Motivated by some work of Thurston on defining a Teichmuller
theory based on best Lipschitz maps between surfaces, we study
infinity-harmonic maps from a manifold to a circle. The best
Lipschitz constant is taken on on a geodesic lamination...
There are striking analogies between topology and arithmetic
algebraic geometry, which studies the behavior of solutions to
polynomial equations in arithmetic rings. One expression of these
analogies is through the theory of etale cohomology, which...
Suppose we have a cancellative binary associative operation * on
a finite set X. We say that it is delta-associative if the
proportion of triples x, y, z such that x*(y*z) = (x*y)*z is at
least delta.
DNA rearrangement is observed at developmental and evolutionary
scale. The recombination process can be directly modeled by
4-regular graphs and Gauss codes, also called double occurrence
words. We discuss properties of these graphs, their spatial...
A dark matter candidate lighter than about 30 eV exhibits wave
behavior in a typical galactic environment. Examples include the
QCD axion as well as other axion-like-particles. We review the
particle physics motivations, and discuss experimental and...
Following Bourgain, Gamburd, and Sarnak, we say that the Markoff
equation x2+y2+z2−3xyz=0 satisfies strong approximation at a prime
p if its integral points surject onto its Fp points. In 2016,
Bourgain, Gamburd, and Sarnak were able to establish...
This is the last talk towards understanding
Bezrukavnikov-Finkelberg's derived geometric Satake equivalence.
With the preparations from previous talks, we will introduce two
filtrations: a topological filtration on the equivariant cohomology
and an...
A countable group G is called sofic if it admits a sofic
approximation: a sequence of asymptotically free almost actions on
finite sets. Given a sofic group G, it is a natural problem to try
to classify all its sofic approximations and, more...
One of the key objectives of modern astrophysics is to
understand the formation and evolution galaxies. In this regard,
the Milky Way is a critical testing ground for our theories of
galaxy formation. However, dissecting the assembly history of
the...
