Curriculum of studies
Degree in Mathematics (1979); Università di Firenze , with a
thesis "Singolarità isolate di varietà complesse" (director: prof.
F.Gherardelli, : 110/110 e lode).
Ph.D. in Matematica (Febbraio 1987) at the Queen's University of
Kingston (Canada), PhD thesis: "On linear systems of plane curves",
supervisor: Prof. A.V.Geramita .
Positions.
From 7/7/79 to 14/11/82 several fellowships at the 'Istituto
Mat. "U.Dini",
From 15/11/82 to 15/6/83 positions teaching in in High
schools
From 1/11/83 to 31/8/84 fellowship of Istituto Naz. di Alta
Matematica "F.Severi".
From 1/9/84 to 16/2/87 PhD student (several fellowships) at the
Dept. of Math. della Queen's University, Kingston, Canada,.
From 16/2/87 to 25/10/88 researcher at the Dip. di Matematica
(Facoltà di Ingegneria) of II Università degli Studi di Roma.
From 26/10/88 to 28/10/89 associate professor at Università
della Basilicata (Potenza).
From 29/10/89 to 31/10/92 associate professor atl Dip. di
Matematica della Facoltà di Scienze MM.FF.NN. della Università di
Genova.
From 30/11/92 to 31/10/2000 associate professor at Dip. di
Matematica, Facoltà di Scienze MM.FF.NN. della Università di
Bologna.
From 1/11/2000 till today full professor at Dip. di Matematica
della Università di Bologna .
Teaching Activities:
Present Courses:
- Geometria e Algebra (6 CFU, Scuola di Ingegneria e Architettura, C.d.L. Ing. Gestionale) Modulo del corso integrato di Analisi Matematica e Geometria e Algebra.
- Geometria e Matematica di Base (8 CFU, Scuola di Psicologia e Scienze della Formazione, LMCU Sc. della Formazione Primaria)
- Geometria Proiettiva (6 CFU Scuola di Scienze, C.d.L. Matematica).
- Storia della Matematica , un modulo (9CFU, Laurea Magistrale in Matematica)
Past Courses at C.d.L Sc. Naturali, Informatica, Geologia, Chimica e Chimica Ind. (in Bologna and in other Universities), SISS, Master in Didattica della Matematica.
Advisor for theses in Mathematics and in Sc. della Formazione.
I am the coordinator for the project Matematic@ (Math on line: help on line for math learning): http://progettomatematica.dm.unibo.it
I am member of the European Project (Comenius) FAMT&L (Formative Assessment for Mathematics teaching and Learning).
Research interests:
All the following subjects are in the field of Algebraic Geometry,
Commutative Algebra and their Applications.
1) THe study of higher secant verieties of projective varieties is
a classical subject in Algebraic Geometry. In the last decade it
received a reniewed and strong interest by many authors in virtue
of its links with many other sectors in Applied Math (Algebraic
Statistics, Complexity Theory, Code Theory). The main problem
appointed here is to determine the dimensions of secant variety for
projective varieties, classifying the ones which have a different
dimension from the expected one; it would be quite relevant (also
for applications) to be able to give equations for secant
varieties.
I worked mainly on "classical varieties ((Segre, verones,
Grassmannian, Segre-Veronese); for many of them I classified
defective ones and found dimensions and/or equations.
2) How to efficently decompose given tensors into sums of
decomposible ones is the core of the generalization of the common
notion of "rank of matrices" to "tensor rank". I worked on
several classes of tensors (generic ones; symmetric, skew-symmetic
and partially symmetric ones). In several cases it has been
possible to find the "tensor rank" strata in the space
parameterizing them.
3) It is now almost 30 years since the ideals of several
0-dimensional schemes (in particolar the "Fat points") have been a
subject of intense study in Algebric Geometry and in
Commutative Algebra. Many interesting congectures are still open
even in "simple" cases.
In particolar I have been studying their postulation (i.e.
the Hilbert function) and their minimal resolution. Such studies,
in the case of the plane, lead to the interest toward the problems
about how the restriction of the conormal bundle of P2 decomposes
when restricted to athe desingularization of a rational curve; a
problem which is interesting "per se", but revesaled to have many
connections with the other one.
Publications: see the web site:
http://www.dm.unibo.it/~gimiglia/pubbl.htm
