Andrew Sommese
Duncan Professor of Mathematics
Department of Applied & Computational Mathematics & Statistics
University of Notre Dame        

Notre Dame, Indiana 46556

(574) 631-6498 (Office: Hurley 156A)
(574) 631-8630 (Department)

sommese@nd.edu

 

 
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My current research is in Numerical Algebraic Geometry and the numerical solution of systems of nonlinear differential equations. 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.


For details on numerical algebraic geometry see my book with Charles Wampler, NUMERICAL SOLUTION OF POLYNOMIAL SYSTEMS ARISING IN ENGINEERING AND SCIENCE. Here is a list of errata for the book. A SIAM book NUMERICALLY SOLVING POLYNOMIAL SYSTEMS WITH BERTINI by Daniel Bates, Jonathan Hauenstein, Andrew Sommese, and Charles Wampler will be in print soon.

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), that was the first cluster for our numerical work. We have a new cluster, skoll.  Skoll has 296 cores: 28 nodes with two quad-Xeon 5410’s and 8 GB RAM; 9 nodes with two quad-Xeon E5520’s and 12 GB RAM; plus a 16 terabyte disk array.


Assorted information:


Click here for the webpage of ACMS 40485 (Applied Complex Analysis): Fall 2013.

Click here for the webpage of ACMS 60690 (Numerical Analysis I): Fall 2012.

Click here for the webpage of ACMS 750 (Introduction to Applied Mathematics II): Spring 2012.

Click here for the webpage of ACMS 550 (Introduction to Applied Mathematics I): Fall 2011.

Click here for the webpage of ACMS 750 (Introduction to Applied Mathematics II): Spring 2011.

Click here for the webpage of ACMS 550 (Introduction to Applied Mathematics I): Fall 2010.

Click here for the webpage of Mathematics 790 (Numerical Analysis II): Spring 2010.

Click here for the webpage of Mathematics 690 (Numerical Analysis I): Fall 2009.

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.

 

Last updated December 9, 2012.