New York Area Theory Day
Organized by: IBM/NYU/Columbia
Friday, May 4, 2012
Davis Auditorium, Columbia University, New York.
The New York Area 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.
Program:
Program
9:30  10:00 Coffee and bagels
10:00  10:55 Prof. Michael Kearns (U Penn)
Experiments in Social Computation
10:55  11:05 Short break
11:05  12:00 Prof. Eli BenSasson (Technion and Microsoft Research  New England)
An additive combinatorics approach relating rank to communication complexity
12:00  02:00 Lunch break
02:00  02:55 Dr. Aleksander Madry (Microsoft Research New England)
Online Algorithms and the Kserver Conjecture
02:55  03:15 Coffee break
03:15  04:10 Dr. Shubhangi Saraf (IAS)
The Method of Multiplicities
For directions, please see here
To subscribe to our mailing list, follow instructions at
http://www.cs.nyu.edu/mailman/listinfo/theoryny
Organizers:
Yevgeniy Dodis dodis@cs.nyu.edu
Tal Rabin talr@us.ibm.com
Baruch Schieber sbar@us.ibm.com
Rocco Servedio rocco@cs.columbia.edu
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Abstracts
Experiments in Social Computation
Michael Kearns
(University of Pennsylvania)
What does the theory of computation have to say about the emerging
phenomena of crowdsourcing and social computing? Most successful
applications of crowdsourcing to date have been on problems we might
consider "embarrassingly parallelizable" from a computational perspective.
But the power of the social computation approach is already evident,
and the road cleared for applying it to more challenging problems.
In part towards this goal, for a number of years we have been conducting
controlled humansubject experiments in distributed social computation
in networks with only limited and local communication. These experiments
cast a number of traditional computational problems  including graph
coloring, consensus, independent set, market equilibria, and voting
 as games of strategic interaction in which subjects have financial
incentives to collectively "compute" global solutions. I will overview
and summarize the many behavioral findings from this line of
experimentation, and draw broad comparisons to some of the predictions
made by the theory of computation and microeconomics.
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An additive combinatorics approach relating rank to
communication complexity
Eli BenSasson
(Technion and Microsoft Research  New England)
For a {0,1}valued matrix M let CC(M) denote the deterministic
communication complexity of the boolean function associated with M.
It is wellknown since the work of Mehlhorn and Schmidt [STOC 1982]
that CC(M) is bounded from above by rank(M) and from below by log rank(M)
where rank(M) denotes the rank of M over the field of real numbers.
Determining where in this range lies the true worstcase value of CC(M)
is a fundamental open problem in communication complexity. The state of
the art is
log^{1.631} rank(M) < CC(M) < 0.415 rank(M),
the lower bound is by Kushilevitz [unpublished, 1995] and the upper bound
is due to Kotlov [Journal of Graph Theory, 1996]. Lovasz and Saks [FOCS 1988]
conjecture that CC(M) is closer to the lower bound, i.e., CC(M) < log^c(rank(M))
for some absolute constant c  this is the famous ''logrank conjecture''
 but so far there has been no evidence to support it, even giving a slightly
nontrivial (o(rank(M))) upper bound on the communication complexity.
Our main result is that, assuming the Polynomial FreimanRuzsa (PFR) conjecture
in additive combinatorics, there exists a universal constant c such that
CC(M)< c rank(M)/ log rank(M).
Although our bound is stated using the rank of M over the reals, our proof goes
by studying the problem over the finite field of size 2, and there we bring to
bear a number of new tools from additive combinatorics which we hope will
facilitate further progress on this perplexing question.
In more detail, our proof is based on the study of the ''approximate duality
conjecture'' which was suggested by BenSasson and Zewi [STOC 2011] and studied
there in connection to the PFR conjecture. First we improve the bounds on
approximate duality assuming the PFR conjecture. Then we use the approximate
duality conjecture (with improved bounds) to get our upper bound on the
communication complexity of lowrank martices.
Joint work with Shachar Lovett (IAS) and Noga RonZewi (Technion)
==================================================================
Online Algorithms and the Kserver Conjecture
Aleksander Madry
(Microsoft Research New England)
Traditionally, in the problems considered in optimization, one
produces the solution only after the whole input is made available.
However, in many realworld scenarios the input is revealed gradually,
and one needs to make irrevocable decisions along the way while having
only partial information on the whole input. This motivates us to
develop models that allow us to address such scenarios.
In this talk, I will consider one of the most popular approaches to
dealing with uncertainty in optimization: the online model and
competitive analysis; and focus on a central problem in this area: the
kserver problem. This problem captures many online scenarios  in
particular, the widely studied caching problem  and is considered by
many to be the "holy grail" problem of the field.
I will present a new randomized algorithm for the kserver problem
that is the first online algorithm for this problem that achieves
polylogarithmic competitiveness.
Based on joint work with Nikhil Bansal, Niv Buchbinder, and Joseph
(Seffi) Naor.
==================================================================
The Method of Multiplicities
Shubhangi Saraf
(IAS)
Polynomials have played a fundamental role in the construction of objects with
interesting combinatorial properties, such as error correcting codes,
pseudorandom generators, randomness extractors etc. Somewhat strikingly,
polynomials have also been found to be a powerful tool in the analysis of
combinatorial parameters of objects that have some algebraic structure. This
method of analysis has found applications in works on listdecoding of error
correcting codes, constructions of randomness extractors, and in obtaining
strong bounds for the size of Kakeya Sets. Remarkably, all these applications
have relied on very simple and elementary properties of polynomials
such as the sparsity of the zero sets of low degree polynomials.
In this talk we will discuss improvements on several of the results mentioned
above by a more powerful application of polynomials that takes into account
the information contained in the *derivatives* of the polynomials. We call
this technique the ``method of multiplicities". The information about higher
multiplicity vanishings of polynomials, which is encoded in the derivative
polynomials, enables us to meaningfully reason about the zero sets of
polynomials of degree much higher than the underlying field size.
We will discuss some of these applications of the method of multiplicities, to
obtain improved constructions of error correcting codes, and qualitatively
tighter analyses of Kakeya sets, and randomness extractors.
(Based on joint works with Zeev Dvir, Swastik Kopparty, Madhu Sudan, Sergey
Yekhanin)
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