Elliptic, Yangian-Invariant "Leading Singularity".

We derive closed formulas for the first examples of nonalgebraic, elliptic "leading singularities" in planar, maximally supersymmetric Yang-Mills theory and show that they are Yangian invariant.

All-Multiplicity Nonplanar Amplitude Integrands in Maximally Supersymmetric Yang-Mills Theory at Two Loops.

We give a prescriptive representation of all-multiplicity two-loop maximally-helicity-violating (MHV) amplitude integrands in fully-color-dressed (nonplanar) maximally supersymmetric Yang-Mills theory.

Deep Into the Amplituhedron: Amplitude Singularities at All Loops and Legs.

In this Letter we compute a canonical set of cuts of the integrand for maximally helicity violating amplitudes in planar N=4 supersymmetric Yang-Mills theory, where all internal propagators are put on shell. These "deepest cuts" probe the most complicated Feynman diagrams and on-shell processes that can possibly contribute to the amplitude, but are also naturally associated with remarkably simple geometric facets of the amplituhedron. The recent reformulation of the amplituhedron in terms of combinatorial geometry directly in the kinematic (momentum-twistor) space plays a crucial role in understanding this geometry and determining the cut.

Regular and chaotic dynamics of a piecewise smooth bouncer.

The dynamical properties of a particle in a gravitational field colliding with a rigid wall moving with piecewise constant velocity are studied. The linear nature of the wall's motion permits further analytical investigation than is possible for the system's sinusoidal counterpart. We consider three distinct approaches to modeling collisions: (i) elastic, (ii) inelastic with constant restitution coefficient, and (iii) inelastic with a velocity-dependent restitution function.