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
Hokkaido Summer Institute (HSI)
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
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.
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:
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
The school is partly funded by:
GNSAGA - Gruppo Nazionale per le Strutture Algebriche, Geometriche e
le loro Applicazioni
Please contact Anna Maria Bigatti if you are a member of GNSAGA and
you wish to apply.
If you have
any questions, please don't hesitate to write to us.
We look forward to seeing you in Sapporo this coming August.