3 papers
math.CT2026
The Synthetic SierpiÅski Cone
Fredrik Bakke, Jonathan Sterling, Mark Damuni Williams +1
In domains, categories, and toposes, the SierpiÅski cone construction glues onto a space a universal closed point lying below all the other points. Although this is a lax colimit,…
math.AP2026
Propagation of nonlinear pulses near diffractive points of any order
Jian Wang, Mark Williams
We construct pulse-type approximate solutions to nonlinear hyperbolic equations near diffractive points, allowing arbitrary (even infinite) order of grazing. We show that in low re…
math.AP2025
Convex waves grazing convex obstacles to high order
Jian Wang, Mark Williams
In a recent paper [WW23] we studied the transport of oscillations in solutions to linear and some semilinear second-order hyperbolic boundary problems along rays that graze a conve…