Professor Hadi Salmasian of the University of Ottawa, with Professor Vera Serganova (Department of Mathematics, University of California at Berkeley), Professor Siddhartha Sahi (Department of Mathematics, Rutgers University), and Professor Alexander Alldridge (Mathematical Institute, University of Cologne)
Department of Mathematics and Statistics
Together with the help of three international partners, Professor Hadi Salmasian has made substantial progress in solving a classical and influential mathematical problem known as the Capelli Eigenvalue Problem (CEP).
The goal of the CEP is to understand the general structure of certain algebraic transformations known in the mathematics community as "invariant differential operators". These transformations are of high importance to mathematicians and physicists because of their emergence in seemingly unrelated circumstances, such as quantum physics and abstract algebra. However, in natural coordinates, the formulas for these transformations are quite complicated. An explicit solution for the CEP will help to provide a concrete description of these transformations and a deeper understanding of their associated directional dilation ratios, which in turn play an invaluable role in many domains such as physics, algebra and combinatorics.
Together with Professors Vera Serganova (University of California at Berkeley), Siddhartha Sahi (Rutgers University, New Jersey), and Alexander Alldridge (University of Cologne, Germany), Prof. Salmasian has determined the dilation ratios for transformations acting on geometric spaces that emerge from the notion of supersymmetry in particle physics. Furthermore, recently Profs. Salmasian and Sahi discovered invariant differential operators associated to a family of interpolation polynomials that had surprisingly remained unknown for many years. The partnership to solve the CEP was conceived during a conference on campus that attracted more than 70 senior researchers, postdoctoral fellows, and graduate students to the University of Ottawa. This successful event brought substantial exposure to the Faculty of Science and the University of Ottawa, and allowed Prof. Salmasian and his collaborators to gather input for future endeavors.
Read more about the research stemming from this partnership:
- The Capelli eigenvalue problem for Lie superalgebras
- Quadratic Capelli operators and Okounkov polynomials
- Schur Q-functions and the Capelli eigenvalue problem for the Lie superalgebra q(n)