The Lipschitz extension problem is the following basic “meta
question” in metric geometry: Suppose that X and Y are metric
spaces and A is a subset of X. What is the smallest K such that
every Lipschitz function f:A\to Y has an extension F:X\to Y...
A CSS quantum code C=(W1,W2) is a pair of orthogonal subspaces
in 𝔽n2. The distance of C is the smallest hamming weight of a
vector in W⊥1−W2 or W⊥2−W1. A large distance roughly means that the
quantum code can correct many errors that affect the...
If f is a real polynomial and A and B are finite sets of
cardinality n, then Elekes and Ronyai proved that either f(A×B) is
much larger than n, or f has a very specific form (essentially,
f(x,y)=x+y). In the talk I will tell about an analogue of...
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...
