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Alessandro Gimigliano

Full Professor

Department of Mathematics

Academic discipline: MAT/03 Geometry

Curriculum vitae

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).

Past Courses  at  C.d.L Sc. Naturali, Informatica, Geologia, Chimica e Chimica Ind. (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

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