# Joint Projects & Networks

## Polynomial Methods in Combinatorics

Project Reference: Polinomial Methods in Combinatorics. 5-HH2004-0007.

Main Researchers: Tamas Szónyi (Budapest), Oriol Serra (Barcelona) 2005-2006.

Investigating combinatorial, algebraic and geometrical structures with the help of associating polynomials to them has proved to be very fruitful. Both the UPC and the ELTE group of this project developed such techniques and applied them to various problems. In the last 10 years the polynomial method proved to be very useful in both the theory of finite geometries and additive number theory. In the two areas analogous, but not identical techniques have been developed to attack different problems, which are similar in nature. In general, we have a structure in a finite geometry or in an abelian group with some combinatorial properties and we want either to give an estimation on their sizes or to determine the extremal examples.

The main goal of the project is to combine the expertise of the researchers in both teams involved in it to analyze the use of polynomial methods in finite geometry and in additive number theory by combining the classical Rédei techniques with the recent Alon’s Combinatorial Nullstellensatz.

## COMBSTRU. Combinatorial Structure of Intractable Problems

Projecte Reference: COMBSTRU Combinatorial Structure of Intractable problems. UE- RTN2-2001-00231.

Main Researcher: Josep Díaz (UPC) (2002-2006).

COMBSTRU is a Research Training Network funded through the European Commission, whose main scientific goal is the analysis of intractable combinatorial problems, focusing on structural properties of the problems and using tools from algebra, logic, probability, geometry, statistical physics and other fields. Training of PhD students and postdoctoral researchers through appointed positions, workshops and summer schools is a main issue in the network.

## i-Math

COMBGRAF is a member of the Spanish project Ingenio Matematica, i-Math (2006-2011) whose main purpose is to increase the weight of mathematics in science, technology, industry and society in Spain as well as worldwide.

Main Researcher: Enrique Zuazua (2006-2009).

Ingenio MATHEMATICA (i-MATH) es un proyecto de investigacion singular para el periodo 2006-2011 que propone un Programa de Actividad Investigadora integral para la matemática española con el objetivo básico de promover y ejecutar actuaciones estratégicas de ámbito estatal que incrementen cualitativa y cuantitativamente el peso de las matemáticas en el panorama internacional y en el sistema español de ciencia, tecnología, empresa y sociedad.

## DIMATIA

Discrete Mathematics, Theoretical Computer Science and Applications

Charles University, Academy of Sciences of the Czech Republic and Institute of Chemical Technology, Prague.

COMBGRAF belongs to its network of associate members.

DIMATIA is the Center for Discrete Mathematics, Theoretical Computer Science and Applications. It was founded at Faculty of Mathematics and Physics, Charles University in Prague, Czech Republic, as a joint project of Charles University, Academy of Sciences of the Czech Republic and Institute of Chemical Technology, Prague. A network of associate members of DIMATIA was soon developed. The center is open and actively seeks partners from all parts of the world.

The purpose of the center is to foster research in all fields of discrete mathematics and its modern applications and relationship to computer science, operations research and fields as diverse as biology, chemistry and social sciences. Towards this end the center organizes a continuing program of workshops, conferences and research visits both in Prague and all sites of participating institutions.

The activity of the center concentrates in the following directions:

- research workshops and conferences,
- postdoctoral positions announced and supported jointly with our participating institutions, and
- short-term visits of senior researchers.