Institute for Advanced Study
IAS/Park City Mathematics Institute (PCMI)
HISTORY 1994-1997
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1994
1995
1996
1997
The Institute for Advanced Study/Park City Mathematics Institute (PCMI) was begun in 1991 at the University of Utah as one of the National Science Foundation’s Regional Geometry Institutes. In 1993 the Institute for Advanced Study was asked to assume institutional sponsorship, and the name was changed in 1994 in order to reflect the new affiliation. The first Summer Session under this new sponsorship was held in 1994.
1994 Summer Session
Gauge Theory and the Topology of Four-Manifolds
Organizers: John Morgan, Columbia University Robert Friedman, Columbia UniversityThe 1994 Summer Session was held in Park City, Utah, from July 10 to 30 and was attended by 80 graduate students, 56 researchers, 20 undergraduates and 34 high school teachers. The following four programs were held: the Graduate Summer School, the Research Program, the Undergraduate Program and the High School Teacher Program. The Research Topic was Gauge Theory and the Topology of Four-Manifolds.
Courses and Lecture Series:
Graduate Summer School: Introduction to Gauge Theory, John Morgan, Columbia University; Introduction to Complex Surfaces, Coherent Sheaves, and Algebro-Geometric Computation of Donaldson Polynomials, Robert Friedman, Columbia University; Hermitian Differential Geometry and Holomorphic Vector Bundles, Jun Li, Stanford University; ASD Connections on Cylinders and the L2 Moduli Space, Cliff Taubes, Harvard University; Decompositions of Four-Manifolds along Homology Three-Spheres and Computations of Donaldson Polynomials, Ron Stern, University of California at Irvine; Spaces of ASD Connections Singular along a Riemann Surface and Universal Relations Among the Donaldson Polynomial Invariants, Tom Mrowka, California Institute of Technology; Introduction to Geometric Invariant Theory, David Gieseker, University of California at Los Angeles.
Undergraduate Program: Computer Projects, Robert Bryant, Duke University; Tilings and the Topology of Surfaces, John Harer, Duke University; An Introduction to Riemann Surfaces and Connections, Karen Uhlenbeck, University of Texas at Austin.
High School Teacher Program: Mathematics in the Classroom, Naomi Fisher, University of Illinois at Chicago; Technology for Teaching Mathematics, James King, University of Washington; Advanced Classical Mathematics, John Polking, Rice University and John Wood, University of Illinois at Chicago.
1995 Summer Session
Nonlinear Wave Phenomena
Organizers: Luis Caffarelli, University of Texas at Austin Weinan E,
Courant Institute
The 1995 Summer Session was held in Park City, Utah, July 9-29. Participating were 51 graduate students, 33 researchers, 20 undergraduate students, and 38 high school teachers. The Research Topic for 1995 was Nonlinear Wave Phenomena. There were four programs at the Summer Session: the Graduate Summer School, the Research Program, the Undergraduate Program, and the High School Teacher Program.
Courses and Lecture Series:
Graduate Summer School: Nonlinear Schrödiger Equations, Jean Bourgain, Institute for Advanced Study; Harmonic Analysis, Wavelets and Applications, Ingrid Daubechies, Princeton University; Nonlinear Waves: Patterns, Oscillations, Singularities, and Stochasticity, David W. McLaughlin, Courant Institute and Alan Newell, University of Arkansas; Waves in Random Media, George Papanicolaou, Stanford University; High Frequency Nonlinear Hyperbolic Waves, Jeffrey B. Rach, University of Michigan.
Undergraduate Program: An Introduction to Linear and Nonlinear Waves, Roger Knobel, University of Texas - Pan American; An Introduction to Solitons, Steve Cox, Rice University; The Computation of Linear and Nonlinear Waves, Richard Palais, Brandeis University.
High School Teacher Program: Building Mathematics in the Classroom, Naomi Fisher, University of Illinois at Chicago and Cynthia Hays, McCallum High School, Austin, Texas; Technology for Teaching Mathematics, James King, University of Washington; Mathematical Modeling in the Classroom, Frank K. Lester Jr., Indiana University; Advanced Mathematics, John Polking, Rice University.
All-Institute Activities:
Mathematics, Music and Waves, Robert Bryant, Duke University; Nonlinear Waves in Traffic, Barbara Keyfitz, University of Houston; Shock Waves and Some Recent Problems, Cathleen Morawitz, Courant Institute; Surface Water Waves, Kathleen Socha, Oregon State University.
1996 Summer Session
Probability Theory
Organizers: Srinivasa Varadhan, Courant Institute Elton Pei Hsu, Northwestern UniversityIn 1996, over two hundred participants attended the PCMI Summer Session, which was held for the first time at the Institute for Advanced Study in Princeton, NJ. The dates were June 23 to July 13, and the Research Topic was Probability, organized by Elton Pei Hsu, Northwestern University, and Srinivasa Varadhan, Courant Institute.
Participating were 60 graduate students, 50 researchers, 20 undergraduate students, and 38 high school teachers in four programs: the Graduate Summer School, the Research Program, the Undergraduate Program, and the High School Teacher Program.
Courses and Lecture Series:
Graduate Summer School:
Mathematical Finance: An Introduction, Marco Avellaneda, Courant Institute; Independent and Dependent Percolation, Jennifer Chayes, University of California, Los Angeles; Stochastic Spatial Models, Rick Durrett, Cornell University; Stochastic Analysis on Path and Loop Spaces, Elton Pei Hsu, Northwestern University; Stochastic Analysis on Space of Paths on a Riemannian Manifold, Dan Stroock, Massachusetts Institute of Technology; Scaling Limit of Interacting Particle Systems, Horng-Tzer Yau, Courant Institute.
The Undergraduate Program was organized by Gregory Lawler, Duke University, and Emily Puckette, Occidental College and offered the following courses: Contemporary Probability, Gregory Lawler; Random Walk, Emily Puckette; and Random Walk Simulations, Lester Coyle, Duke University.
High School Teacher Program:
Building Mathematics in the Classroom, Naomi Fisher, University of Illinois at Chicago and Cynthia Hays, McCallum High School (Austin, Texas); Technology for Teaching Mathematics, James King, University of Washington; and Advanced Mathematics, John Polking, Rice University and Virginia Warfield, University of Washington.Cross Program Activities:
Geometry and Elementary Probability, Robert Bryant, Duke University; Education Seminar: Pedagogical principles and the teaching of mathematics with particular reference to the teaching of linear algebra, Guershon Harel, Purdue University; CBL (Calculator Based Laboratory) Demonstration, Dennis Donovan, Rice University; The Ph.D. Job Market, Moderator: John Polking, Rice University; Panelists: Gerard Ben Arous, École Normale Supérieure; Elizabeth Brooks, Duke University; Jennifer Chayes, University of California, Los Angeles; Mike Cranston, University of Rochester; Carolyn Cross, University of California, San Diego; Education Seminar: Students’ Proof Schemes, Guershon Harel, Purdue University; On the History of the Institute and the School of Mathematics, Armand Borel, School of Mathematics, IAS; Teaching Seminar: Student Attitudes and Calculus Reform, Jack Bookman, Duke University; Investigating the Complexity of Learning and Teaching, Carolyn A. Maher, Rutgers University; Probability with Infinitesimals, Gregory Lawler, Duke University; Teaching Seminar: Block Scheduling in High School; Electronic Publication: An informal discussion, Rene Carmona, Princeton University and Gregory Lawler, Duke University; Investigating the Complexity of Learning and Teaching, Part II - Participant Interaction, Carolyn A. Maher, Rutgers University; Content Characteristics of Eighth Grade Mathematics Classes: A Three Nation Study, Alfred Manaster, University of California, San Diego; Poincaré and the Improbable: Historical Interlude on Randomness and Determinism, Daniel Goroff, Harvard University; Pictures of Particle Systems, Richard Durrett, Cornell University; and Rice University School Math Project, Anne Papakonstantinou, Rice University.
Pilot Program:
In 1996, the Undergraduate Faculty Program was begun on a pilot basis. This program was designed to enhance the teaching ability of a small group of undergraduate faculty. Faculty attending gained experience with recent advances and experimental techniques in their fields and explored ways to incorporate these into their classroom instruction.
Special Events:
Joan Ferrini-Mundy, a member of the PCMI Steering Committee, organized a two-day conference for professional mathematics educators to explore the feasibility of a program for researchers in mathematics education as a component of the PCMI.On June 27, one hundred attendees of the Second Conference for African American Research Mathematicians (AARMS) joined PCMI participants for an afternoon of research talks and breakout sessions, followed by an evening banquet.
On July 11, the Institute honored the National Science Foundation and its director, Neal Lane, with a day-long celebration of the NSF’s commitment to excellence in mathematics and to the integration of research and education. Leaders in the public and private sectors, along with participants in the PCMI and the DIMACS Research and Education Institute, recognized the NSF’s successful Regional Institutes in the Mathematical Sciences (RIMS) and acknowledged its long history of supporting developing mathematicians. Following opening remarks by Phillip A. Griffiths, Director, Institute for Advanced Study, Jake Garn, United States Senate-Utah (Retired), and Leo F. Klagholz, New Jersey Commissioner of Education, Neal Lane gave the Keynote Address, Integration of Research and Education: Vision, Value and Vulnerability. Then, leaders of two NSF RIMS programs, John C. Polking, IAS/PCMI, and David P. Dobkin, DREI, described their activity. The afternoon session began with a panel discussion, A Cornerstone for the Future: Connecting Mathematics Researchers and Educators, moderated by Hyman Bass, Adrain Professor, Columbia University. Panelists included Judy Ann Brown, DREI Teacher Program/DIMACS Leadership Program (K-8), Margaret Cozzens, Division Director, ESIE, National Science Foundation, Joan Ferrini-Mundy, Director, MSEB, National Academy of Sciences, Cynthia Hays, PCMI High School Teacher Program, Donald J. Lewis, Division Director, DMS, National Science Foundation, and Fred S. Roberts, Director, DIMACS. A concert by Pianist Robert Taub, Artist-in-Residence, Institute for Advanced Study completed the program.
1997 Summer Session
Symplectic Geometry
Organizers: Yakov Eliashberg, Stanford University Lisa Traynor, Bryn Mawr
College
In 1997, over 250 participants attended the PCMI summer session held at the Inn at Prospector Square in Park City, Utah, June 29 to July 19. Programs offered were: Graduate Summer School, Research Program, Undergraduate Program, High School Teacher Program, and, for the first time, the Undergraduate Faculty Program. There were 80 graduate students, 80 researchers, 20 undergraduate students, 7 undergraduate faculty, 39 high school teachers, 5 Teachers-in-residence, and many guest lecturers and visitors.
The research topic for the Graduate Summer School and Research Program was Symplectic Geometry and Topology, organized by Yakov Eliashberg of Stanford University and Lisa Traynor of Bryn Mawr College.
Courses and Lectures Series:
Graduate Summer School: Quantum Cohomology, Alexander Givental, University of California at Berkeley; Holomorphic Curves and Dynamics and Topology in Dimension Three, Helmut Hofer, Eidgen Technische Hochschule; Hamiltonian Group Actions and Symplectic Quotients, Lisa Jeffrey, McGill University; Morse Theory and Singularities, Robert MacPherson, Institute for Advanced Study; Mechanics: Symmetry and Dynamics, Jerrold Marsden, California Institute of Technology; Introduction to Symplectic Topology, Dusa McDuff, SUNY at Stony Brook; Floer Homology, Dietmar Salamon, University of Warwick; and The Geometry of the Seiberg-Witten Invariants, Clifford Taubes, Harvard University.Undergraduate Program: The Geometry of Differential Equations and Conservation Laws, Lucas Hsu, University of Arizona; Symmetry and Symplectic Geometry, Robert Bryant, Duke University; and Computer Lab Session, Richard Palais, Brandeis University.
High School Teacher Program: Building Mathematics in the Classroom, Naomi Fisher, University of Illinois at Chicago, and Cynthia Hays, McCallum High School, Austin, Texas; Technology for Teaching Mathematics, James King, University of Washington; and Advanced Mathematics, James Carlson, University of Utah.
Cross Program Activities:
What Is Symplectic Geometry?, Robert Bryant, Duke University; Panel on the Ph.D. Job Market, Judith Arms, University of Washington, Jim Bryan, MSRI, James Carlson, University of Utah, and Luis O’Shea, Cornell University; Third International Mathematics and Science Study (TIMSS), Daniel Goroff, Harvard University; Upper Bounds for the Writhing of Knots and the Helicity of Vector Fields, Dennis DeTurck, University of Pennsylvania; The Use of Discovery Method Teaching in Undergraduate Courses, Virginia Warfield, University of Washington; Pre-Collegiate Mathematics Education Around the World, Moderator: Naomi Fisher, University of Illinois at Chicago; Panelists: Veronique Lizan, École Normale Supérieure de Lyon, Richard Hind, Stanford University, Hansjorg Geiges, Eidgen Technische Hochschule, Tadashi Tokeida, McGill University, and Donald Davenport, University of Michigan Site; The Language of Mathematics and K-16 Mathematics Education, Stephanie Frank Singer, Haverford College; The Mathematics of the Rainbow, David Fried, Boston University; Mathematics and Music, Edward Rothstein, The New York Times, and Robert Taub, Institute for Advanced Study; Marsden’s Toys, Jerrold Marsden, California Institute of Technology; The Connection Between High School Mathematics and Collegiate Mathematics, Moderator: John Polking, Rice University; Panelists: Andrew McInerny, Bronx Community College (CUNY), Kimya Moyo, School for Creative and Performing Arts, Cincinnati, Jennifer Slimowitz, SUNY at Stony Brook, Ronald Stern, University of California at Irvine, Mark Tomforde, Gustavus Adolphus College, and Christopher Sinclair, University of Arizona.
Cross-program interaction inspired a prize-winning entry in Park City’s annual July 4 Parade. Participants from all programs joined together to form the "Human Legendrian Wave Front" and to design the "Bubble Mobile" (a car covered with balloons of every shape and color), among other attractions. In addition to being a semi-serious demonstration of knot theory, the design of the entry grew out of intense collaborations and mathematical discussions. In recognition of this effort, parade officials bestowed the "Most Creative" award upon the PCMI.
