The LEONARDO DA VINCI LECTURES, born in 1990, are organized (4/5 each year) by the Department of Mathematics of the University of Milano, the Department of Mathematics and Applications of the University of Milano-Bicocca, and the Department of Mathematics of the Politecnico of Milano. The Lectures, given by mathematicians of international prominence, are intended to give to a general audience an overview of some of the modern developments of mathematics, with a particular emphasis on the interrelations between different fields. The Leonardo da Vinci Lectures have acquired over the years a considerable prestige, as can be testified by the impressive list of lectures, among which many Field medallists.

Ma le vere scienze son quelle che la sperienza ha fatto penetrare per li sensi, e posto silenzio alle lingue de' litiganti, e che non pasce di sogno li suoi investigatori, ma sempre sopra li primi veri e noti principii procede successivamente e con vere seguenzie insino al fine, come si dinota nelle prime matematiche, cioè numero e misura, dette arismetica e geometria, che trattano con somma verità della quantità discontinua e continua. Leonardo da Vinci La filosofia è scritta in questo grandissimo libro che continuamente ci sta aperto innanzi a gli occhi (io dico l'universo), ma non si può intendere se prima non s'impara ad intender la lingua, e conoscer i caratteri, né quali è scritto. Egli è scritto in lingua matematica, e i caratteri son triangoli, cerchi, ed altre figure geometriche, senza i quali mezi è impossibile a intenderne umanamente parola; senza questi è un aggirarsi vanamente per un oscuro laberinto. Galileo Galilei ...creare un anuova teoria è come inerpicarsi su per una montagna, raggiungendo nuovi e più vasti orizzonti e scoprendo inattesi rapporti fra il nostro punto di partenza e le bellezze dei suoi dintorni. tuttavia, il sito dal quale partimmo è sempre lì e possiamo tuttora scorgerlo, ancorchè paia più piccolo e non sia ormai più che un dettaglio nella vasta veduta raggiunta superando gli ostacoli che si opponevano alla nostra avventurosa ascesa. Albert Einstein

Year 1990 Year 1991 Year 1992 Year 1993 Year 1994 Year 1995 Year 1996 Year 1997 Year 1998 Year 1999 Year 2000 Year 2001 Year 2002

Year 1990

L. CAFFARELLI Princeton, USA SULLA GEOMETRIA DELLE SOLUZIONI DI EQUAZIONI ELLITTICHE

J. TITS Collège de France MOSTRO  E ''MOONSHINE'': UNA PANORAMICA

G. C. ROTA M.I.T., USA SGUARDO PANORAMICO SULLA TEORIA CLASSICA DEGLI INVARIANTI

E. BOMBIERI Princeton, USA ARITMETICA E GEOMETRIA

M. GROMOV Bures-sur-Yvette, France IDEA DELLA CURVATURA NELLA GEOMETRIA RIEMANNIANA

Year 1991

V. G. KAC M.I.T., USA BOSON-FERMION CORRESPONDENCE. APPLICATIONS TO COMBINATORICS AND SOLITON EQUATIONS

P. J. HILTON SUNY at Binghamton, USA THE BIRTH OF HOMOLOGICAL ALGEBRA

V. I. ARNOL'D Steklov Inst., Moscow WAWES, SINGULARITIES AND PLATONICS-STRANGE UNITY IN MATHEMATICS AND IN NATURE

F. E. P. HIRZEBRUCH Max-Planck Inst., Bonn MANIFOLDS, CHARACTERISTIC CLASSES AND MODULAR FORMS

J. K. MOSER E.T.H., Zurigo ON STABILITY IN DYNAMICAL SYSTEMS

Year 1992

R. PENROSE Oxford, U.K. MAGIC DODECAHEDRA AND THE MYSTERY OF QUANTUM ENTANGLEMENT

J. L. LIONS Collège de France MATHEMATICS AND ENVIRONMENT-SOME REMARKS

YU. I. MANIN Steklov Inst., Moscow ANALOGIES BETWEEN NUMBERS AND FUNCTIONS

L. NIRENBERG Courant Inst., New York ON THE MAXIMUM PRINCIPLE

Year 1993

J. MILNOR Suny at Stony Brook, USA ITERATED POLYNOMIAL MAPS

M. ASCHBACHER Caltech, Pasadena, USA FINITE SIMPLE GROUPS, ALGEBRAIC TOPOLOGY AND GEOMETRIC COMBINATORICS

S. NOVIKOV Landau Inst., Moscow DIFFERENTIAL GEOMETRY AND HYDRODINAMIC TYPE SYSTEMS

I. EKELAND Université Paris-Dauphine THE SYMPLECTIC WORLD: GEOMETRY, INVARIANTS AND TOPOLOGY

L. SCHWARTZ Ecole Polytechnique, Paris BROWNIAN MOTION

Year 1994

P. D. LAX Courant Inst., N.Y. DISORDERED MOTION CAUSED BY DISPERSION

P. ERDOS Hungarian Academy of Sciences, Budapest SOME OF MY FAVORITE PROBLEMS AND THEOREMS

E. M. STEIN Princeton University, USA THE ERGODIC THEOREM FOR FREE GROUPS

A. BOREL Inst. for Advanced Study, Princeton, USA GROUP REPRESENTATIONS AS A LINK BETWEEN MATHEMATICS AND PHYSICS

Year 1995

D. W. STROOCK MIT, USA PERTURBING BROWNIAN PATHS WITH AN EYE TOWARDS RIEMANNIAN GEOMETRY

E. I. ZELMANOV University of Chicago, USA ON THE BURNSIDE PROBLEM

P. CARTIER Inst. des Hautes Etudes Scientifiques, Paris FEYNMAN PATH INTEGRALS AS A CHALLENGE TO MATHEMATICIANS

I. M. GELFAND Rutgers University, USA SOME PROBLEMS IN GEOMETRY AND NON-COMMUTATIVE ALGEBRA

D. P. RUELLE Inst. des Hautes Etudes Scientifiques, Paris FUNCTIONAL DETERMINANTS RELATED TO DYNAMICAL SYSTEMS

Year 1996

NICOLAI KRYLOV University of Minnesota, USA OPTIMIZATION PROBLEMS AND FULLY NONLINEAR ELLIPTIC EQUATIONS

HAIM BREZIS Université P. et M. Curie & Rutgers University HOW TO HANDLE INFINITE ENERGY; THE GINZBURG-LANDAU MODEL

ANDREI SUSLIN Northwestern University, Chicago, USA COHOMOLOGY OF FINITE GROUP SCHEMES

KAREN UHLENBECK University of Texas at Austin, USA GEOMETRIC PARTIAL DIFFERENTIAL EQUATIONS

Year 1997

DAVID MUMFORD Harvard University, USA SEEING AS A VARIATIONAL PROBLEM FROM DA VINCI TO KANIZSA

PIERRE-LOUIS LIONS Université de Paris-Dauphine ON COMPRESSIBLE EULER AND NAVIER-STOKES EQUATIONS

PERSI DIACONIS Harvard University, USA THE SEARCH FOR RANDOMNESS

ALEXANDER LUBOTZKY Hebrew University, Jerusalem PROPERTY t AND ITS APPLICATIONS IN COMBINATORICS, GEOMETRY, AND GROUP THEORY

Year 1998

A. FRIEDMAN University of Minnesota, Minneapolis, USA WHAT IS INDUSTRIAL MATHEMATICS?

J. LINDENSTRAUSS Hebrew University, Jerusalem DIFFERENTIABILITY OF LIPSCHITZ FUNCTIONS AND EXCEPTIONAL SETS

B. ECKMANN ETH Zurich LINEARIZATION: SOME RELATIONS BETWEEN ALGEBRA, TOPOLOGY AND ANALYSIS

P. SARNAK Princeton University, USA ZEROS OF ZETA FUNCTIONS AND SYMMETRY

C. S. MORAWETZ Courant Inst., N.Y. University SHOCK WAWES AND THEIR REFLECTION

Year 1999

OLGA A. LADYZHENSKAYA Academy of Science, St Petersburg ON THE DYNAMICS OF INCOMPRESSIBLE VISCOUS FLUIDS

VICTOR KLEE University of Washington, Seattle, USA SHAPES OF THE FUTURE: UNSOLVED PROBLEMS FROM INTUITIVE GEOMETRY

YVES MEYER Ecole Normale Supérieure, Cachan OSCILLATIONS, VIBRATIONS, TIME FREQUENCY ANALYSIS AND THE VIRGO PROGRAM

ALBRECHT DOLD Università di Heidelberg GEOMETRY OF UNIVERSAL BUNDLES

Year 2000

M. KONTSEVICH IHES, Bures sur Yvette GEOMETRY OF THE ASSOCIATIVITY LAW

A. J. MAJDA Courant Inst., N.Y. MATHEMATICS AND ATMOSPHERE/OCEAN SCIENCE

J. -C. YOCCOZ Collège de France STABILITY OF DYNAMICS IN PHASE SPACE AND PARAMETER SPACE

M. MARTIN M.I.T., Cambridge, USA GEOMETRY OF NON-COMMUTATIVE ALGEBRAIC SURFACES

S. HILDEBRANDT Università di Bonn, Germania GEOMETRIC VARIATIONAL PROBLEMS

Year 2001

ANDREW J. WILES Princeton University, USA FERMAT'S LEGACY

JOHN M. BALL University of Oxford, U.K. MICROGEOMETRY AND PHASE TRANSFORMATIONS

MICHAEL ATIYAH University of Edinburgh, U.K. POLYHEDRA IN GEOMETRY, PHYSICS AND CHEMISTRY

J.-P. BOURGUIGNON IHES, Bures-sur-Yvette KAEHLERIAN GEOMETRY, A CROSSROAD OF GEOMETRY

Year 2002

ROGER TEMAN Université de Paris-Sud MATHEMATICAL PROBLEMS IN METEOROLOGY AND OCEANOGRAPHY

ELLIOTT H. LIEB Princeton University QUANTUM MECHANICS AND THE STABILITY OF MATTER

EUGENIO CALABI University of Pennsylvania RECENT RESULTS IN KAEHLER GEOMETRY

BERNARD MALGRANGE Institut Fourier, Université de Grenoble DIFFERENTIAL GALOIS THEORY: AN ALGEBRAIC VIEW ON DIFFERENTIAL EQUATIONS