Big numbers matter too!

Consider the number 61,917,364,224. What's so special about it? Nothing really comes to mind. But this exact number was crucial towards a two-sentence published paper that gave a counterexample to one of Euler's famous conjectures that tried to generalize Fermat's Last Theorem. In this talk, I'll discuss why we can't just assume conjectures from famous people are "obviously'' true. This talk is a recap and continuation from last semester.

Max Engelstein - Winding for Wave Maps

Wave maps are harmonic maps from a Lorentzian domain to a Riemannian target. Like solutions to many energy critical PDE, wave maps can develop singularities where the energy concentrates on arbitrary small scales but the norm stays bounded. Zooming in on these singularities yields a harmonic map (called a soliton or bubble) in the weak limit. One fundamental question is whether this weak limit is unique, that is to say, whether different bubbles may appear as the limit of different sequences of rescalings.

Digging through DiRT: Investigating how Trap Recharge Time Influences the Statistics of Particle Diffusion

Many diverse biological systems are described by randomly moving particles that can be captured by traps in their environment. Examples include neurotransmitters diffusing in the synaptic cleft before binding to receptors, the delivery of nanoparticles to targeted receptors, and prey roaming an environment before being captured by predators.