Several classical results in Ramsey theory (including famous
theorems of Schur, van der Waerden, Rado) deal with finding
monochromatic linear patterns in two-colourings of the
integers. Our topic will be quantitative extensions of such
results. A...
Suppose you have a set S of integers from {1 , 2 , … , N} that
contains at least N / C elements. Then for large enough N , must S
contain three equally spaced numbers (i.e., a 3-term arithmetic
progression)?
Extremal combinatorics is a central research area in discrete
mathematics. The field can be traced back to the work of Turán and
it was established by Erdős through his fundamental contributions
and his uncounted guiding questions. Since then it has...
Suppose you have a set S of integers from {1 , 2 , … , N} that
contains at least N / C elements. Then for large enough N , must S
contain three equally spaced numbers (i.e., a 3-term arithmetic
progression)?
A central goal of physics is to understand the low-energy
solutions of quantum interactions between particles. This talk will
focus on the complexity of describing low-energy solutions; I will
show that we can construct quantum systems for which the...
Randomness is a vital resource in computation, with many
applications in areas such as cryptography, data-structures and
algorithm design, sampling, distributed computing, etc. However
generating truly random bits is expensive, and most sources
in...
In the minimum cost set cover problem, a set system is given as
input, and the goal is to find a collection of sets with minimum
cost whose union covers the universe. This NP-hard problem has long
been known to admit logarithmic approximations...
Robust sublinear expansion represents a fairly weak notion of
graph expansion which still retains a number of useful properties
of the classical notion. The general idea behind it has been
introduced by Komlós and Szemerédi around 25 years ago and...
Suppose we are given matchings M1,....,MN of size t in some
r-uniform hypergraph, and let us think of each matching having a
different color. How large does N need to be (in terms of t and r)
such that we can always find a rainbow matching of size t...