Matroids are combinatorial abstractions of the notion of linear
independence. They are one of the main objects studied in the
current special year in the School of Mathematics. I will talk
about a notion of scattering amplitudes for matroids. It is...
Tree decompositions, and in particular path decompositions, are
a powerful tool in both structural graph theory and graph
algorithms. Many hard problems become tractable if the input graph
is known to have a tree decomposition of bounded “width”...
This talk will be about joint work with Fabian Ziltener in which
we show that a compact n-rectifiable subset of R^2n with vanishing
n-Hausdorff measure can be displaced from itself by a Hamiltonian
diffeomorphism arbitrarily close to the identity...
We introduce an SFT-type invariant for Legendrian knots in R^3,
which is a deformation of the Chekanov-Eliashberg differential
graded algebra. The differential includes components that count
index zero pseudoholomorphic disks with up to two positive...
One of the earliest achievements of mirror symmetry was the
prediction of genus zero Gromov-Witten invariants for the quintic
threefold in terms of period integrals on the mirror. Analogous
predictions for open Gromov-Witten invariants in closed...
We prove an effective equidistribution theorem for
semisimple
closed orbits on compact adelic quotients. The obtained error
depends polynomially on the minimal complexity of intermediate
orbits and the complexity of the ambient space. As an...
The second lecture features the nuts and bolts of the invariants
from first lecture, which we call foundations. We explain the
structure theorem for foundations of ternary matroids, which is
rooted in Tutte's homotopy theorem. We show how this...
The search for signs of life beyond Earth is a key motivator in
exoplanet research. A suitable “biosignature gas” is one
that: can accumulate in an atmosphere against atmospheric radicals
and other sinks; has strong atmospheric spectral features...
