
The IBM Research  NYU  Columbia Theory Day
 
Davis Auditorium
 
The IBM Research  NYU  Columbia Theory Day is a semiannual
conference,
aimed to bring together people in the New York Metropolitan area for
one day of
interaction and discussion. The Theory Day features several
(usually 45) hourlong
presentations by leading theoretical computer scientists about
stateoftheart advances
in various areas. Some presentations give a survey of the latest
advances in some area,
while others may concentrate on a particular result.
The meeting is free and open to everyone; in particular, students are
encouraged to attend.  

Prof. Bernard Chazelle (Princeton University) Motivated by the need to cope with data that is massive, highdimensional, noisy, uncertain, unevenly priced, lowentropic, or all of the above, algorithm design is undergoing profound changes. I will discuss some of these developments; in particular, sublinear algorithms, online reconstruction, selfimproving algorithms, and dimension reduction. 
Prof. Michael Saks (Rutgers University) In a noisy broadcast channel, processors communicate as follows: in each time step, one processor broadcasts a bit. Each of the other processors receives a bit, but the received bit is incorrect with some known probability p. Reception errors are assumed to be independent. In such an environment, a group of n broadcasters, each possessing a bit, wish to transmit all n bits to a receiver so that, with probability close to 1, the receiver learns all of the bits correctly. This can be done easily with O(n log n) broadcasts, by having each processor broadcast its input bit C log n times (for some sufficiently large constant C) and having the receiver decode each bit by majority vote. This naive algorithm was improved by Gallager who, in 1988, gave an algorithm that uses only O(n log log n) broadcasts. I'll describe a recent result, obtained with Navin Goyal and Guy Kindler, showing that Gallager's algorithm is optimal up to a constant factor. 
Prof. Subhash Khot (Georgia Institute of Technology) Goemans and Williamson, in their seminal 1994 paper, introduced the use of semidefinite programming as an algorithmic tool. Using a natural SDPrelaxation and a rounding procedure, they obtained 0.878.. approximation to MAXCUT problem. Since then, the technique has found several applications including the recent breakthrough result of Arora, Rao and Vazirani that gave O(sqrt{log n}) approximation to the Sparsest Cut problem. I will talk about recent results proving lower bounds on the appr oximatbility of MAXCUT and Sparsest Cut. These lower bounds are of two types: firstly, hardness of approximation results assuming the Unique Games Conjecture and secondly, unconditional and explicit intergrality gaps for the SDP relaxations (even with socalled triangle inequality constraints). The lower bound for MAXCUT matches exactly with the Goemans Williamson's bound. The integrality gap result for Sparsest Cut disproves a conjecture of Goemans and Linial that the negative type metrics embed into L_1 with constant distortion. Based on joint works with [Guy Kindler, Elchanan Mossel and Ryan O'donnell], [Nisheeth Vishnoi] and [Nikhil Devanur, Rishi Saket and Nisheeth Vishnoi]. 
Dr. Corinna Cortes (Google Labs) Search engines have been around for more than a decade. Some of the problems that seemed at first intractable have found common practical solutions. But much is still left to organize the information in the world. What are the next challenges faced by search engines? How can search be further improved? This talk presents and discusses several algorithmic and theoretical problems that arise in this context of the design of search engines. 