fundamental theorem in linear algebra is that any real n x d
matrix has a singular value decomposition (SVD). Several important
numerical linear algebra problems can be solved efficiently once
the SVD of an input matrix is computed: e.g. least...
There are two important measures of the complexity of a boolean
function: the sensitivity and block sensitivity. Whether or not
they are polynomial related remains a major open question. In this
talk I will survey some known results on this...
We discuss three areas of algorithmic game theory that have
grappled with intractability. The first is the complexity of
computing game-theoretic equilibria, like Nash equilibria. There is
an urgent need for new ideas on this topic, to enable...
I will continue the exposition of different derandmization
techniques for probabilistic logspace algorithms.
The material of this talk will assume only little knowledge from
the first talk.
Since the foundational results of Thomason and
Chung-Graham-Wilson on quasirandom graphs over 20 years ago, there
has been a lot of effort by many researchers to extend the theory
to hypergraphs. I will present some of this history, and
then...
The trace formula has been the most powerful and mainstream tool
in automorphic forms for proving instances of Langlands
functoriality, including character relations. Its generalization,
the relative trace formula, has also been used to prove...
Fundamental questions in basic and applied ecology alike involve
complex adaptive systems, in which localized interactions among
individual agents give rise to emergent patterns that feed back to
affect individual behavior. In such systems, a...
