, and gives 2 credits (some exercises will be assigned during the course).

The course is organized in two threads.
In the first thread, we will describe the basic theory of hyperplane arrangements introducing various invariants that are associated to an arrangement. In particular, we will describe three types of invariants: combinatorial, topological and algebraic. The class of combinatorial invariants includes intersection lattices, matroids, characteristic (quasi)-polynomial and (arithmetic) Tutte polynomial. The class of topological invariants includes Orlik-Solomon algebras and Milnor fibers (together with their monodromy). The class of algebraic invariants is related to the notion of freeness and the famous Terao's conjecture.
In the second thread, we will introduce the basic theory of computational commutative algebra and we will teach how to use CoCoA to do computations with particular attention to the ones related with hyperplane arrangements. In particular, we will describe the theory of Gröbner bases, Hilbert functions and sectional matrices, and how to compute several arrangements' invariants on CoCoA.

Official page on the Hokkaido Summer Institute web site

(Details, pdf)

Registration and Tuition fees

The registration for students outside Hokkaido closes at the end of February (Please note that it's on the 28th in Japanese time, so consider it to be the 27th if you are in Europe or America!!!)
The tuition fee is 29 600 JPY: http://hokkaidosummerinstitute.oia.hokudai.ac.jp/fees_payments/.

This fee will be waived for students who enroll in the program as exchange students from partner institutions with which HU has concluded a memorandum of understanding on mutual tuition waivers: Hokkaido University (HU)'s partner institutions (pdf)

This registration process is only for Master and PhD students, but we also welcome any other type of participants. Please contact Michele Torielli if you wish to attend.


Accomodation for registered students is available on campus at very cheap rates.


The school is partly funded by:

If you have any questions, please don't hesitate to write to us.
We look forward to seeing you in Sapporo this coming August.

John Abbott
Anna Bigatti
Elisa Palezzato
Michele Torielli
Masahiko Yoshinaga