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1948–1950: Snapshots
By Cécile DeWitt-Morette
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Cécile DeWitt-Morette with (from left to right) Isadore Singer, Freeman Dyson, and Raoul Bott at the Institute in the 1950s |
In Brief
It all began with a cable from Oppenheimer that I received on March 10, 1948, in Trondheim, Norway: ON THE RECOMMENDATION OF BOHR AND HEITLER I AM GLAD TO OFFER YOU MEMBERSHIP SCHOOL OF MATHEMATICS FOR THE ACADEMIC YEAR 1948 – 1949 WITH STIPEND OF $3500. ROBERT OPPENHEIMER.
I did not know that this was a great offer. I did not even know where Princeton was, but as a general rule, I would rather say “yes” than “no.” I was then on leave from the French Centre National de la Recherche Scientifique (CNRS), having been awarded a Rask-Oersted Fellowship for the academic year 1947–48 at the Nordiska Institutet för Teoretisk Fysik in Copenhagen.
In retrospect, I think that in the days of the Marshall plan, Oppie was looking for a couple of European young postdocs who would benefit from a year at the Institute. Did I benefit? More than I could ever have imagined.
During my two-year stay, 1948–50, Bryce DeWitt, a postdoc at the Institute, 1949–50, asked me to marry him, and I conceived the Les Houches Summer School as my self-imposed condition for marrying a “foreigner.” Thanks to Freeman Dyson and Richard Feynman, I learned about functional integration and am still fascinated by it.
Identifying Novel Genes Associated with Autism
By Chang S. Chan, Suzanne Christen, and Asad Naqvi
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This plot of genetic data from an individual with autism shows a deletion in the gene NCAM2, one of four genes that researchers in the Simons Center for Systems Biology found to be associated with autism. |
Autism is a common childhood neurodevelopmental disorder affecting one in 180 children. It is characterized by impaired social interaction and communication, and by restricted interests and repetitive behavior. Autism is a complex disease exhibiting strong genetic liability with a twenty-five-fold increased risk for individuals having affected first-degree relatives. Moreover, the concordance for developing autism is over 90 percent in identical twins, but only 5–10 percent for fraternal twins. Recent advances in genetics show that autism is associated with many diverse genes, with each gene accounting only for a few percent of cases, as well as complicated multigenic effects.
Researchers at the Simons Center for Systems Biology have been studying autism for the past two years. We have identified novel genes associated with autism. Our approach is to use single nucleotide polymorphism (SNP) genotyping chips that measure differences between individuals and can uncover candidate genes or regulatory elements (which control gene activity) associated with the disease.
Most individuals differ very little from one another across the human genome. SNPs are the largest class of DNA sequence variation among individuals. A SNP occurs when one base out of the four bases used in DNA is exchanged for another base at the same locus, such that the minor allele frequency is at least 1 percent in a given population. SNPs are found at the rate of roughly one out of every 1,000 base pairs of the human genome. These SNPs provide the best chance of detecting genetic variation, both normal and otherwise, between people.
The Fundamental Lemma: From Minor Irritant to Central Problem
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The simplest case of the fundamental lemma counts points with alternating signs at various distances from the center of a certain tree-like structure. As depicted in the above image by former Member Bill Casselman, it counts 1, 1–3=–2, 1–3+6=4, 1–3+6–12=–8, etc. But this case is deceptively simple, and Bao Châu Ngô’s final proof required a huge range of sophisticated mathematical tools. |
The proof of the fundamental lemma by Bao Châu Ngô that was confirmed last fall is based on the work of many mathematicians associated with the Institute for Advanced Study over the past thirty years. The fundamental lemma, a technical device that links automorphic representations of different groups, was formulated by Robert Langlands, Professor Emeritus in the School of Mathematics, and came out of a set of overarching and interconnected conjectures that link number theory and representation theory, collectively known as the Langlands program. The proof of the fundamental lemma, which resisted all attempts for nearly three decades, firmly establishes many theorems that had assumed it and paves the way for progress in understanding underlying mathematical structures and possible connections to physics.
The simplest case of the fundamental lemma counts points with alternating signs at various distances from the center of a certain tree-like structure. As depicted in the above image by former Member Bill Casselman, it counts 1, 1–3=–2, 1–3+6=4, 1–3+6–12=–8, etc. But this case is deceptively simple, and Ngô’s final proof required a huge range of sophisticated mathematical tools.
The story of the fundamental lemma, its proof, and the deep insights it provides into diverse fields from number theory and algebraic geometry to theoretical physics is a striking example of how mathematicians work at the Institute and demonstrates a belief in the unity of mathematics that extends back to Hermann Weyl, one of the first Professors at the Institute. This interdisciplinary tradition has changed the course of the subject, leading to profound discoveries in many different mathematical fields, and forms the basis of the School’s interaction with the School of Natural Sciences, which has led to the use of ideas from physics, such as gauge fields and strings, in solving problems in geometry and topology and the use of ideas from algebraic and differential geometry in theoretical physics.
Measuring the Cosmos, Mapping the Galaxy, Finding Planets
By David H. Weinberg
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An SDSS-III plugplate, which admits light from preselected galaxies, stars, and quasars, superposed on an SDSS sky image. |
Why is the expansion of the universe speeding up, instead of being slowed by the gravitational attraction of galaxies and dark matter? What is the history of the Milky Way galaxy and of the chemical elements in its stars? Why are the planetary systems discovered around other stars so different from our own solar system? These questions are the themes of SDSS-III, a six-year program of four giant astronomical surveys, and the focal point of my research at the Institute during the last year.
In fact, the Sloan Digital Sky Survey (SDSS) has been a running theme through all four of my stays at the Institute, which now span nearly two decades. As a long-term postdoctoral Member in the early 1990s, I joined in the effort to design the survey strategy and software system for the SDSS, a project that was then still in the early stages of fundraising, collaboration building, and hardware development. When I returned as a sabbatical visitor in 2001–02, SDSS observations were—finally—well underway. My concentration during that year was developing theoretical modeling and statistical analysis techniques, which we later applied to SDSS maps of cosmic structure to infer the clustering of invisible dark matter from the observable clustering of galaxies. By the time I returned for a one-term visit in 2006, the project had entered a new phase known as SDSS-II, and I had become the spokesperson of a collaboration that encompassed more than three hundred scientists at twenty-five institutions around the globe. With SDSS-II scheduled to complete its observations in mid-2008, I joined a seven-person committee that spent countless hours on the telephone that fall, sorting through many ideas suggested by the collaboration and putting together the program that became SDSS-III.
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