6 papers
Sorries Are Not the Hard Part: An Expert-Review Case Study of a Semi-Autonomous Formalization
Vasily Ilin, Brian Nugent
Large language models can often close proof gaps in interactive theorem provers, but a verified theorem is not the same thing as a reusable library contribution. We study this dist…
Higher Du Bois and Higher Rational Pairs
Haoming Ning, Brian Nugent
We extend the notions of higher Du Bois and higher rational singularities to pairs in the sense of the minimal model program. We extend numerous results to these higher pairs, incl…
Moduli of Very Ample Line Bundles
Brian Nugent
Let be a projective variety over a field. In this paper, we will construct a moduli space of very ample line bundles on . In doing so, we develop a generalization of Fitting…
Extending a problem of Pillai to Gaussian lines
Elsa Magness, Brian Nugent, Leanne Robertson
Let be a primitive Gaussian line, that is, a line in the complex plane that contains two, and hence infinitely many, coprime Gaussian integers. We prove that there exists an in…
Walking to infinity on gaussian lines
Elsa Magness, Brian Nugent, Leanne Robertson
We study analogies between the rational integers on the real line and the Gaussian integers on other lines in the complex plane. This includes a Gaussian analog of Bertrands Postul…
Pure -sequences arising from -dimensional PS ear-decomposable simplicial complexes
Steven Klee, Brian Nugent
We show that the -vector of a -dimensional PS ear-decomposable simplicial complex is a pure -sequence. This provides a strengthening of Stanley's conjecture for…