When Hilbert and Bézout Go Arithmetic

Speaker: Prof. Teresa Krick，University of Buenos Aires, Argentina     

Title: When Hilbert and Bézout Go Arithmetic

Language: English 

Time & Venue: 2026.10.29   10:00-11:00   南楼N202

Abstract: I will describe arithmetic aspects of two theorems that are fundamental pillars of algebraic geometry, which I will explain—the famous Hilbert Nullstellensatz and the Bézout inequality—as well as some of their consequences. More specifically, I will address effective questions in the case where the polynomials describing these problems have integer coefficients: I will present bounds not only for the degrees of the polynomials involved in the results, but also for the height (binary size) of their coefficients. These bounds are of interest as a measure of complexity, and they can also be useful to know a priori when applying an algorithm, or to certify results obtained with numerical algorithms, among other applications.