Emma Previato (1952–2022) was a formidable figure in the landscape of late 20th and early 21st-century mathematics. A scholar who bridged the gap between the abstract elegance of algebraic geometry and the pragmatic rigors of mathematical physics, Previato spent nearly four decades as a cornerstone of the Boston University faculty. Her work on "integrable systems"—physical systems that can be solved exactly—remains a vital touchstone for researchers exploring the hidden symmetries of the universe.
1. Biography: From Padua to the Ivy League
Emma Previato was born on October 20, 1952, in Badia Polesine, Italy. Her academic journey began at the University of Padua, one of the world’s oldest and most prestigious institutions, where she earned her Laurea in Mathematics in 1974.
Seeking to broaden her horizons, she moved to the United States for her doctoral studies. She attended Harvard University, where she studied under the tutelage of David Mumford, a Fields Medalist known for his transformative work in algebraic geometry. Previato earned her Ph.D. in 1985 with a dissertation titled "Hyperelliptic quasi-periodic signals in the Hirota bilinear form," which set the stage for her lifelong fascination with the intersection of geometry and differential equations.
In 1985, she joined the faculty at Boston University (BU). She rose through the ranks to become a Professor of Mathematics, a position she held until her passing in June 2022. Throughout her 37-year tenure at BU, she was not only a prolific researcher but also a dedicated educator and a fierce advocate for women in the mathematical sciences.
2. Major Contributions: The Geometry of Solitons
Previato’s primary contribution to mathematics lay in the field of Integrable Systems. While many physical phenomena are described by "chaotic" equations that can only be approximated, integrable systems possess enough internal symmetry to be solved exactly.
Finite-Gap Solutions
Previato was an expert in finding "finite-gap" solutions to non-linear partial differential equations (PDEs), such as the Korteweg-de Vries (KdV) equation, which describes shallow water waves. She used the tools of algebraic geometry—specifically the study of Riemann surfaces and Abelian varieties—to describe these waves.
The KP Hierarchy
Much of her work focused on the Kadomtsev-Petviashvili (KP) hierarchy, a set of equations used to model complex wave interactions. She explored the Sato Grassmannian, an infinite-dimensional space that acts as a unifying structure for these equations.
Spectral Curves
She developed methodologies for using "spectral curves" to linearize complex dynamical systems. By mapping a physical system onto a geometric curve, she could use the properties of the curve to predict the behavior of the system over time.
3. Notable Publications
Previato’s bibliography includes over 100 research papers and several influential books. Her writing was noted for its clarity and its ability to connect disparate fields.
- "Hyperelliptic quasi-periodic signals in the Hirota bilinear form" (1985): Her foundational work that applied algebraic geometry to the Hirota method, a key technique in soliton theory.
- "The Calogero-Moser system and the KP equation" (1994): A highly cited exploration of the relationship between particle systems and wave equations.
- "Advances in Curves, Cryptography, and Quantum Computing" (2012): As an editor and contributor, she helped bridge her geometric expertise with modern applications in computer science and security.
- "Dictionary of Applied Math for Engineers and Scientists" (Contributed Sections): Reflecting her commitment to making high-level math accessible to other disciplines.
4. Awards & Recognition
Previato’s excellence was recognized by both her peers and the broader scientific community:
- Fellow of the American Mathematical Society (AMS): She was elected to the inaugural class of Fellows in 2012, a distinction reserved for mathematicians who have made outstanding contributions to the creation, exposition, and utilization of mathematics.
- Merten M. Hasse Prize (2003): Awarded by the Mathematical Association of America (MAA) for her exceptional expository writing, specifically for her paper "The Concept of Genus," which traced the history and utility of one of geometry's most important ideas.
- Simons Foundation Fellowship: She received support from this prestigious foundation for her research in the geometric aspects of integrable systems.
- Teaching Awards: She was a recipient of the Metcalf Award for Excellence in Teaching (2001) at Boston University, one of the university’s highest honors for educators.
5. Impact & Legacy
Emma Previato’s legacy is twofold: intellectual and human.
Intellectually, she helped keep the "classical" beauty of algebraic geometry alive by showing its indispensable utility in modern physics. Her work influenced the development of Quantum Integrable Systems and Mirror Symmetry, fields that are central to contemporary theoretical physics and string theory.
Humanly, her impact was felt through her mentorship. She supervised over 20 Ph.D. students and mentored countless undergraduates. She was a tireless member of the Association for Women in Mathematics (AWM), working to dismantle the barriers that women faced in the field. She famously organized the "BU Math Salon," an informal gathering that encouraged students to view mathematics as a collaborative, creative, and joyful endeavor rather than a solitary grind.
6. Collaborations
Previato was a deeply collaborative mathematician who thrived on the exchange of ideas. Her key partnerships included:
- David Mumford: Her advisor, with whom she maintained a lifelong professional respect.
- Victor Enolski: A frequent collaborator on the study of hyperelliptic functions and their applications to physics.
- The "Integrable Systems" Community: She worked closely with scholars like J. Harnad and B.A. Dubrovin, participating in the prestigious Montreal-based research groups focused on mathematical physics.
7. Lesser-Known Facts
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Polyglot and Bibliophile
Previato was fluent in several languages and possessed a deep knowledge of classical literature. She often peppered her mathematical lectures with references to Dante, Virgil, or historical anecdotes from the Renaissance.
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Mathematical Historian
She was deeply interested in the history of her craft. She wrote extensively on the history of Italian mathematics, ensuring that the contributions of 19th-century Italian geometers were not forgotten by the modern English-speaking world.
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The "Emma Style"
Colleagues often remarked on her unique style of "blackboard mathematics." She rarely used notes, instead weaving complex geometric diagrams and equations across the board in a continuous, flowing narrative that students described as "mathematical performance art."
Emma Previato passed away on June 29, 2022. She remains remembered as a scholar who saw no boundary between the beauty of a geometric curve and the physical reality of a crashing wave, and as a mentor who believed that the highest form of mathematics was the one shared with others.