# Emma Previato

Emma Previato (November 29, 1952 – June 29, 2022) was an Italian-born, American mathematician, specializing in algebraic geometry and partial differential equations. She was elected a Fellow of the American Mathematical Society in 2012.

## Quotes

* The nature of theta functions 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 PDEs that have KP as a prototype.
* "Theta functions, old and new by Emma Previato". The Ubiquitous Heat Kernel: AMS Special Session, the Ubiquitous Heat Kernel, October 2-4, 2003, Boulder, Colorado. Contemporary Mathematics, volume 398. American Mathematical Society. 2006. pp. 347–367. doi:10.1090/conm/398/07496. ISBN 9780821836989. edited by Jay Jorgensen & Lynn Walling
* 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) Hitchin systems, is interpreted in the setting of the classical geometry of Klein's quadratic complex, following the Newstead and Narasimhan-Ramanan programme of studying moduli spaces through projective models.
** "Chapter 11. Dualities on 𝒯$^∗$𝒮𝒰$_X$(2,𝒪$_X$) by Emma Previato". Moduli Spaces and Vector Bundles. Cambridge University Press. 2009. pp. 367–387. ISBN 9780521734714. edited by Steve B. Bradlow, Leticia Brambila-Paz, Oscar García-Prada, & Sundararaman Ramanan
* ... 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 other's progress. I am inspired to see more intentional examples of mentoring taking panel for women and girls interested in the STEM field.
** "Chapter 10. Mentoring Practices for Female Faculty: The Role of Professional Networks by Emma Previato". Mentoring Away the Glass Ceiling in Academia: A Cultured Critique. Lexington Books. 10 June 2015. ISBN 9781498515313. p. 176 (edited by Brenda Marina; quote from pp. 175–176; See Every Other Thursday by Ellen Daniell.)

## External links

Encyclopedic article on Emma Previato on Wikipedia