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\title{Curriculum vitae}
\author{Luca Giuzzi}
\date{\selectlanguage{british}\today}
\begin{document}
\maketitle
\section{Personal details}
\hskip.4cm
\begin{minipage}{8cm}
\begin{tabular}{ll}
Surname: & Giuzzi \\
Name: & Luca \\
Title: & Dr. (DPhil, Sussex) \\
Role: & Associate Professor of Geometry \\
Date of Birth: & 30 September 1973 \\
Citizenship: & Italian \\
Known languages: & Italian (mother-tongue), \\
& English (fluent). \\
% & French (basic) \\
%Telephone (home): & +39 347 2521817 \\
Telephone (BS): & +39 030 3715739 \\
Fax: & +39 030 3715745 \\
E-mail: & \href{mailto:luca.giuzzi@unibs.it}{luca.giuzzi@unibs.it} \\
Web page: & \url{http://luca-giuzzi.unibs.it} \\
ORCID: & 0000-0003-3975-7281 \\
ResearcherID: & F-4066-2010 \\
Address (work): &
DICATAM \\
& Section of Mathematics \\
& Facolt\`a di Ingegneria \\
& Universit\`a degli studi di Brescia \\
& via Branze 43 \\
& 25123 Brescia \\
& ITALY \\
Address (home): &
via Cesare Battisti 42 \\
& 25018 Montichiari (BS) \\
& ITALY \\
\end{tabular}
\end{minipage}
\setsechook{\begin{center}\sepP\end{center}}
\section{Studies}
\begin{enumerate}
\item {\em Laurea in matematica} (degree in mathematics) with a score
of 110 {\em cum laude}/110,
Universit\`a Cattolica del Sacro Cuore; thesis
``Gruppi di Frobenius e strutture geometriche associate'' under
the supervision of Prof. Silvia Pianta, 1996.
\item DPhil in Mathematics, University of Sussex; thesis
``Hermitian varieties over finite field'' under the supervision of
Prof. James Hirschfeld, 2001.
\end{enumerate}
\section{Employment history}
\begin{enumerate}
\item 1992-1996: Undergraduate student at Universit\`a Cattolica del Sacro
Cuore.
\item 1996-1997: Unix system administrator at Universit\`a Cattolica.
\item 1997-2000: DPhil student at University of Sussex.
\item 2000-2004: research fellow at Universit\`a degli studi di Brescia.
\item 2002-2003: work on ``Development of a cryptosystem based on
elliptic or hyperelliptic curves'' (POP 342) in collaboration with
Universit\`a della Basilicata.
\item 2004-April 2008: research associate in Geometry
at Politecnico di Bari.
\item May 2008-2018: research associate in Geometry at Universit\`a degli
Studi di Brescia.
\item June 2018-now: associate professor of Geometry at Universit\`a degli
Studi di Brescia.
\end{enumerate}
\section{Habilitations}
Luca Giuzzi has been qualified (habilitated) by the italian MUR to the role of
\begin{enumerate}
\item \emph{associate professor in Geometry} on March 28, 2017;
\item \emph{full professor in Geometry} on July 8, 2024.
\end{enumerate}
\section{Refereeing activity}
Luca Giuzzi has been acting as \emph{referee} for several international
journals, including \emph{Annals of Combinatorics},
\emph{Designs Codes and Cryptography}, \emph{Discrete
Mathematics}, \emph{Finite Fields and their Applications}, \emph{Journal of
Number Theory}, \emph{International Journal of Computer Mathematics},
\emph{International Journal of Algebra and Computation}
He is also a reviewer for \emph{MathSciNet} and
\emph{Zentralblatt MATH}.
\section{Expert reviews}
Luca Giuzzi has acted as an expert reviewer in the following capacities:
\begin{enumerate}
\item 2023: Expert reviewer for the European Research Executive Agency (REA-EU), HORIZON-MSCA-2023-PF-01 AS2.
\item 2023: Expert reviewer for Junior Positions and Associate tenure track positions on behalf of the Le Fonds de la Recherche Scientifique (FNRS), Belgium.
per il FNRS (Belgio);
\item 2023: Reviewer for proposals submitted to the project \emph{Galileo2024 -- Universit\`a Italo-Francese};
\item 2020: Part of the evaluation board for the admittance to the title of PhD, Universit\`a di Modena e Reggio Emilia (IT);
\item 2020: Reviewer of some papers for the VQR 2015-2019 campaign (Italy);
\item 2019: Part of the evaluation board for the award of a tenure track position (Ricercatore RtdB) at Universit\`a degli Studi di Brescia (IT);
\item 2018: External referee of a doctoral thesis presented at the University of Melbourne (Australia).
\end{enumerate}
\section{Awards and grants}
\begin{enumerate}
\item May 1997: grant for `advanced studies abroad' by Universit\`a Cattolica
\item July 1997: research grant for `doctoral studies' by Istituto Nazionale
di Alta Matematica; this grant has been renewed for the
years 1998-1999 and 1999-2000.
\item September 1997-2000: British EPSRC award
(covering tuition fees at Sussex University).
\item June 2000: research grant for `Progetto e realizzazione di un criptosistema
per comunicazioni'' (Project and implementation of a cryptosystem for
communication systems), POP-FESR 1994/99, Universit\`a della Basilicata.
\item September 2000-December 2004: research fellowship at Universit\`a
degli studi di Brescia.
\item 2001: Exhonerated from compulsory military service as
``Citizen involved with special merits in activities of national or
international relevance in science, art or culture'', Art. 7(d) DLG 504/97.
\item 2015, ``Incentivo una tantum anno 2011'' (competitive
award from the from the University of Brescia for activities in the years
2008-2011).
\item 2017, ``Incentivo una tantum anno 2013'' (for activities in the years
2011-2013)
\item 2017, FABR (Individual Grant for Basic Research), ANVUR prot. 20/2017, 15 June 2017.
\end{enumerate}
\section{Conference organization}
\begin{enumerate}
\item 2007: Member of the organizing committee of the ``XVIII Congresso
UMI'', Bari.
\item 2008: Organizer of the international conference
``Combinatorics 2008'', Brescia.
\item 2017: Organizer of the international conference
``Fq13'', Gaeta.
\item 2017: Organizer of the international conference
``HyGraDe'', S. Alessio Siculo (Messina).
\item 2018: Organizer of the international conference
``Combinatorics 2018'', Arco (TN).
\item 2020: Organizer of the international conference
``Combinatorics 2020'', Mantova (MN).
\end{enumerate}
\section{Involvment with National Research Projects (PRIN)}
\begin{enumerate}
\item 2001: ``Strutture geometriche, combinatorica e loro applicazioni'',
as member;
\item 2003: ``Strutture geometriche, combinatoria e loro applicazioni'',
as member;
\item 2005: ``Grafi e Geometrie'' (2005018845\_002), as member;
\item 2008: ``Strutture di incidenza e combinatorie'' (2008BHF4AW\_003),
as member;
\item 2012: ``Strutture geometriche, combinatoria e loro applicazioni,''
(2012XZE22K\_009) as Scientific Coordinator of the local research unit.
%
%\item 2010 (pending): ``Strutture geometriche, combinatoria e loro
% applicazioni'' (2010HR2XTA\_008) as associated investigator
\end{enumerate}
\section{European Projects}
\begin{enumerate}
\item Participant to COST action IC1104: ``Random Network Coding and Designs over $\mathrm{GF}(q)$''
\end{enumerate}
\section{Institutional teaching}
Prof. Giuzzi has been a \emph{professore aggregato} since September 2006.
Since 2018 he is Associate Professor in Geometry.
\begin{enumerate}
\item 1998-1999: teaching assistant for Discrete Mathematics at
University of Sussex.
\item 1999-2000: teaching assistant for Discrete Mathematics and
Group Theory at University of Sussex.
\item 2000-2001: mini-course (10 hours) on cryptography at
Universit\`a Cattolica del Sacro Cuore.
\item 2001-2002: mini-course on ``Cryptography: from
DES to AES'', Universit\`a di Brescia.
\item 2003-2004: course (10 hours) on "Discrete Mathematics", Universit\`a
di Brescia.
\item 2004-2005: main lecturer for "Geometria Superiore 2",
Universit\`a Cattolica del Sacro Cuore.
\item 2004-2005: teaching assistant at Politecnico di Bari (3 courses).
\item September 2005: introductory course on geometry at Politecnico di
Bari (10 hours).
\item 2005-2006: teaching assistant at Politecnico di Bari (3 courses).
\item 2006-2007: main lecturer for
"Geometria e Algebra", Mechanical Engineering, A,
Politecnico di Bari.
\item 2007-2008: main lecturer for
"Geometria e Algebra", Mechanical Engineering, A,
Politecnico di Bari.
\item 2007: seminars (3 hours) on Coding Theory at Universit\`a degli
studi di Brescia, within the European Social Found project n. 411498
Ob. 3 Mis. C3 (2006), 414809, no. 671794 ``Corso di alta formazione
nell'ambito di dottorati afferenti al settore dell'Ingegneria
dell'informazione'' (Higher education course for doctoral studies
related to information engineering).
\item 2008: co-supervisor for first and second level degree theses in
Mathematics at Universit\`a Cattolica.
\item 2008-2010: main lecturer for
``Complementi di Geometria e Algebra'', Universit\`a degli Studi
di Brescia.
\item 2010-2011: main lecturer for ``Algebra per Codici e Crittografia''
(Algebra for codes and cryptography), Universit\`a degli Studi di
Brescia.
\item 2011-2012: main lecturer for
\begin{itemize}
\item ``Algebra per Codici e Crittografia'', Universit\`a degli Studi
di Brescia;
\item ``Geometria combinatorica'' (Combinatorial geometry),
Universit\`a Cattolica del S. Cuore (BS).
\end{itemize}
\item 2012-2018: main lecturer for
\begin{itemize}
\item ``Algebra per Codici e Crittografia'', Universit\`a degli Studi
di Brescia;
\item ``Algebra e Geometria'', Universit\`a degli studi di Brescia.
\end{itemize}
\item 2018-2020: professor of
\begin{itemize}
\item ``Algebra per Codici e Crittografia'' ($6$ CFU), Universit\`a degli Studi
di Brescia;
\item ``Algebra e Geometria'' ($9$ CFU), Universit\`a degli studi di Brescia.
\end{itemize}
\item 2020-now: professor of
\begin{itemize}
\item ``Algebra per Codici e Crittografia'' ($6$ CFU), Universit\`a degli Studi
di Brescia;
\item ``Algebra e Geometria'' ($9$ CFU), Universit\`a degli studi di Brescia.
\item ``Algebra lineare e geometria analitica''' ($6$ CFU), Universit\`a
degli studi di Brescia.
\end{itemize}
\end{enumerate}
\section{Advanced courses}
\begin{itemize}
\item 2020: advanced
Winter School \emph{Mathematics for Engineering Applications},
``Blockchains from bitcoin to robotics --- distributed data security
for industry 4.0'', Politecnico di Bari (IT).
\item 2021: Doctoral course ``From finite fields to post-quantum cryptography'' at
Universit\`a di Siena (IT).
\item 2023: Doctoral course ``Data protection: Security, Integrity and
Secrecy'', Politecnico di Bari (IT).
\item 2023: Advanced course ``Finite geometry: advanced topics''
at \emph{CIMPA-NCM School on Finite Geometry and Coding Theory}, Indian
Institute of Technology Hyderabad (IN).
\end{itemize}
\section{Accepted papers}
\begin{raggedright}
\input{papers}
\end{raggedright}
\section{Books}
\begin{enumerate}
\item L. Giuzzi, ``Hermitian varieties over finite fields'', DPhil thesis
under the supervision of Prof. J.W.P. Hirschfeld (University of
Sussex).
\item L. Giuzzi, ``Codici correttori'', UNITEXT Springer Verlag {\bfseries 27}
(2006), ISBN: 88--470--0539--6.
\end{enumerate}
\section{Proceedings/Extended Abstracts}
\input{proceedings}
\section{Other printed works}
\begin{enumerate}
\item L. Giuzzi, ``Gruppi di Frobenius e strutture geometriche associate''
(Frobenius groups and associated geometrical structures, in Italian):
{\em tesi di laurea} at Universit\`a Cattolica di Brescia,
under the supervision of Prof. S. Pianta.
\end{enumerate}
\section{Patents}
\begin{enumerate}
\item L. Giuzzi, G. Korchm\`aros, A. Sonnino,
``Perfezionamenti nella crittografia a chiave pubblica
basata su curve ellittiche'', patent no. 0001379714, August 2010.
\end{enumerate}
\section{Selected schools and workshops}
\begin{enumerate}
\item July 1995: ``Summer school on combinatorics and finite geometry'',
Potenza.
\item July 1996 ``Summer school Giuseppe Tallini on finite geometry'',
Brescia.
\item August 1996, ``Scuola di Matematica Interuniversitaria'', Perugia.
\item September 1997, ``Summer school on finite geometry'', Potenza.
\item April 1998, Intensive course ``Galois Geometry and Generalised
Polygons'', Ghent.
\item July 1998, ``Advanced school on Combinatorial Geometry'', Cortona.
\item August 1998, NATO Advanced Study Institute ``Difference sets,
sequences and their correlation properties'', Bad Winsheim.
\item September 1998, ``Summer school Giuseppe Tallini on finite geometry'',
Brescia.
\item November 1998, Workshop ``SUNCAGe'98'', Caserta.
\item May 1999, summer school ``Methods of discrete mathematics:
Association schemes, Lattices and Codes'', Braunschweig.
\item June 1999, Socrates Intensive programme ``Finite geometries and
their automorphisms'', Potenza.
\item September 1999, ``International meeting on coding theory and
cryptography'', Medina del Campo (ES).
\item October 2000, ``ECC 2000: 4th workshop on elliptic curve cryptography'',
Essen.
\item May 2001, ``CHES 2001: Workshop on cryptographic hardware and
embedded solutions'', Paris.
\item July 2002, ``Summer school Giuseppe Tallini'' on finite geometry,
Brescia.
\item September 2005, ``Summer school Giuseppe Tallini
on Combinatorial Geometries'', Potenza.
\item 10--16 September 2006,
``Second Irsee Conference on Finite Geometries'',
Irsee (DE).
\item 24--29 September 2007, ``XVIII Congresso UMI'', Bari (IT).
\item 22--28 June 2008, ``Combinatorics 2008'', Brescia (IT).
\item 13--17 June 2009, ``Fq9 -- Finite Fields and their Applications'',
Shannon Institute, Dublin (IE).
\item 30 May -- 4 June 2010, ``Fourth Pythagorean Conference'',
Corfu (GR).
\item 5--11 June 2010, NATO Advanced Study Institute, ``Information Security
and Related Combinatorics'', Opatija (HR).
\item 27 June -- 3 July 2010, ``Combinatorics 2010'', Verbania (IT).
\item 19--25 June 2011,
``Third Irsee Conference on Finite Geometries'',
Irsee (DE).
\item 10--16 July 2011,
``Fq10 -- Finite Fields and their Applications'', Ghent (BE).
\item 6--10 February 2012,
``Incidenge geometry and buildings'', Ghent (BE).
\item 13--14 February 2012,
``Giornate di Geometria'', Vicenza (IT).
\item 9--15 September 2012,
``Combinatorics 2012'', Perugia (IT).
\end{enumerate}
\section{Conference talks}
\begin{enumerate}
\item 6 November 1997, ``Spazi co--Minkowski e loro struttura di riflessione'',
GNSAGA national meeting, Perugia (IT).
\item 19 June 1998, ``Co-Minkowski spaces and their reflection structure'',
Combinatorics '98, Palermo (IT).
\item 31 May 2000, ``Intersection numbers for Hermitian varieties'',
Combinatorics 2000, Gaeta (IT).
\item 19 July 2000, ``Groups stabilising the intersection of two classical
unitals'', Fourth Isle of Thorns conference of finite geometries (invited
participation),
Isle of Thorns (UK).
\item 5 July 2001, ``A short characterisation of classical unitals'',
18th British Combinatorial Conference, Brighton.
\item 8 June 2002, ``Ovoids of the Hermitian surface'', Combinatorics
2002, Maratea (IT).
\item 3 October 2003, ``A family of ovoids of the Hermitian Surface in
$PG(3,q^2)$ with odd $q\geq 5$'', International Symposium on
Graphs, Designs and Applications 2003, Messina (IT).
\item 26 June 2006, ``LDPC Codes from Projective Spaces'', Combinatorics
2006, Ischia (IT).
\item 30 January 2010, invited speaker, ``Geometry and codes'', workshop in honour of Prof.
M. Marchi, on occasion of his 70th birthday.
\item 29 June 2010, ``On samplings of graphs'', Combinatorics 2010, Verbania
(IT).
\item 12 July 2011, ``Unitals in $PG(2,q^2)$ with a large $2$-point stabiliser'',
Fq10 --- 10th International Conference of Finite Fields and their Applications, Ghent (BE).
\item 10 September 2012, ``Caps and codes from Polar Grassmannians'',
Combinatorics 2012, Perugia (IT).
\item 19 September 2013, ``Linear codes from orthogonal Grassmannians'',
Conference on Random network codes and Designs, Ghent (BE).
\item 5 June 2014, ``On Line Polar Grassmann Codes'', Combinatorics 2014,
Gaeta (IT).
\item 19 June 2014, ``Linear Polar Grassmann Codes'',
Algebra, codes and Networks, Bordeaux (FR).
\item 18 September 2014, ``Intersection of Hermitian Surfaces and quadrics'',
Finite Geometries --- Fourth IRSEE conference (invited participation), Kloster Irsee (DE).
\item 16 March 2015, ``Polar Grassmann codes --- Part II'', ALCOMA15,
Kloster Banz (DE).
\item 19 June 2015, ``Polar Grassmannians and their Codes'', MEGA2015,
Trento (IT).
\item 3 June 2016, ``Implementing Polar Gra{\ss}mann Codes'', Combinatorics
2016, Maratea (IT).
\item June 2017, ``Hermitian Line Polar Gra{\ss}mann Codes'', Fq13, Gaeta (IT).
\item September 2017, ``Transparent embeddings of point-line geometries'',
Fifth Irsee Conference (invited participation), Kloster Irsee (DE).
\item September 2019, ``Generating and embedding polar Grassmannians'',
Buildings 2019, Magdeburg (DE).
\item August 2022, ``On subspaces of classical polar spaces'',
Finite Geometries 2022 --- Sixth Irsee Conference (invited participation), Irsee (DE).
\item September 2022, ``On symplectic polar spaces'', Polygons, buildings and related geometries, Ghent (BE).
\item January 2023, invited speaker, ``Grassmannians, their embeddings and applications'',
GL70 --- A conference in honor of Guglielmo Lunardon, Naples (IT).
\item February 2023, ``Linear codes and Grassmann graphs'', Conference on
Algebraic varieties over finite fields and Algebraic geometry codes (COGNAC) (invited
participation), Marseille (FR).
\item December 2023, invited speaker, ``On orthogonal polar spaces'',
International Conference on Algebraic Geometry, Coding Theory and
Combinatorics, Indian Institute of Technology Hyderabad (IN).
\end{enumerate}
\section{Seminars}
All the seminars in this section have been given upon invitation
by the hosting institutions.
\begin{enumerate}
\item June 1997, ``Kinematic spaces derived from Frobenius Groups'', School of
Mathematical Sciences, University of Sussex.
\item 23 and 24 September 1998, ``Cryptography and finite geometries
(I and II)'', Mathematics department at Universit\`a Cattolica del
Sacro Cuore, Brescia.
\item 16 October 1998, ``Public-key cryptosystems and elliptic curves'',
School of Mathematical Sciences, University of Sussex, Brighton.
\item 24 November 1999, ``Of entropy and keys'', School of Mathematical
Sciences, University of Sussex, Brighton.
\item 10 February 2000, public seminar in ``Trust, information and privacy:
theory of {\em secret writings} and their legal issues'',
Universit\`a Cattolica del Sacro Cuore, Brescia.
\item 23 May 2001, ``Intersection of Hermitian varieties'', Universit\`a di
Brescia.
\item 5 December 2001, ``Hermitian varieties over finite fields: why?'',
Universit\`a Cattolica del Sacro Cuore, Brescia.
\item 10 April 2002, ``Caps and ovoids in the Hermitian surface: a
comutational approach'', Universit\`a di Brescia.
\item 11 July 2002, ``An introduction to modern cryptography: from RSA to
AES'', Summer School ``Giuseppe Tallini'' 2002, Brescia.
\item 5 February 2003, ``Introduction to Coding theory'', Universit\`a
Cattolica del Sacro Cuore, Brescia.
\item 12 February 2003, ``From Codes to Designs'', Universit\`a
Cattolica del Sacro Cuore, Brescia.
\item 6 November 2003, ``Incidence configurations in the Hermitian surface'',
Giornate di Geometria, Universit\`a Cattolica del Sacro Cuore, Brescia.
\item 20 November 2003, ``Mathematics plus secrecy'', Museum of Sciences,
Brescia.
\item 4 May 2004, ``Finite geometry and Cryptography'', Politecnico di Bari.
\item 6 May 2004, ``Finite fields in C++'', Dipartimento di Matematica,
Universit\`a di Napoli.
\item 9 September 2005, ``A defense of cryptography'', Universit\`a
della Basilicata.
\item 29 May 2006 and 31 May 2006, ``An introduction to algebraic
decoding of cyclic codes'', Facolt\`a di Ingegneria, Universit\`a
di Brescia.
\item 25 October 2006, ``Security, privacy and secrecy: several
faces of cryptography'',
Dipartimento di matematica, Universit\`a di Bari.
\item 21 November 2006, ``Reed--Solomon codes'', Facolt\`a di
Ingegneria, Universit\`a di Brescia.
\item 23 Novembre 2006, ``Cryptography of (in)security'',
Facolt\`a di Ingegneria, Universit\`a di Brescia.
\item 4 and 6 December 2006, ``Uses of cryptography: from secrecy
to security'',
Facolt\`a di Economia di Bari.
\item 5 December 2008, ``Elliptic Curves: theory'', Universit\`a Cattolica,
Brescia
\item 13 February 2009, ``Elliptic Curves: practice'', Universit\`a
Cattolica, Brescia.
\item 8 April 2009, ``Non--binary BCH codes'', Dipartimento di
Matematica, Universit\`a Federico II, Napoli.
\item 30 January 2010, ``Geometry and codes'', Worshop in honor of M.Marchi,
Universit\`a Cattolica, Brescia.
\item 29 October 2010, ``Mathematics and secrets'', Universit\`a Cattolica,
Brescia.
\item From 15 till 21 May 2011 L.~Giuzzi has been a guest of the
Mathematics Department of the University of Gent (BE).
\item 15 March 2012, ``Non--linear codes'', Dipartimento di Matematica,
Universit\`a Federico II, Napoli.
\item 24 April 2012, ``Algebraic and geometric methods in cryptography'',
Dipartimento di Matematica, Politecnico di Milano.
\item 21 January 2014, ``Strutture geometriche, combinatorica ed applicazioni'',
DICATAM, Universit\`a di Brescia.
\item 28 May 2019, ``Polar Grassmannians'', Universit\`a di Siena.
\end{enumerate}
\section{Summary of research interests}
\begin{enumerate}
\item Incidence geometries.
\item Coding theory and Cryptography.
\item Finite geometries and varieties over finite fields.
%\item Graph designs.
\end{enumerate}
\section{Computer skills}
\begin{enumerate}
\item Very good knowledge of Linux (since 1994);
\item
Experience as system administrator of Solaris (from 2.5 up to 2.8)
and Digital Unix (4.0A - 4.0E) systems;
\item Good knowledge of C and C++; knowledge of Julia.
\item Good knowledge of HTML, XHTML and CSS;
\item Working knowledge of several Computer Algebra systems.
\end{enumerate}
\begin{comment}
\section{Summary of recent work}
\subsection{Ovoids of the Hermitian surface}
An ovoid $\cO$ of the polar space arising from the non--degenerate
Hermitian surface $\cH(3,q^2)$ consists of $q^3+1$ points in
$\cH(3,q^2)$ meeting each generator of the surface in exactly one
point. The so--called {\em classical ovoid} is provided by the
intersection of the Hermitian surface with a non--tangent plane.
However, computational evidence suggests that there are several
classes of possible ovoids. Recently, a new family of non--classical
ovoids has been found and characterised. Current research is aimed
towards the construction of derivations of known non--classical
ovoids which produce non--isomorphic ones.
\subsection{Hermitian varieties over finite fields}
In the DPhil thesis ``Hermitian varieties over finite fields'', some of
the properties of the configurations arising from the intersection of
Hermitian varieties in a finite projective space have been investigated.
\par
The following results have been obtained:
\begin{enumerate}
\item the full linear collineation group stabilising the intersection
of two Hermitian curves has been determined and it has been proven
that if two such intersections determine the same point-line
incidence structure, then they are projectively equivalent;
\item a new proof of the characterisation of the classical unital as
the unital in $\PG(2,q^2)$ stabilised by a cyclic collineation
group of order $q^2-q+1$ has been provided;
\item the point-line-plane configurations arising from the intersection
of two Hermitian surfaces have been described;
\item the list of possible cardinalities for the intersection of any
two Hermitian varieties in $\PG(n,q^2)$ has been determined.
\end{enumerate}
The current research deals with complete systems of subspaces on a
Hermitian Surface and the possibility of describing such systems as
algebraic sub--varieties.
\subsection{Cryptography and geometry}
\begin{enumerate}
\item
A well--known example of pseudo--random binary sequence is
provided by the orbit of a point of $\PG(n,2)$ under the action of a Singer
cycle; however, such a sequence is of no cryptographic value. The aim of
the research, given a design $D$, is to determine the properties of
sequences generated by a suitable cyclic group of automorphisms of $D$.
\item
It is possible to provide an algorithm which describes the group operation
in the Jacobian of some hyper-elliptic curves. A project is being carried
out in order to implement this algorithm in C and evaluate its performance
and security with respect to traditional elliptic curve cryptography and
design suitable `paddings' for data to be encoded.
\end{enumerate}
\subsection{Fibred algebraic structures and related geometries}
An algebraic structure $(A,\cdot,1)$ is {\em fibred}, if and only if
$A$ is the union of some subsets $A_1,\ldots, A_n$ such that:
\begin{enumerate}
\item if $i\neq j$, then $A_i\cap A_j=\{1\}$;
\item for any $i=1,\ldots n$, $(A_i,\cdot_{\mid A_i},1)$ is a
proper substructure of $(A,\cdot,1)$.
\end{enumerate}
Given a fibred structure $(A,\cdot,1)$, it is possible to build an incidence
configuration $(P,L,\in)$, whose set of points is the set $A$ and
whose set of lines is
\[ L=\{ x\cdot A_i : x\in A; i=1,\ldots,n \}. \]
\par
In the {\em tesi di laurea}
``Gruppi di Frobenius e strutture geometriche associate'',
the incidence structure arising from the fibration of a finite Frobenius
group has been studied and some of its properties have been listed.
\par
A family of co--Minkowski planes has been investigated
in ``co--Minkowski spaces, their reflection structure and K-loops'' and
a new infinite family of K--loops which are fibred in sub--groups has
been determined.
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\input{curriculum-epilogue}
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