Stephan Klaus 2-4

We give an explicit polynomial of degree 14 in three real variables x, y and z such that the zero set gives the solid trefoil knot. The polynomial depends on two further parameters which enable a deformation from an embedded torus. We use only elementary methods such that the proofs are also accessible to graduate math work groups for pupils in secondary schools. The results can be easily visualized using the free SURFER software of Oberwolfach.

J. Basto-Gonçalves 5-12

Very basic results and ideas of symplectic topology are presented in the context of symplectic embeddings of ellipsoids. A simple version of symplectic capacities is defined and used to prove rigidity results, and the “symplectic folding” construction is explained and used to prove flexibility results.

Margarida Melo 13-16

Géometrie Algébrique en Liberté is a school and conference organized by and for algebraic geometers in the beginning of their scientific careers. The 18th edition of GAeL took place in the Mathematics Department of the University of Coimbra, Portugal, on June 7-11 2010. It gathered together about 70 participants coming from whole parts of the world who got the opportunity to learn and discuss together and “en Liberté” the most recent developments in this area of research. The senior speakers for this year were the Professors Olivier Debarre (C.N.R.S.-Paris), Gerard van der Geer (Amsterdam) and Bernd Sturmfels (Berkeley).

Isabel M. Narra Figueiredo 17

The Summer School and Workshop on Imaging Sciences and Medical Applications was an initiative of the UTAustin|Portugal Program, for Mathematics, in partnership with CIM (Center for International Mathematicics).

18-19

- July, 05 and 07, 2010: Pedro Nunes Lectures, by Maxim Kontsevich.

- July, 07, 2010: Jornada Matemática SPM/CIM on “Trends in Quantum Geometry”

- October, 11-15, 2010: Educational Interfaces between Mathematics and Industry.

- July, 9-10, 2010: 8th EUROPT Workshop “Ad- vances in Continuous Optimization”

- July, 18-31, 2010: MatCampus2010

- September 26-29, 2010: Raising European Pub- lic Awareness in Mathematics

Maxim Kontsevich 20

Professor Maxim Kontsevich work concentrates on geometric aspects of mathematical physics, most notably on knot theory, quantization, and mirror symmetry. His most famous result is a formal deformation quantization that holds for any Poisson manifold. He also introduced knot invariants defined by complicated integrals analogous to Feynman integrals.

In topological field theory, he introduced the moduli space of stable maps, which may be considered a mathematically rigorous formulation of the Feynman integral for topological string theory.

He received a Fields Medal in 1998, at the 23rd International Congress of Mathematicians in Berlin. He also received the Henri Poincaré Prize in 1997 and a Crafoord Prize in 2008.