Tootfinder

Photos from the May 12-13 2026 #PurdueFortWayne #Commencement 🐘 🎓
https://photos.app.goo.gl/wmxvRBhYWZEz

New arXiv preprint!  With my #PurdueFortWayne colleague Yifei Pan.  🐘 Here's a thread (1/n)
https://arxiv.org/abs/2606.01447

Constructing Discontinuous but Locally Bounded Rational Functions using Łojasiewicz Inequalities
For real multivariate polynomials $P$ and $Q$ both vanishing at a point, if the zero set of $Q$ is contained in the zero set of $P$, then there exists a rational function of the form $P^{p}/Q^{q}$ which is locally bounded and such that its extension that vanishes on the zero set of $Q$ is discontinuous. The proof uses inequalities of Lojasiewicz.