Clifford Geertz once quipped: “It is difficult to see what is
always there. Whoever discovered water, it was not a fish.” In the
same way, seeing familiar environments can prove challenging. Those
of us who live our lives in a given space become...
If a monomorphism of abstract groups H↪G induces an isomorphism
of profinite completions, then (G,H) is called a Grothendieck pair,
recalling the fact that Grothendieck asked about the existence of
such pairs with G and H finitely presented and...
The classification of geometric structures on manifolds
naturally leads to actions of automorphism groups, (such as mapping
class groups of surfaces) on "character varieties" (spaces of
equivalence classes of representations of surface groups).
Reproducibility is vital to ensuring scientific conclusions are
reliable, but failures of reproducibility have been a major issue
in nearly all scientific areas of study in recent decades. A key
issue underlying the reproducibility crisis is the...
A compact four dimensional completely integrable system f:M→R2
is semitoric if it has only non-degenerate singularities, without
hyperbolic blocks, and one of the components of generates a circle
action. Semitoric systems have been extensively...
Consider the action of a group on a finite-dimensional vector
space. Given some natural conditions on the group, Hilbert showed a
famous "duality" between invariant polynomials and closures of
group orbits. Namely, the orbit closure of a vector is...
I will discuss some quantitative aspects for Legendrians in a
(more or less) general contact manifold. These include lower bounds
on the number of Reeb chords between a Legendrian and its contact
Hamiltonian image, the non-degeneracy of the Chekanov...
We describe a general principle of completeness in QFT. It
asserts that the physical observable algebras produced by local
degrees of freedom are the maximal ones compatible with causality.
We elaborate on equivalent statements to this principle...
