I will present and discuss new analytical solutions to high
eccentricity perturbed Keplerian orbits undergoing Kozai-Lidov
oscillations. In particular, I will show that the complex dynamics
of hierarchical few body stellar systems - can be reduced...
I will employ twistor string theory to construct a bulk dual of
N = 4 super Yang-Mills in the regime of weak 't Hooft coupling. I
will also discuss applications of this duality to the study of
scattering amplitudes, giant graviton correlators, and...
Every o-minimal structure determines a collection of "tame" or
"definable" subsets of bbRn. We can then ask about the fragment of
complex geometry present in the structure: Which holomorphic
functions are definable, and which spaces are cut out by...
We present solutions to two problems on indefinite integral
ternary quadratic forms. The first, highlighted by Margulis in
1990, concerns the distribution of the ternary Markoff spectrum
associated with minima of forms. The second, initiated by...
In the theory of error-correcting codes, list decoding allows a
decoder to output a list of candidates when attempting to remove
noise from a corrupted input. The constructions and algorithms for
such list decodable codes has had numerous...
This talk, which is based on two joint works, one with Pedro
Salomão and Richard Siefring and another with Michael Hutchings and
Vinicius Ramos, revolves around the role that restrictions on the
knot types of periodic Reeb orbits imposed by the...
The ubiquity of substructures in protoplanetary discs has opened
debate regarding the alignment of planet formation timescales with
protostellar disc evolution. Under the hypothesis of the planetary
interpretation, a robust conclusion is that a...
I will prove Gromov's conjecture that every 3-manifold of
positive scalar curvature contains a short closed geodesic. The
proof uses Min-Max theory of minimal surfaces and a combinatorial
version of mean curvature flow. Time permitting, I will...
