triangulations in Santander

[Francisco Santos]

Announcing a summer course:

             TRIANGULATIONS OF POLYHEDRA AND POINT SETS

                 Santander (SPAIN), July 3-7, 2000
                      Course length: 20 hours

Lecturers: 

 Jesus A. de Loera, assistant professor, U. of California at Davis.
 Joerg Rambau, scientific assistant, 
                     Konrad-Zuse-Zentrum fuer Informationstechnik, Berlin.
 Francisco Santos, associate professor, U. de Cantabria, Santander.

A short description of the course and tentative program is included below.
For more information, including travel hints, registration, accomodation,
etc. see:  http://matsun1.matesco.unican.es/~santos/triancourse

SHORT DESCRIPTION OF THE COURSE:
-------------------------------
The topic are optimization and enumeration problems in the set of all
triangulations of a polytope or point configuration. The course is
addressed to graduate students and researchers in mathematics
(specially algebra, geometry and applied mathematics), computer
science (complexity theory, algorithmics) and some parts of engineering
(those related to GIS, CAD, etc). On the theoretical side, the core of the
course is the theory of secondary and universal polytopes, and the notion
of geometric bistellar flip. 

The pre-requisites from the student are, basically, linear algebra
and affine geometry. Some familiarity with projective geometry,
theoretical combinatorics and complexity of algorithms would be desirable,
but not strictly necessary. For the applications in algebraic geometry
and topology mentioned in the last day (see the program below) some
knowledge of these areas is needed, but the rest of the course can be
followed without them.

TENTATIVE PROGRAM:
-----------------
Monday, July 3:
09:00 h. - 09:30 h. WELCOME.
09:30 h. - 11:30 h. FUNDAMENTAL NOTIONS AND MOTIVATION.
                    JESUS DE LOERA
11:30 h. - 12:00 h. BREAK
12:00 h. - 14:00 h. LIFE IN TWO DIMENSIONS. FLIPS.
                    FRANCISCO SANTOS

Tuesday, July 4
09:30 h. - 11:30 h. COMBINATORICS OF POLYHEDRAL SUBDIVISIONS. GALE
                    DIAGRAMS AND CHAMBERS.
                    JORG RAMBAU
11:30 h. - 12:00 h. BREAK 
12:00 h. - 14:00 h. SECONDARY POLYTOPES. BISTELLAR FLIPS.
                    JORG RAMBAU

Wednesday, July 5
09:30 h. - 11:30 h. THE UNIVERSAL POLYTOPE: A TOOL FOR OPTIMIZATION.
                    JESUS DE LOERA 
11:30 h. - 12:00 h. BREAK
12:00 h. - 14:00 h. OPTIMIZATION. MINIMAL AND MAXIMAL TRIANGULATIONS.
                    JESUS DE LOERA

Thursday, July 6
09:30 h. - 11:30 h. THE BEST OF WORLDS: CYCLIC POLYTOPES.
                    JORG RAMBAU
11:30 h. - 12:00 h. BREAK
12:00 h. - 14:00 h. A CRUCIAL EXAMPLE: PRODUCTS OF SIMPLICES.
                    TRIANGULATIONS WITHOUT FLIPS. 
                    FRANCISCO SANTOS

Friday, July 7
09:30 h. - 11:30 h. FIBER POLYTOPES AND BEYOND.
                    JORG RAMBAU
11:30 h. - 12:00 h. BREAK
12:00 h. - 14:00 h. APPLICATIONS IN ALGEBRAIC GEOMETRY.
                    JESUS DE LOERA
14:00 h. - 14:15 h. DELIVER OF DIPLOMAS


+--------------------------------------------------------+
| Francisco Santos              santos at matesco.unican.es |
| Departamento de Matematicas, Estadistica y Computacion |
| Universidad de Cantabria,          Tel: +34-942-201522 |
| E-39005 Santander, SPAIN           Fax: +34-942-201402 |
| http://www.matesco.unican.es/~santos                   |
+--------------------------------------------------------+







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