Prospects in Theoretical Physics (PiTP) 2010
Prospects in Theoretical Physics is an intensive two-week summer program designed for graduate students and postdoctoral scholars considering a career in theoretical physics. The 2010 program, “Aspects in Supersymmetry,” took place from July 19 to July 30.
Asset Allocation Strategies for the New Decade
The Einstein Legacy Society recognizes those friends of the Institute who have made a planned gift or who have included a commitment to the Institute in their estate plans.The Society honors the memory Albert Einstein, one of the Institute’s first Faculty members, serving from 1933 until his death in 1955. The Einstein Legacy Society was created in 1996, and is co-chaired by Trustee Emeritus Martin A. Chooljian and Charles and Rosanna Jaffin.
Workshop on Pseudorandomness in Mathematical Structures
June 14 - 18, 2010
Organizers: Jean Bourgain, Russell Impagliazzo, Peter Sarnak and Avi Wigderson
Workshop Homepage:http://www.math.ias.edu/pseudo2010
Program: http://www.math.ias.edu/pseudo2010/program.
The Stepanov Method
The Stepanov method is an elementary method for proving bounds on the number of roots of polynomials. At its core is the following idea. To upper bound the number of roots of a polynomial f(x) in a field, one sets up an auxiliary polynomial F(x) , of (magically) low degree, which vanishes at the roots of f with high multiplicity. That appropriate F exits is usually proved by a dimension argument.
Subsampling Mathematical Relaxations and Average-case Complexity
We consider the following two questions:
Reductions Between Expansion Problems
The small-set expansion conjecture introduced by Raghavendra and Steuerer is a natural hardness assumption concerning the problem of approximating edge expansion of small sets (of size $\delta n$) in graphs. It was shown to be intimately connected to the well-known Unique Games Conjecture.
Pursuing this line of research further, we obtain the following results:
Small-Bias Sets
An epsilon-biased set X in {0,1}n is a set so that for every non-empty set T in [n] the following holds. The random bit B(T) obtained by selecting at random a vector x in X, and computing the mod-2 sum of its T-coordinates, has bias at most epsilon. Such sets may be viewed as generating matrices of binary error correcting codes of distance (1/2 - epsilon), as well as pseudorandom sets in the sense that all their nontrivial Fourier coefficients are at most epsilon in absolute value.
Return to Space
Charles Simonyi, Chairman of the Institute’s Board of Trustees and President and CEO of Intentional Software Corporation, is the first and only “space tourist” to fly twice: first in 2007 and most recently in 2009, for a combined total of twenty-eight days in space. In this talk, Dr. Simonyi discusses daily life in a spacecraft and on the International Space Station, and shows footage of the dynamic return trip from orbit to the ground in Kazakhstan.
Bethlehem: American Utopia, American Tragedy
Bethlehem, Pennsylvania, was founded in the 1740s as a utopian religious community. At the turn of the twentieth century, it became one of the iconic steel towns of industrial America, a destination for working-class immigrants and the producer of steel for a century of skyscrapers and battleships. At the turn of the twenty-first century, it underwent the familiar fate of deindustrialization, as steel production came to an end.