One powerful theme in complexity theory and pseudorandomness in
the past few decades has been the use of lower bounds to give
pseudorandom generators (PRGs). However, the general results using
this hardness vs. randomness paradigm suffer a...
One morning an office worker starts to read aloud a copy of
The Great Gatsby he finds in the clutter on his desk. At
first his coworkers hardly notice, but after a series of
coincidences, it’s no longer clear whether he’s reading the book or
the...
Gowers' uniformity norms are defined by average of a function
over specific sets of linear forms. We study norms that are
similarly defined by a system of linear forms. We prove that for
bounded complex functions over $F_p^n$, each such norm is...
Employment contracts are central to many current policy debates.
New York City is experimenting with rewarding teachers based on
value added in the hope that it will improve performance.
Compensation practices in the financial sector are often...
We consider the problem of constructing pseudorandom generators
for read-once circuits. We give an explicit construction of a
pseudorandom generator for the class of read-once constant depth
circuits with unbounded fan-in AND, OR, NOT and...
Shannon's notion of entropy measures the amount of "randomness"
in a process. However, to an algorithm with bounded resources, the
amount of randomness can appear to be very different from the
Shannon entropy. Indeed, various measures of...
I will report on some recent work on multiple zeta values. I
will sketch the definition of motivic multiple zeta values, which
can be viewed as a prototype of a Galois theory for certain
transcendental numbers, and then explain how they were used...
