Andrew J. Sommese

Vincent J. Duncan and Annamarie Micus Duncan Professor of Mathematics
Director of the Center for Applied Mathematics

B.A., Fordham University, 1969
Ph.D., Princeton University, 1973

Research Interests

My current research centers on the numerical solution of systems of polynomials in several variables that arise in engineering and science.

In the last few years I and my collaborators (Jan Verschelde, University of Illinois at Chicago: www.math.uic.edu/~jan and Charles Wampler, General Motors Research Laboratories: www.nd.edu/~cwample1) have been developing the fundamental algorithms of Numerical Algebraic Geometry, a new subject whose goal is to numerically describe and manipulate the solution sets of polynomial systems, including the positive dimensional components of the solution sets. A recent success has been our carrying out the irreducible decomposition of a complex algebraic variety numerically. One consequence of this decomposition is the first numerical algorithm to compute the precise set of isolated solutions of a polynomial system. As applications of our new algorithms, we have been investigating applied questions from the design of mechanisms and developing algorithms for theoretical questions such as how to factor polynomials in several variables over the complex numbers.

Selected Publications

• M. Beltrametti and A.J. Sommese, The adjunction theory of complex projective varieties, Expositions in Mathematics, 16 (1995), 398+xxi pages, Walter De Gruyter, Berlin.
• S. Kebekus, T. Peternell, A.J. Sommese, and J.A. Wisniewski, Projective contact manifolds, Inventiones Math. 142 (2000), 1--15.
• A.J. Sommese, J. Verschelde, and C.W. Wampler, Numerical decomposition of the solution sets of polynomial systems into irreducible components, SIAM Journal on Numerical Analysis 38 (2001), 2022--2046.
• A.J. Sommese, J. Verschelde, and C.W. Wampler, Homotopies for intersecting solution components of polynomial systems, SIAM Journal on Numerical Analysis, 42 (2004), 1552-1571.
• A.J. Sommese, C.W. Wampler, Numerical solution of polynomial systems arising in engineering and science, (2005), 401+xxii pages, World Scientific Press, Singapore.

Please direct questions and comments to: sommese@nd.edu