Emma Previato

"The notion of Algebraic Complete Integrability (ACI) of certain mechanical systems, introduced the early 1980s, has given great impetus to the study of moduli spaces of holomorphic vector bundles over an algebraic curve (or a higher-dimensional variety, still at a much less developed stage). Several notions of duality have been the object of much interest in both theories. There is one example, however, that appears to be a beautiful isolated feature of genus-2 curves. In this note such example, which belongs to a universal class of ACIs, namely (generalized) s, is interpreted in the setting of the classical geometry of Kleins quadratic complex, following the Newstead and Narasimhan-Ramanan programme of studying moduli spaces through projective models."

"The nature of s comes down to a differential equation and a duality. The interplay between the two variables is still something of a mystery (to this writer). By virtue of the lattice of periods, the theta function is at the same time one of the most powerful objects of algebraic geometry. Much classical mathematics of curve theory (Riemann surfaces) is derived using this algebraic aspect. The key idea is to interpret the moduli space of line bundles over the curve as a principally polarized abelian variety. Exploitng its self-dual property provides two variables whose duality establishes a linearization of the class of non-linear s that have as a prototype."

"... As a mathematician coming of age in the early years when women were underrepresented, namely the 1970s, I received informal mentoring in the form of experiential advice from rare encounters with females who had achieved professional recognition; their words of wisdom were substantive resources that allowed me to persevere. I am inspired by the book Every Other Thursday (Daniell 2006) which tells the story of a group of professional women, including scientists, university professors, and administrators, who met twice a month for twenty-five years, establishing specific practices such as goal setting, networking, and checking on each others progress. I am inspired to see more intentional examples of mentoring taking panel for women and girls interested in the ."