Learning outcomes

The aim of this course is to somewhat offer "involvement opportunities" to the students in either academic research or towards the world outside academy. Personalities active in several areas of applied mathematical research will deliver lectures inside this course to propose some problems to the students so that maybe some of them will decide to try to do some research with us or on their own.
Our commitment with this course is to try the young students of the so called "lost generation" in discovering opportunities to get involved into something constructive. The course is mostly a windows-shop of invited personalities.

Program

This is a seminar course comprising:
+ classes by external personalities (seminars and short courses);
+ classes by the internal referent. In particular, a part on modelling and the use of gurobi;
+ seminars by the students on topics of interest as agreed upon.

CLASSES BY EXTERNALS:
+ Jérôme Bolte (Univ. Toulouse Capitole),
big data, 1 week, 8-10h, october, first semester.
Topics: first order algorithms for problems of big dimension (like imaging, web crowling, data extraction).
Convexity and complexity: splitting algorithms, Nesterov, Kurdyka-Lojasiewicz inequalities and their consequences.

+ Luigi Laura, 24-26 february, 2+2h,
Topics: big data, some computational models (streaming, map/reduce, ...)

+ Ariela Briani (Univ. Tours), controllo lineare, 1 week, 8-10h, secondo semestre, 18-25 aprile.
Topics: Hamilton-Jacobi in relazione a un problema di controllo
standard: per esempio HJ al primo ordine e orizzonte finito con costo
finale.

+ Stefano Benati, 3+3h, secondo semestre
Topics: one or two among the following:
1) Optimization methods to select variables for Clustering.
2) Using medians in portfolio optimization.
3) Power Indexes.

+ Stephane Vialette, 1 week, March-April,
Topics: problems and opportunities in computational biology.

INTERVENTI REFERENTE (secondo semestre) e lavoro autonomo degli interessati (anche da subito!):

0.0. gli studenti si scaricano e si installano guroby:
http://www.gurobi.com/

0.1. gli studenti esplorano e sperimentano le funzionalia' di gurobi
(dentro guroby ci sono degli ottimi tutorial);
1. l'uso di modelli di programmazino matematica;
2. modelli classici di programmazione lineare (PL) o di programmazione lineare intera (PLI);
3. metamodelli e metalinguaggi per l'espressione di modelli;
Un'implementatazione nell'ambiente supportato da guroby di un modello di PL o di PLI.
4. applicazione a problemi industriali o simil tali. (Marco Calliari, Luca Di Persio).
5. lo studente interessato su questa parte potra' sviluppare, come progetto, un modello di PL o PLI per una qualche problematica a scelta.

Examination Methods

The hope is that at least some of the students will get involved into some of the proposed problems or areas and begin to actively work on a project or idea.
Where this should happen (and appear), the exam becomes a secondary issue.

Where we do not get lucky, the students is asked to try on every proposal: he's due to attend the great part of both the external and the internal lectures, and he must also attend the seminars of the classmates. Finally, he's expected to study an argument of his choice and deliver such a seminar or conduct a mathematical modeling project under gurobi.