Italian mathematician seeks position

[Anya C. Hurlbert]

ATTENTION: The following is the c.v. of Cesare Furlanello, a young mathematician with
an Italian Ph.D.  who is interested in using the techniques of logic and analysis
to model human reasoning. He presently works at the Insitute for Research in Science
and Technology (which specializes in image understanding and speech and pattern
recognition) and would like to spend next year or a part thereof working in the U.S.
He will probably come with his own funding. If you know of any research positions for
which he might be suitable, or if you yourself are interested in having him work
with you, please send mail directly to him, with a cc to me, lest the uunet goes down again.
I am hurlbert at wheaties.ai.mit.edu.

Thank you !!!!!


Cesare Furlanello - IRST - June 1988




CESARE FURLANELLO                          CURRICULUM VITAE


Age: 27
Nationality: Italian
Address: IRST, 38050 Povo (Trento), Italia
Tel.No: 0461/810105
Email: furlan at irst.uucp

EDUCATION

HIGH SCHOOL: 	Sc. Grammar School; maturita'1980 with 60/60 (A Level).

UNIVERSITY: 	graduated in pure Mathematics on 11 November 1986
		110/110 cum laude (maximum with distinction);
		I was particularly interested in Algebraic
		Geometry; other topics of major interest before
 		and during the preparation of the thesis were, amongst others,
		Category Theory,General Topology and Commutative Algebra.
		On these topics I regularly attended lectures and meetings.

Supervisor: 	Professor Francesco Baldassarri

Title of the thesis:	Linear Differential Equations with algebraic
			relations between the solutions

Abstract of the thesis.  It is attempted to apply modern results of
differential algebra and projective geometry to the work of Gino Fano
on homogeneous linear differential equations with coefficients in C(z)
and algebraic relations between their fundamental solutions.One of the
major interests in this topic consists in describing the fundamental
solutions in terms of those of equations of lower order.The
originality of this approach consists in the study of the integral
curve g of such an equation L, curve which can be defined in the
(n-1)-th projective space V if L is of n-th order. It is therefore
possible to study the differential Galois group G of L by means of the
group Gpr of projective transformations of the variety defined in V by
the algebraic relations existing between the fundamental solutions. In
this thesis two cases are investigated: a) the integral curve g is
algebraic; b) g is contained in a quadric hypersurface and n<7. A
theorem and other results are established giving a characterization of
Gpr not previously known in the literature of differential algebra.
Those tools, and the concept of symmetric powers of linear
differential operator introduced in a recent work of M.F.Singer, are
used together with some sophisticated notions of projective geometry
like flecnodal curves and the theory of Schuberts cycles in order to
simplify the proofs of several results of Fano. Explicit conditions
for case a) and b) are found.

FELLOWSHIPS: 	a 12 months undergraduate studentship from the CNR
		(Consiglio Nazionale delle Ricerche).


POSTGRADUATE STUDY AND WORK EXPERIENCE (at IRST)

-	A tutorial on GCLisp (January 87, Trento).
-	A course on general techniques of Pattern Recognition
	(Spring 87,Trento Univ.).
-	A course on Symbolic Computation with the MAPLE language
	(Feb 87, SASIAM, Bari)
-	Studies on formal approaches to PR: the categorical
	and topological approach.
-	Summer school of categorical Topology
	(7-12 June 87, Italian Group of Research in Topology, Bressanone)
-	UNIX operative system (Fall 87, internal course, IRST)
-	A course on Logic Programming
	(Spring 1987, Dept. of Mathematics, Trento Univ.).
-	I have been admitted to the '88 CIME  "Logic and CS" Summer School
	(lessons held by A.Nerode, J.Hartmanis, R.Platek, G.Sacks,A.Scedrov,
	 20-28 June 1988,Montecatini)

I was assigned at IRST the task of studying concepts using
mathematical methods by the Director of IRST, Dr Luigi Stringa. Dr
Stringa is looking for an approach successful in answering
comprehensively to the various problems of AI and Pattern Recognition.
Due to my background in Algebraic Geometry, I started studying
geometrical-topological methods. An idea that seems very challenging
to me is that of using those powerful formal techniques which are
major tools in various fields of Mathematics like Category Theory
(and, within that framework, Sheaves and Topoi Theory) for modelling
some aspects of human reasoning. My opinion is that some formalization
can be attempted, even if limited to a specific domain, and it is
supported by the fact that the use of Category Theory is by now well
established in Logic and in Logic for CS due to Dana Scott and many
others. Categorical models are especially used for the non-traditional
logics which have been recently receiving wide attention for
computation and in the AI environment. Anyway it is obvious that a
valid approach should be sensitive to computational and
cognitive paradigms.