Andrew J. Sommese's Home Page

Picture of Andrew Sommese Andrew Sommese
Director, Center for Applied Mathematics
Duncan Professor of Mathematics
Department of Mathematics
University of Notre Dame
Notre Dame, Indiana 46556-4618

(574) 631-6498 (Office: Hurley 291)
(574) 631-7245 (Department)
(574) 631-6579 (Fax)

sommese @nd.edu

My current research is in Numerical Algebraic Geometry. This work involves the numerical solution of polynomial systems and the numerical manipulation of the solution sets. A major focus of this work is the solution of systems of polynomials arising in engineering and science, and in particular the theory of mechanisms.

Bertini is a new software package that Daniel J. Bates, Jonathan D. Hauenstein, Charles W. Wampler, and I have created to carry out numerical algebraic geometry computations.

My new book with Charles Wampler, NUMERICAL SOLUTION OF POLYNOMIAL SYSTEMS ARISING IN ENGINEERING AND SCIENCE, has appeared. Here is a list of errata for the book.

One particularly interesting example (studied by Husty and Karger) discussed in this book is the Griffis-Duffy platform robot, a special type of Stewart-Gough platform robot, that moves when all legs are held to be fixed length. Here is a movie made by Charles Wampler showing the motion of of an example of type GD1 having a degree 28 motion curve as the locus of its motion. It is in AVI format, which plays on PCs using the Windows Media Player. The starOfDavid.mw is a Maple 9.5 worksheet showing one of the movements of the special Stewart-Gough platform robot two parallel isomorphic equilateral triangular plates with legs of fixed length set so that after a 90 degree turn, the upper plate triangle is exactly on the lower triangle. At the start of the movement, viewed directly above the two plates form a star of David.

Read a popularization of some of my work here.

Click here here, for a picture of runge (on the right). Runge (named after the famous German numerical and complex analyst) is an eight node dual opteron 250 cluster (with a two terabyte disk array) from Western Scientific, that we are using for our numerical work. We have added a second cluster, skoll, that is linked to runge: skoll is a 28 node (each node having two quad-Xeon 5410’s and 8 GB RAM) from Western Scientific.

Assorted information:

Biography and List of Publications (pdf-file); (postscript-file); (LaTeX-file); (dvi-file)
Some Preprints
Slides of my talk, Numerical Algebraic Geometry, at the Satellite Conference on Algebraic Geometry, Segovia, Spain, August 16-19, 2006.
Slides of my talk, Exceptional Sets and Fiber Products, at the Komplexe Analysis Workshop, Mathematische Forschungsinstitut Oberwolfach, Germany, August 27 - September 1, 2006.
Slides of my September 13, 2006 talk, Solving Polynomial Systems by Homotopy Continuation, at the Algebraic Geometry and Applications Seminar of the Institute for Mathematics and Its Applications (IMA), University of Minnesota, Minneapolis.
Slides of my October 5, 2006 colloquium talk, Computing the Genus of a Curve Numerically, in the School of Mathematics at the University of Minnesota.
Slides of my October 2, 2007 talk, Recent Results in Numerical Algebraic Geometry, in the Commutative Algebra and Algebraic Geometry Seminar at the University of California at Berkeley.
Slides on Alt's Problem.

Click here for the webpage of Mathematics 790 (Computational Differential Equations): Spring 2009.

Click here for the webpage of Mathematics 850 (Applied Probability): Fall 2008.

Click here for the webpage of Mathematics 610 (Discrete Mathematics): Spring 2008.

Click here for the webpage of Mathematics 850 (Applied Probability): Fall 2007.

Click here for the webpage of Mathematics 860 (Stochastic Modeling): Spring 2006.

Click here for the webpage of Mathematics 850 (Applied Probability): Fall 2005.

Click here to go to the webpage for Mathematics 328 (Probability and Statistics): Spring 2005.

Click here to go to the webpage for Mathematics 617 (Numerical Analysis): Fall 2004.

Click here to go to the home page of Center for Applied Mathematics, which I became Director of on July 1, 2005.

Click here to go to the Department of Mathematics home page.

Click here to go to the College of Science home page.

Click here to go to the University of Notre Dame home page.

Click here, here, and here for a few beautiful places to hike to in Glacier Park.

Click here, here, and here for some beautiful places to hike to in the Canadian Rockies.

We did the strikingly beautiful "Akamina Ridge Hike from Forum Lake to Wall Lake" in August 2007 at the Akamina-Kishinena Park in British Columbia (next to Waterton Park). Here are some photos from the hike: the location, Forum Lake, above Wall Lake, part of the ridge we hiked, more of the ridge, and some more. Here is a "triple lake" seen on the descent from Carthew Summit at Waterton.

You are visitor number since May 22, 2006.

Last updated April 2, 2008.