Alexander R. Its, Distinguished Professor

 

Alexander R. Its Department of Mathematical Sciences School of Science IUPUI

Interim President Gerald Bepko, Its and IUPUI Acting Chancellor William Plater at the Founders Day ceremony

Alexander Its works at the interface between mathematics and physics and has been a central figure in the development of the theory of integrable systems for the past 25 years.

Although the origin of the theory of integrable systems can be traced back to the 19th century or even earlier, the modern era of the subject began in 1967 with the discovery of what was then believed to be a rather specialized technique for solving the Korteweg–de Vries (KdV) equation from the nonlinear theory of water waves. Since then, the subject has undergone almost explosive development, and the resulting analytical framework has been considered one of the great achievements of the mathematical and physical sciences in the second half of the 20th century.

According to colleagues, Its has had a vital hand in almost every aspect of the field. Among his acclaimed achievements is his derivation—collaborating with his mentor V. Matveev and using techniques of algebraic geometry—of an elegant formula that describes certain periodic solutions of the KdV equation. This formula and its subsequent generalizations for a host of other nonlinear evolution equations are now ubiquitous in the theory of integrable systems and constitute one of the basic building blocks of the subject.

In the mid-1980s, Its published his now classic monograph, The Isomonodromic Deformation Method in the Theory of Painlevé Equations, which he co-authored. This work has revolutionized the study of special functions by recasting the subject in a nonlinear setting.

Its also has played a pivotal role in the development of the Riemann-Hilbert (RH) approach to the study of evolution equations. His algebro-geometric and isomonodromic approaches to the study of nonlinear evolution equations, nonlinear special functions and the RH method have become a powerful arsenal of analytic tools for tackling fundamental problems arising from many areas of modern mathematics and physics.

To date, Its has published more than 80 research papers and four books, and given more than 100 invited lectures at leading institutions and scientific meetings all over the world. Aside from his research accomplishments, Its also is very much in demand as an organizer of research conferences.

A distinguished panel of Its’ peers has described him as “one of the best applied mathematicians of our time” and his work as “definitive, revolutionary and transformative.”

For a quarter of a century, Alexander Its has been a central figure in the development of the theory of integrable systems. His peers consider him one of the best applied mathematicians of our time and his work ‘definitive, revolutionary and transformative.’