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IMA Annual Program Year Workshop

Non-Linear Computational Geometry

May 29-June 2, 2007
Organizers:
Ioannis Z. Emiris Informatics & Telecommunications, National University of Athens
Ron Goldman Computer Science, Rice University
Frank Sottile Mathematics, Texas A&M University
Thorsten Theobald Fachbereich Informatik und Mathematik, J.W. Goethe-Universität

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Abstracts and Talk Materials Dining Guide
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Description:

One of the original goals in the historical development of algebraic geometry was to understand the behavior of curves and surfaces in three dimensions. The recent theoretical and technological advances in areas such as Robotics, Manufacturing, Computer Vision and Computer-Aided Geometric Design, in synergy with the increased availability of computational resources, have brought this aspect once more into the forefront of research.

Mechanical design problems (like the relatively simple device known as the Stewart platform), or questions such as the determination of all aspects graphs in computer vision or the implicitation of surfaces, can prove extremely challenging from the computational algebraic geometry perspective. The need for reliable algorithms for these and other problems has provided stimulus for an exciting new array of closely interrelated techniques, that include both symbolic and numerical elements, and that are increasingly demonstrating their practical relevance. Applications of algebraic geometry in these areas are expected to interact well with the proven techniques of piecewise-linear computational geometry (e.g. Voronoi diagrams, hyperplane arrangements).

This workshop will explore the applications of algebraic tools in computational geometry. Tools from Elimination Theory and Resultants will play an important role, as will effective methods in real algebraic geometry (e.g., the work of Emiris, Gonzalez-Vega, Manocha, Mourrain, Roullier, Sottile, etc.). The results have encouraged research directions emphasizing the complexity-theoretic aspects (e.g., the work of Basu), but also have enabled many successful applications in computer vision and geometric design (e.g. Petitjean, Pottmann, Sederberg, etc.).

Monday, May 28 is Memorial Day, a national holiday. The IMA is closed.

Schedule
Tuesday | Wednesday | Thursday | Friday | Saturday | 
  Tuesday, May 29
8:15a-9:00a Registration and coffee   EE/CS 3-176
9:00a-9:15a Welcome and introduction Douglas N. Arnold (University of Minnesota) EE/CS 3-180
9:15a-10:05a The bitstream Descartes method Kurt Mehlhorn (Max-Planck-Institut für Informatik) EE/CS 3-180
10:05a-10:40a Coffee   EE/CS 3-176
10:40a-11:30a Discrete geometry processing with topological guarantees Dinesh Manocha (University of North Carolina) EE/CS 3-180
11:25a-1:30p Lunch    
1:30p-2:00p Resultants of polynomials with two separated variables Andre Galligo (Université de Nice Sophia Antipolis) EE/CS 3-180
2:00p-2:30p Fast and exact geometric analysis of real algebraic plane curves Nicola Wolpert (Stuttgart University of Applied Sciences) EE/CS 3-180
2:30p-3:10p Coffee   EE/CS 3-176
3:10p-3:40p The Voronoi diagram of three lines Sylvain Lazard (Institut National de Recherche en Informatique Automatique (INRIA)-Lorraine) EE/CS 3-180
3:50p-4:20p Second Chances   EE/CS 3-180
4:20p-4:30p Group Photo   EE/CS 3-180
4:30p-6:30p Reception and Poster Session
Lind Hall 400
Real-time algebraic surface visualization Tor Dokken (SINTEF)
The Voronoi circle of smooth closed curves Ioannis Z. Emiris (National University of Athens)
Linear precision for toric patches Luis Garcia-Puente (Texas A & M University)
An algorithm for lifting points in a tropical variety Anders Nedergaard Jensen (Aarhus University)
Hannah Markwig (University of Minnesota)
Thomas Markwig (Universität Kaiserslautern)
Arrangements of real algebraic plane curves Michael Kerber (Max-Planck-Institut für Informatik)
Detecting and handling degeneracies for robust boundary evaluation John Keyser (Texas A & M University)
Towards a list of challenging visualization problems in real algebraic geometry Oliver Labs (Universität des Saarlandes)
Static balancing of parallel mechanisms Brian Moore (Johann Radon Institute for Computational and Applied Mathematics )
Guided surfaces Jorg Peters (University of Florida)
Discriminants and new real topological complexity bounds J. Maurice Rojas (Texas A & M University)
Linkage problems and real algebraic geometry Reinhard Steffens (Johann Wolfgang Goethe-Universität Frankfurt)
Real solving bivariate polynomial systems: theory and maple implementation Elias P. Tsigaridas (Institut National de Recherche en Informatique Automatique (INRIA))
An implicit equation of a canal surface Severinas Zube (Vilnius State University)
  Wednesday, May 30
8:30a-9:00a Coffee   EE/CS 3-176
9:00a-9:50a New methods for computing the topology of algebraic curves and surfaces Bernard Mourrain (Institut National de Recherche en Informatique Automatique (INRIA)) EE/CS 3-180
9:50a-10:30a Coffee   EE/CS 3-176
10:30a-11:00a Implicitization of rational surfaces via linear syzygies Laurent Busé (Institut National de Recherche en Informatique Automatique (INRIA)) EE/CS 3-180
11:00a-11:30a On protocols for the automatic discovery of elementary geometry theorems Tomas Recio (University of Cantabria) EE/CS 3-180
11:30a-2:00p Lunch    
2:00p-2:30p Sextics and spheres Ciprian S. Borcea (Rider University) EE/CS 3-180
2:30p-3:00p Helly-type theorems for line transversals to disjoint balls Xavier Goaoc (Institut National de Recherche en Informatique Automatique (INRIA)-Lorraine) EE/CS 3-180
3:00p-3:30p Coffee   EE/CS 3-176
3:30p-4:00p Rational convolution surfaces of quadratic Bezier triangles Martin Peternell (Technische Universität Wien) EE/CS 3-180
4:10p-4:40p Second Chances   EE/CS 3-180
  Thursday, May 31
8:30a-9:00a Coffee   EE/CS 3-176
9:00a-9:50a Geometry and computation of mesh surfaces with planar hexagonal faces Wenping Wang (University of Hong Kong) EE/CS 3-180
9:50a-10:30a Coffee   EE/CS 3-176
10:30a-11:20a Rational surfaces with rational offsets and their applications to blending constructions Rimvydas Krasauskas (Vilnius State University) EE/CS 3-180
11:20a-1:30p Lunch    
1:30p-2:00p Real monoid surfaces Ragni Piene (University of Oslo) EE/CS 3-180
2:00p-2:30p Approximate implicitization and CAD-type intersection algorithms Tor Dokken (SINTEF) EE/CS 3-180
2:30p-3:10p Coffee   EE/CS 3-176
3:10p-3:40p Geometric applications of the Bezout matrix in the bivariate tensor-product Lagrange basis Laureano Gonzalez-Vega (University of Cantabria) EE/CS 3-180
3:50p-4:20p Second Chances   EE/CS 3-180
6:30p-8:30p Group Dinner at Caspian Bistro   Caspian Bistro 2418 University Ave SE Minneapolis, MN 55414 (612) 623-1113 
  Friday, June 1
8:30a-9:00a Coffee   EE/CS 3-176
9:00a-9:50a Application of algebraic geometry to kinematics Manfred Husty (Leopold-Franzens Universität Innsbruck) EE/CS 3-180
9:50a-10:30a Coffee   EE/CS 3-176
10:30a-11:20a Geometric representation of rigidity-related matroids Ileana Streinu (Smith College) EE/CS 3-180
11:20a-1:30p Lunch    
1:30p-2:00p Geometric and topological inference in the non linear realm: on the importance of singularity theory Frederic Cazals (Institut National de Recherche en Informatique Automatique (INRIA)) EE/CS 3-180
2:00p-2:30p Bezier subdivision for inverse molecular kinematics Ming Zhang (University of Texas) EE/CS 3-180
2:30p-3:10p Coffee   EE/CS 3-176
3:10p-3:40p Bezout's theorem and implicitization Carlos D'Andrea (University of Barcelona) EE/CS 3-180
3:50p-4:20p Second Chances   EE/CS 3-180
  Saturday, June 2
8:30a-9:00a Coffee   EE/CS 3-176
9:00a-9:50a Algebraic splines for molecular modeling Chandrajit L. Bajaj (University of Texas) EE/CS 3-180
9:50a-10:30a Coffee   EE/CS 3-176
10:30a-11:20a Topics in curve and surface implicitization David A. Cox (Amherst College) EE/CS 3-180
11:30a-12:00p Second Chances and closing remarks   EE/CS 3-180

LIST OF CONFIRMED PARTICIPANTS

Name Department Affiliation
Iman Aganj Department of ECE University of Minnesota
Pankaj Kumar Agarwal Department of Computer Science Duke University
Douglas N. Arnold Institute for Mathematics and its Applications University of Minnesota
Donald G. Aronson Institute for Mathematics and its Applications University of Minnesota
Xue Bai Department Electrical and Computer Engineering University of Minnesota
Chandrajit L. Bajaj Department of Computer Science University of Texas
Hélène Barcelo Department of Mathematics and Statistics Arizona State University
Phillip Barry Department of Computer Science and Engineering University of Minnesota
Saugata Basu School of Mathematics Georgia Institute of Technology
Daniel J. Bates Institute for Mathematics and its Applications University of Minnesota
Ciprian S. Borcea Department of Mathematics Rider University
Laurent Busé Project GALAAD Institut National de Recherche en Informatique Automatique (INRIA)
Frederic Cazals Project Geometrica Institut National de Recherche en Informatique Automatique (INRIA)
Adarsh Chandran Department of ECE University of Minnesota
Ionut Ciocan-Fontanine Institute for Mathematics and its Applications University of Minnesota
David A. Cox Department of Mathematics and Computer Science Amherst College
Carlos D'Andrea Departament d'Algebra i Geometria University of Barcelona
Alicia Dickenstein Departamento de Matematica - FCEyN University of Buenos Aires
Sandra Di Rocco Department of Mathematics Royal Institute of Technology (KTH)
Tor Dokken Department of Geometry SINTEF
Kenneth R. Driessel Department of Mathematics Iowa State University
Fayssal El Moufatich Department of Intelligent Transportation Systems (VPE-ITS) Vodafone Group R&D Germany
Ioannis Z. Emiris Department of Informatics and Telecommunications National University of Athens
Makan Fardad Department of Electrical and Computer Engineering University of Minnesota
Michael S. Floater Department of Informatics University of Oslo
Andre Galligo Department of Mathematics Université de Nice Sophia Antipolis
Luis Garcia-Puente Department of Mathematics Texas A & M University
Tryphon T. Georgiou Department of Electrical Engineering University of Minnesota
Xavier Goaoc Project Vegas Institut National de Recherche en Informatique Automatique (INRIA)-Lorraine
Ron Goldman Department of Computer Science Rice University
Laureano Gonzalez-Vega Departamento de Matemáticas University of Cantabria
Jason E. Gower Institute for Mathematics and its Applications University of Minnesota
Milena Hering Institute for Mathematics and its Applications University of Minnesota
Christopher Hillar Department of Mathematics Texas A & M University
Benjamin J. Howard   University of Minnesota
Evelyne Hubert Project CAFE Institut National de Recherche en Informatique Automatique (INRIA)
Manfred Husty Institute for Engineering Mathematics Leopold-Franzens Universität Innsbruck
Farhad Jafari Department of Mathematics University of Wyoming
Ravi Janardan Department of Computer Science and Engineering University of Minnesota
Itnuit Janovitz-Freireich Department of Mathematics North Carolina State University
Anders Nedergaard Jensen Institut for Matematiske Fag Aarhus University
Gabriela Jeronimo Departamento de Matematica - FCEyN University of Buenos Aires
Steve Kaliszewski Department of Mathematics and Statistics Arizona State University
Michael Kerber Algorithms and Complexity Max-Planck-Institut für Informatik
Michael Kettner School of Mathematics Georgia Institute of Technology
John Keyser Department of Computer Science Texas A & M University
Rimvydas Krasauskas Department of Mathematics and Informatics Vilnius State University
Song-Hwa Kwon   University of Minnesota
Oliver Labs Mathematik und Informatik Universität des Saarlandes
Niels Lauritzen Institut for Matematiske Fag Aarhus University
Sylvain Lazard Project Vegas Institut National de Recherche en Informatique Automatique (INRIA)-Lorraine
Anton Leykin Institute for Mathematics and its Applications University of Minnesota
Hstau Y Liao   University of Minnesota
Gennady Lyubeznik School of Mathematics University of Minnesota
Dinesh Manocha Department of Computer Science University of North Carolina
Hannah Markwig   University of Minnesota
Thomas Markwig Department of Mathematics Universität Kaiserslautern
Kurt Mehlhorn Max Planck Institute Max-Planck-Institut für Informatik
Richard B. Moeckel School of Mathematics University of Minnesota
Brian Moore Department of Symbolic Computation Johann Radon Institute for Computational and Applied Mathematics
Bernard Mourrain Project GALAAD Institut National de Recherche en Informatique Automatique (INRIA)
Uwe Nagel Department of Mathematics University of Kentucky
Jiawang Nie   University of Minnesota
Dmitrii Pasechnik School of Physical and Mathematical Sciences Nanyang Technological University
Martin Peternell Geometric Modeling and Industrial Geometry Technische Universität Wien
Jorg Peters Computer Information Science and Engineering Department University of Florida
Ragni Piene Centre of Mathematics for Applications University of Oslo
Mary Porter Department of Genetics, Cell Biology, and Development University of Minnesota
Bharath Rangarajan Department of Mechanical Engineering University of Minnesota
Tomas Recio Departamento de Matemáticas, Estadística y Computación. University of Cantabria
Victor Reiner School of Mathematics University of Minnesota
Joel Roberts School of Mathematics University of Minnesota
Marie Rognes   University of Oslo
J. Maurice Rojas Department of Mathematics Texas A & M University
Stergios I. Roumeliotis Department of Computer Science and Engineering University of Minnesota
Bjarke Hammersholt Roune Department of Mathematics Aarhus University
David Rusin Department of Mathematical Sciences Northern Illinois University
Arnd Scheel Institute for Mathematics and its Applications University of Minnesota
Chehrzad Shakiban Institute of Mathematics and its Application University of Minnesota
Frank Sottile Department of Mathematics Texas A & M University
Steven Sperber School of Mathematics University of Minnesota
Reinhard Steffens Department of Computer Science and Mathematics Johann Wolfgang Goethe-Universität Frankfurt
Ileana Streinu Department of Computer Science Smith College
Agnes Szanto Department of Mathematics North Carolina State University
Thorsten Theobald Department of Computer Science and Mathematics Johann Wolfgang Goethe-Universität Frankfurt
Louis Theran Department of Computer Science University of Massachusetts
Carl Toews   University of Minnesota
Nikolas Trawny Department of Computer Science and Engineering University of Minnesota
Elias P. Tsigaridas projet VEGAS Institut National de Recherche en Informatique Automatique (INRIA)
John Voight   University of Minnesota
Wenping Wang Department of Computer Science University of Hong Kong
Nicola Wolpert Faculty of Geomatics, Computer Science and Mathematics Stuttgart University of Applied Sciences
William Wood Department of Modeling and Simulation Corning
Fei Yang Department of Biomedical Engineering University of Minnesota
Josephine Yu Department of Mathematics University of California
Ming Zhang Department of Biomathematical Sciences University of Texas
Xun Zhou Department of Computer Science University of Minnesota
Severinas Zube Department of Mathematics and Informatics Vilnius State University

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