The origins of the Colloquium Lectures date back to the 1893 International Congress of Mathematics, held in connection with the
Chicago World's Fair, where the German mathematician
Felix Klein gave the opening address.[2] After the Congress, Klein was invited by one of its organiser, his former student
Henry Seely White, to deliver a two-week-long series of lectures at
Northwestern University in
Evanston.[3]
In February 1896, White proposed in a letter to
Thomas Fiske to repeat the experience of the Evanston lectures, by organising a series of longer talks "for increasing the utility of the
American Mathematical Society".[4][1] The two of them, together with
E. H. Moore,
William Osgood,
Frank Cole, Alexander Ziwet, and
Frank Morley, wrote later an open letter to the AMS, asking the society to sponsor an annual week-long series of Colloquium lectures focussing on a specific mathematical area, in order to complement the traditional shorter talks.[1]
The first official Colloquium Lectures were held in September 1896, after the AMS Summer Meetings in
Buffalo, New York, and consisted of two independent series of lectures given by
James Pierpont and
Maxime Bôcher.[5] A synopse of their lectures was published in the
Bulletin of the AMS; starting from the second Colloquium in 1898, the lectures have been published entirely in book form in the AMS Colloquium Publications series.[6]
List of Colloquium Lectures
1896
James Pierpont (Yale University): Galois's theory of equations.
1896
Maxime Bôcher (Harvard University): Linear differential equations and their applications.
1898
William Fogg Osgood (Harvard University): Selected topics in the theory of functions.
1898
Arthur Gordon Webster (Clark University): The partial differential equations of wave propagation.
1901
Oskar Bolza (University of Chicago): The simplest type of problems in the calculus of variations.
1901
Ernest William Brown (Haverford College): Modern methods of treating dynamical problems, and in particular the problem of three bodies.
1903
Henry Seely White (Northwestern University): Linear systems of curves on algebraic surfaces.
1903
Frederick S. Woods (Massachusetts Institute of Technology): Forms of non-euclidean space.
1903
Edward Burr Van Vleck (Wesleyan University): Selected topics in the theory of divergent series and continued fractions.
1906
E. H. Moore (University of Chicago): On the theory of bilinear functional operations.
1906
Ernest Julius Wilczynski (University of California, Berkeley): Projective differential geometry.
1906
Max Mason (Yale University): Selected topics in the theory of boundary value problems of differential equations.
1909
Gilbert Ames Bliss (University of Chicago): Fundamental existence theorems.
1909
Edward Kasner (Columbia University): Differential-geometric aspects of dynamics.
1913
Leonard E. Dickson (University of Chicago): On invariants and the theory of numbers.
1913
William Fogg Osgood (Harvard University): Topics in the theory of functions of several complex variables.
1916
Griffith C. Evans (Université Rice): Functionals and their applications, selected topics including integral equations.
1931
Marston Morse (Harvard University): The calculus of variations in the large.
1932
Joseph Ritt (Columbia University): Differential equations from the algebraic standpoint.
1934
Raymond Paley (Trinity College, Cambridge University), deceased in 1933 and replaced by
Norbert Wiener (Massachusetts Institute of Technology):[7]Fourier transforms in the complex domain.
1935
Harry Vandiver (University of Texas): Fermat's last theorem and related topics in number theory.
1956
Salomon Bochner (Princeton University): Harmonic analysis and probability.
1957
Norman Steenrod (Princeton University): Cohomology operations.
1959
Joseph L. Doob (University of Illinois, Urbana-Champaign): The first boundary value problem.
1960
Shiing-Shen Chern (University of California, Berkeley): Geometrical structures on manifolds.
1961
George Mackey (Harvard University): Infinite dimensional group representatives.
1963
Saunders Mac Lane (University of Chicago): Categorical algebra.
1964
Charles Morrey (University of California, Berkeley): Multiple integrals in the calculus of variations.
1965
Alberto Calderón (University of Chicago): Singular integrals.
1967
Samuel Eilenberg (Columbia University): Universal algebras and the theory of automata.
1968
Donald Spencer (Standford University): Overdetermined systems of partial differential equations.
1968
John Willard Milnor (Princeton University and University of California, Los Angeles): Uses of the fundamental group.
1969
Raoul Bott (Harvard University): On the periodicity theorem of the classical groups and its applications.
1969
Harish-Chandra (Institute for Advanced Study): Harmonic analysis of semisimple Lie groups.
1970
R. H. Bing (University of Wisconsin, Madison): Topology of 3-manifolds.
1971
Lipman Bers (Columbia University): Uniformization, moduli, and Kleinian groups.
1971
Armand Borel (Institute for Advanced Study): Algebraic groups and arithmetic groups.
1972
Stephen Smale (University of California, Berkeley): Applications of global analysis to biology, economics, electrical circuits, and celestial mechanics.
1972
John T. Tate (Harvard University): The arithmetic of elliptic curves.
1973
Michael Francis Atiyah (Institute for Advanced Study): The index of elliptic operators.
1973
Felix Browder (University of Chicago): Nonlinear functional analysis and its applications to nonlinear partial differential and integral equations.
1974
Errett Bishop (University of California, San Diego): Schizophrenia in contemporary mathematics.
1974
Louis Nirenberg (Courant Institute): Selected topics in partial differential equations.
1989
Nicholas Katz (Princeton University): Exponential sums and differential equations.
1989
William Thurston (Princeton University): Geometry, groups, and self-similar tilings.
1990
Shlomo Sternberg (Harvard University): Some thoughts on the interaction between group theory and physics.
1991
Robert MacPherson (Massachusetts Institute of Technology): Intersection homology and perverse sheaves.
1992
Robert Langlands (Institute for Advanced Study): Automorphic forms and Hasse-Wiel zeta-functions and Finite models for percolation.
1993
Luis Caffarelli (Institute for Advanced Study): Nonlinear differential equations and Lagrangian coordinates.
1993
Sergiu Klainerman (Princeton University): On the regularity properties of gauge theories in Minkowski space-time.
1994
Jean Bourgain (IHES and the University of Illinois, Urbana-Champaign): Harmonic analysis and nonlinear evolution equations.
1995
Clifford Taubes (Harvard University): Mysteries in three and four dimensions.
1996
Andrew Wiles (Princeton University): Modular forms, elliptic curves and Galois representations.
1997
Daniel Stroock (Massachusetts Institute of Technology): Analysis on spaces of paths.
1998
Gian-Carlo Rota (Massachusetts Institute of Technology): Introduction to geometric probability; Invariant theory old and new; and Combinatorial snapshots.
1999
Helmut Hofer (Courant Institute, New York University): Symplectic geometry from a dynamical systems point of view.
2010
Richard P. Stanley (Massachusetts Institute of Technology): Permutations: 1) Increasing and decreasing subsequences; 2) Alternating permutations; 3) Reduced decompositions.[11]
2011
Alexander Lubotzky (The Hebrew University of Jerusalem): Expander graphs in pure and applied mathematics.[12]
2012
Edward Frenkel (University of California, Berkeley): Langlands program, trace formulas, and their geometrization.[13]
2013
Alice Guionnet (Ecole Normale Supérieure de Lyon): Free probability and random matrices.[14]
2015
Michael J. Hopkins (Harvard University): 1) Algebraic topology: New and old directions; 2) The Kervaire invariant problem; 3) Chern-Weil theory and abstract homotopy theory.[16]
2016
Timothy A. Gowers (University of Cambridge): Generalizations of Fourier analysis, and how to apply them.[17]
2017
Carlos Kenig (University of Chicago): The focusing energy critical wave equation: the radical case in 3 space dimensions.[18]
2018
Avi Wigderson (Institute for Advanced Study): 1) Alternate Minimization and Scaling algorithms: theory, applications and connections across mathematics and computer science; 2) Proving algebraic identities; 3) Proving analytic inequalities.[19]
The origins of the Colloquium Lectures date back to the 1893 International Congress of Mathematics, held in connection with the
Chicago World's Fair, where the German mathematician
Felix Klein gave the opening address.[2] After the Congress, Klein was invited by one of its organiser, his former student
Henry Seely White, to deliver a two-week-long series of lectures at
Northwestern University in
Evanston.[3]
In February 1896, White proposed in a letter to
Thomas Fiske to repeat the experience of the Evanston lectures, by organising a series of longer talks "for increasing the utility of the
American Mathematical Society".[4][1] The two of them, together with
E. H. Moore,
William Osgood,
Frank Cole, Alexander Ziwet, and
Frank Morley, wrote later an open letter to the AMS, asking the society to sponsor an annual week-long series of Colloquium lectures focussing on a specific mathematical area, in order to complement the traditional shorter talks.[1]
The first official Colloquium Lectures were held in September 1896, after the AMS Summer Meetings in
Buffalo, New York, and consisted of two independent series of lectures given by
James Pierpont and
Maxime Bôcher.[5] A synopse of their lectures was published in the
Bulletin of the AMS; starting from the second Colloquium in 1898, the lectures have been published entirely in book form in the AMS Colloquium Publications series.[6]
List of Colloquium Lectures
1896
James Pierpont (Yale University): Galois's theory of equations.
1896
Maxime Bôcher (Harvard University): Linear differential equations and their applications.
1898
William Fogg Osgood (Harvard University): Selected topics in the theory of functions.
1898
Arthur Gordon Webster (Clark University): The partial differential equations of wave propagation.
1901
Oskar Bolza (University of Chicago): The simplest type of problems in the calculus of variations.
1901
Ernest William Brown (Haverford College): Modern methods of treating dynamical problems, and in particular the problem of three bodies.
1903
Henry Seely White (Northwestern University): Linear systems of curves on algebraic surfaces.
1903
Frederick S. Woods (Massachusetts Institute of Technology): Forms of non-euclidean space.
1903
Edward Burr Van Vleck (Wesleyan University): Selected topics in the theory of divergent series and continued fractions.
1906
E. H. Moore (University of Chicago): On the theory of bilinear functional operations.
1906
Ernest Julius Wilczynski (University of California, Berkeley): Projective differential geometry.
1906
Max Mason (Yale University): Selected topics in the theory of boundary value problems of differential equations.
1909
Gilbert Ames Bliss (University of Chicago): Fundamental existence theorems.
1909
Edward Kasner (Columbia University): Differential-geometric aspects of dynamics.
1913
Leonard E. Dickson (University of Chicago): On invariants and the theory of numbers.
1913
William Fogg Osgood (Harvard University): Topics in the theory of functions of several complex variables.
1916
Griffith C. Evans (Université Rice): Functionals and their applications, selected topics including integral equations.
1931
Marston Morse (Harvard University): The calculus of variations in the large.
1932
Joseph Ritt (Columbia University): Differential equations from the algebraic standpoint.
1934
Raymond Paley (Trinity College, Cambridge University), deceased in 1933 and replaced by
Norbert Wiener (Massachusetts Institute of Technology):[7]Fourier transforms in the complex domain.
1935
Harry Vandiver (University of Texas): Fermat's last theorem and related topics in number theory.
1956
Salomon Bochner (Princeton University): Harmonic analysis and probability.
1957
Norman Steenrod (Princeton University): Cohomology operations.
1959
Joseph L. Doob (University of Illinois, Urbana-Champaign): The first boundary value problem.
1960
Shiing-Shen Chern (University of California, Berkeley): Geometrical structures on manifolds.
1961
George Mackey (Harvard University): Infinite dimensional group representatives.
1963
Saunders Mac Lane (University of Chicago): Categorical algebra.
1964
Charles Morrey (University of California, Berkeley): Multiple integrals in the calculus of variations.
1965
Alberto Calderón (University of Chicago): Singular integrals.
1967
Samuel Eilenberg (Columbia University): Universal algebras and the theory of automata.
1968
Donald Spencer (Standford University): Overdetermined systems of partial differential equations.
1968
John Willard Milnor (Princeton University and University of California, Los Angeles): Uses of the fundamental group.
1969
Raoul Bott (Harvard University): On the periodicity theorem of the classical groups and its applications.
1969
Harish-Chandra (Institute for Advanced Study): Harmonic analysis of semisimple Lie groups.
1970
R. H. Bing (University of Wisconsin, Madison): Topology of 3-manifolds.
1971
Lipman Bers (Columbia University): Uniformization, moduli, and Kleinian groups.
1971
Armand Borel (Institute for Advanced Study): Algebraic groups and arithmetic groups.
1972
Stephen Smale (University of California, Berkeley): Applications of global analysis to biology, economics, electrical circuits, and celestial mechanics.
1972
John T. Tate (Harvard University): The arithmetic of elliptic curves.
1973
Michael Francis Atiyah (Institute for Advanced Study): The index of elliptic operators.
1973
Felix Browder (University of Chicago): Nonlinear functional analysis and its applications to nonlinear partial differential and integral equations.
1974
Errett Bishop (University of California, San Diego): Schizophrenia in contemporary mathematics.
1974
Louis Nirenberg (Courant Institute): Selected topics in partial differential equations.
1989
Nicholas Katz (Princeton University): Exponential sums and differential equations.
1989
William Thurston (Princeton University): Geometry, groups, and self-similar tilings.
1990
Shlomo Sternberg (Harvard University): Some thoughts on the interaction between group theory and physics.
1991
Robert MacPherson (Massachusetts Institute of Technology): Intersection homology and perverse sheaves.
1992
Robert Langlands (Institute for Advanced Study): Automorphic forms and Hasse-Wiel zeta-functions and Finite models for percolation.
1993
Luis Caffarelli (Institute for Advanced Study): Nonlinear differential equations and Lagrangian coordinates.
1993
Sergiu Klainerman (Princeton University): On the regularity properties of gauge theories in Minkowski space-time.
1994
Jean Bourgain (IHES and the University of Illinois, Urbana-Champaign): Harmonic analysis and nonlinear evolution equations.
1995
Clifford Taubes (Harvard University): Mysteries in three and four dimensions.
1996
Andrew Wiles (Princeton University): Modular forms, elliptic curves and Galois representations.
1997
Daniel Stroock (Massachusetts Institute of Technology): Analysis on spaces of paths.
1998
Gian-Carlo Rota (Massachusetts Institute of Technology): Introduction to geometric probability; Invariant theory old and new; and Combinatorial snapshots.
1999
Helmut Hofer (Courant Institute, New York University): Symplectic geometry from a dynamical systems point of view.
2010
Richard P. Stanley (Massachusetts Institute of Technology): Permutations: 1) Increasing and decreasing subsequences; 2) Alternating permutations; 3) Reduced decompositions.[11]
2011
Alexander Lubotzky (The Hebrew University of Jerusalem): Expander graphs in pure and applied mathematics.[12]
2012
Edward Frenkel (University of California, Berkeley): Langlands program, trace formulas, and their geometrization.[13]
2013
Alice Guionnet (Ecole Normale Supérieure de Lyon): Free probability and random matrices.[14]
2015
Michael J. Hopkins (Harvard University): 1) Algebraic topology: New and old directions; 2) The Kervaire invariant problem; 3) Chern-Weil theory and abstract homotopy theory.[16]
2016
Timothy A. Gowers (University of Cambridge): Generalizations of Fourier analysis, and how to apply them.[17]
2017
Carlos Kenig (University of Chicago): The focusing energy critical wave equation: the radical case in 3 space dimensions.[18]
2018
Avi Wigderson (Institute for Advanced Study): 1) Alternate Minimization and Scaling algorithms: theory, applications and connections across mathematics and computer science; 2) Proving algebraic identities; 3) Proving analytic inequalities.[19]