Professor, Computer and Information Science.

** Before 1993: ** Friendly compilers, incremental compilation,
program verification, automated deduction, unification

** After 1993: **
and its applications
(3D graphics, virtual reality, computer vision), geometric modeling,
geometry of curves and surfaces, motion planning,
differential geometry, classical mechanics

After completing his undergraduate studies at the Lycee de Sevres, Jean Gallier spent three years (1967-1969) in the preparatory classes for the ``Grandes Ecoles''. He was admitted in June 1969 at the ``Ecole Nationale des Ponts et Chaussees'', and graduated with the degree of Civil Engineer in June 1972. Then he went to UCLA and obtained a Ph.D. in Computer Science in May 1978, under the supervision of Sheila Greibach. During 1978, he was a Post Doctoral student in the Math Department at UCSB. He joined the faculty of the University of Pennsylvania in September 1978.

Until two years ago,
the unifying thread of my research interests was
the * semantics and logics of programs*.
I have been interested in both applied and theoretical aspects
of the semantics of programs and programming languages,
and my work ranges from incremental parsing to
proof theory and lambda-calculus.
In particular, I have contributed to the following areas:
compiler generators,
incremental parsing, attribute evaluation, program schemes,
formal languages, tree automata,
program verification, algebraic semantics,
compiler correctness, continuation semantics,
logic programming, automated theorem proving, rewrite systems,
unification, proof theory, type theory and polymorphic
lambda-calculi, and constructive logics.
I am also interested in algorithms
for computational logic. I have designed some
fast algorithms for ground Horn clauses with or without equality,
and a fast algorithm for generating a canonical set of rewrite rules
from a set of ground equations.

In the past two years, I became fascinated with the applications of (3D graphics, vision, robotics, etc). I am particularly interested in the geometry of curves and surfaces and geometric modeling, and I have been writing a book on the subject. I am also very interested in applying notions of Riemannian geometry to motion planning. The problem can be formulated as finding geodesics in manifolds with boundaries, and the area seems wide open. I am also interested in ways of representing surfaces so that deformations are conveniently handled. In this respect, a good way of dealing with triangular-based spline surfaces remains to be found.

**Hot off the Press! **
Work in progress