In this talk I want to discuss two related questions about the
variational structure of the Yang-Mills functional in dimension
four. The first is the question of 'gap' estimates; i.e.,
determining an energy threshold below which any solution
must...
I will give a tour of some of the key concepts and ideas in
proof complexity. First, I will define all standard propositional
proof systems using the sequent calculus which gives rise to a
clean characterization of proofs as computationally limited...
I will discuss some current joint work with Helmut Hofer, in
which we define and establish properties of a new class of
pseudoholomorhic curves (feral J-curves) to study certain
divergence free flows in dimension three. In particular, we show
that...
The goal is to describe how techniques from symplectic dynamics
can be used to study orbit travel in three dimensions, for systems
like the restricted 3-body problem from celestial mechanics. The
pseudo-holomorphic curve theory initiated by Hofer...
We show that, as a consequence of a remarkable new result of
Attila P\'or on universal Tverberg partitions, any large-enough set
$P$ of points in $\Re^d$ has a $(d+2)$-sized subset whose Radon
point has half-space depth at least $c_d \cdot |P|$...
We consider a system of two interacting one-dimensional
quasiperiodic particles as an operator on $\ell^2(\mathbb Z^2)$.
The fact that particle frequencies are identical, implies a new
effect compared to generic 2D potentials: the presence of large...
The thesis of Akshay Venkatesh obtains a ``Beyond Endoscopy''
proof of stable functorial transfer from tori to ${\rm SL}(2)$, by
means of the Kuznetsov formula. In this talk, I will show that
there is a local statement that underlies this work...
A decades-old application of the second variation formula proves
that if the scalar curvature of a closed 3--manifold is bounded
below by that of the product of the hyperbolic plane with the line,
then every 2--sided stable minimal surface has...
Will this procedure be finite or infinite? If finite, how long
can it last? Bjorner, Lovasz, and Shor asked these questions in
1991 about the following procedure, which goes by the name “abelian
sandpile”: Given a configuration of chips on the...
