LEONARDO DA VINCI LECTURES

Towards a unitary view of Mathematics



 
  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