School of Mathematics

Semidefinite programming bounds are widely used in combinatorial optimization, quantum computing and complexity theory. The first semidefinite programming bound to gain fame is the so-called theta number developed by Lov\'asz to compute the Shannon...

We shall discuss new pseudorandom generators for regular read-once branching programs of small width. A branching program is regular if the in-degree of every vertex in it is (either 0 or) 2. For every width d and length n, the pseudorandom...

In this survey I will present several extremal problems, and some solutions, concerning convex lattice polytopes.
A typical example is to determine the smallest area that a convex lattice polygon can have if it has exactly n vertices.

The mathematical problems arising from modern celestial mechanics, which originated with Isaac Newton’s Principia in 1687, have led to many mathematical theories. Poincaré (1854-1912) discovered that a system of several celestial bodies moving under...

Collateralized Default Obligations (CDOs) and related financial derivatives have been at the center of the last financial crisis and subject of ongoing regulatory overhaul.

Despite their demonstrable benefits in economic theory, derivatives suffer...

In this talk, I shall describe an ongoing project to develop a complexity theory for cryptographic (multi-party computations. Different kinds of cryptographic computations involve different constraints on how information is accessed. Our goal is to...

For four years now, we have been conducting "medium-scale" experiments in how human subjects behave in strategic and economic settings mediated by an underlying network structure. We have explored a wide range of networks inspired by generative...

The uniformity norms are defined in different contexts in order to distinguish the ``typical'' random functions, from the functions that contain certain structures. A typical random function has small uniformity norms, while a function with a non...

How many edges of the n-dimensional Boolean hypercube can be sliced by a degree-d polynomial surface? This question can be equivalently stated as "What is the maximum average sensitivity of any degree-d polynomial threshold function?" In 1994...

Algorithms spend time on performing arithmetic computations, but often more on moving data, between the levels of a memory hierarchy and between parallel computing entities. Judging by the hardware evolution of the last few decades, the fraction of...