In this talk, I will begin with a quick primer to parameterized
complexity, present some key insights from recent hardness of
approximation results in the area, and end with a proof sketch of
the following result: Assuming the Exponential Time...
I’ll describe recent work for approaching certain functional
transcendence problems through a combination of model theory and
differential Galois theory. This is based on joint work with
Blazquez-Sanz, Casale, and Nagloo.
Let $k$ be a field and $X$ a geometrically connected variety
over $k$. The Tate or degeneracy locus of a $l$-adic local system
on $X$ is the etale counterpart of the Hodge locus of a VHS. While
in the last decade tremendous progresses have been made...
The cohomology of a family of algebraic varieties carries a
number of interrelated structures, of both Hodge-theoretic and
arithmetic flavors. I’ll explain joint work with Josh Lam
developing analogues of some of these structures and
interrelations...
In 1984 W. B. Johnson and J. Lindenstrauss showed that a random
projection of an arbitrary point set S into low-dimensional space
is approximately distance-preserving, as long as S is of size at
most exponential in the target dimension. The...
Building on previous work of Satake and Baily, Baily and Borel
proved in 1966 that arithmetic locally symmetric varieties admit
canonical projective compactifications whose graded rings of
functions are given by automorphic forms. Such varieties...
Let K be the function field of a smooth projective curve B over
the complex numbers and let g be a positive integer. The uniform
boundedness conjecture predicts that there exists a constant N,
depending only on g and K, such that for any g...
Globally valued fields form a generalisation of global fields
that fits into the context of first order (continuous) logic. I
will describe these structures, and outline how they are connected
to various parts of arithmetic geometry: Arakelov...
I'll introduce o-minimality from a user's perspective assuming
zero background. I'll talk about some of the main examples of
o-minimal structures: as a user of o-minimality your first goal is
to find out whether your favorite set lives in one of...
Given a one-parameter degenerating family of rational maps on
the projective line, it is possible to construct a non-archimedean
limit which captures how this family degenerates. Recently,
Luo used ultrafilters to construct limits for an arbitrary...
