? Ivan Martino - ET'nA 2017

Summer School, Workshop and Mentoring day
ET'nA 2017
Encounter in Topology 'n Algebra
Scuola Superiore di Catania
Catania, Italy, May 31 - June 4, 2017


Organizers: Ivan Martino and Alex Suciu.
Local organizer: Michela Di Marca.
SSC-Staff: Maria Sanfilippo and Francesca Scollo.


The scientific event consists of a one-day Summer School, followed by a Research Workshop. The proposed workshop will bring together several experts in Algebraic Combinatorics, Algebraic Topology and Commutative Algebra in a center famous for the P.R.A.G.M.A.T.I.C., an Algebra and Geometry summer school that have been the incubator for many new young researchers in these fields.

If you are interested in participating, please, send an email to Ivan Martino or Alex Suciu.

The organization is supported by:
Scuola Superiore di Catania
Associazione Alumni


Speakers of the Workshop and the Summer school:
Bruno Benedetti (University of Miami),
Christin Bibby (University of Western Ontario),
Suyoung Choi (Ajou University),
Dan Cohen (Louisiana State University),
Alexandru Constantinescu (Freie Universität Berlin),
Graham Denham (University of Western Ontario),
Afshin Goodarzi (FU Berlin),
Luca Moci (Université Paris 7 - Diderot),
Claudio Procesi (Università di Roma La Sapienza),
Alfio Ragusa (Università di Catania),
Alex Suciu (Northeastern University),
Yury Ustinovskiy (Princeton University),
Matteo Varbaro (Università di Genova),
Masahiko Yoshinaga (Hokkaido University).

List of confirmed participants:

Yassine Amri (Aïn Chock Casablanca),
Bruno Benedetti (University of Miami),
Christin Bibby (University of Western Ontario),
Suyoung Choi (Ajou University),
Dan Cohen (Louisiana State University),
Alexandru Constantinescu (Freie Universität Berlin),
Michela Di Marca (Università di Genova),
Rita Fioresi (Università di Bologna),
Graham Denham (University of Western Ontario),
Afshin Goodarzi (FU Berlin),
Brian Hepler (Northeastern University),
Michael Kaminski (Purdue University),
Lukas Kühne (University of Bonn),
Ye Liu (Hokkaido University),
Yongqiang Liu (KU Leuven),
Rober Low (KU Leuven),

Viswambhara Makam (University of Michigan),
Dmitry Malinin (The University of the West Indies),
Luca Moci (Université Paris 7 - Diderot),
Jiyeon Moon (Ajou University),
Claudio Procesi (Università di Roma La Sapienza),
Alfio Ragusa (Università di Catania),
Mohammad Reza Rahmati (CIMAT),
Marcel Rubio (KU Leuven),
Alex Suciu (Northeastern University),
Yury Ustinovskiy (Princeton University),
Matteo Varbaro (Università di Genova),
Yohannes Tadesse (Högskolan i Skövde – Högskolevägen),
Tan Nhat Tran (Hokkaido University),
Robin van der Veer (KU Leuven),
Masahiko Yoshinaga (Hokkaido University).


Topics of the Summer School:
Resonance varieties
Polytopes, Dual Graphs, and Line Arrangements
Graham Denham, Alex Suciu

Bruno Benedetti, Matteo Varbaro

In its simplest form, the Bernstein-Gelfand-Gelfand (BGG) correspondence associates a chain complex of free graded modules over a polynomial algebra to a module over an exterior algebra in way that generalizes the classical Koszul complex. The resonance varieties measure deviations from exactness of this chain complex in a concrete, geometric fashion.

In these introductory lectures, we will explain the algebraic notions underlying these constructions, and present some structural results. We will illustrate the general theory with a number of examples, such as the computation of resonance varieties of the Stanley-Reisner ring associated to a simplicial complex, or of the Orlik-Solomon algebra associated to a hyperplane arrangement. We will indicate how computer algebra can help investigate resonance varieties explicitly, using Macaulay2, and we will conclude with a brief overview of some topics of current research.

Polytopes (like cubes, pyramids, prisms)... have always been studied since the beginning of mankind. They exist in nature and are replicated by architects.
In the past century, with the advent of computers, they've regained central interests also in connection with optimization problems and digital data.

We will focus on the notion of the "graph" of the polytope, namely, the structure formed by its vertices and edges. This apparently easy subject hides important open questions, like the polynomial Hirsch conjecture.
It also hides a fascinating connection with the intersection graphs of arrangements of lines. This opens bridges to old and new techniques in commutative algebra and algebraic geometry.

Some reading about it:



How to get to Catania:
A lot of companies fly directly to the Catania airport. The airport and the city center are well connected with public transportations.
Another option is the Palermo airport. There are buses leaving approximately every hour from the Palermo railway station to the Catania station.
Finally, Ryan Air flies to Trapani and to Comiso, but it takes quite a while to commute from there to Catania (Trapani-Palermo via bus is 90 minutes, then one has to change to the Palermo-Catania bus.).
Palermo and Catania are also accessible via ferry from any big city in the mediterranean area and using public train transportations from Rome or Naples.

Suggested accomodations: We suggest the following accomodation. Please, specify that you participate to this conference (and mention Maria Sanfilippo) when you make your reservation:

How to get to Scuola Superiore di Catania:
The exact address is the following:
Scuola Superiore di Catania,
Via Valdisavoia, 9,
95123 Catania CT,
Italy

Here it is a map: