### Researchers

CMM: Marcos Kiwi, Martín Matamala, Ivan Rapaport, José Soto, Maya Stein

U. Concepción: Julio Aracena, Anahí Gajardo

UNAB: Cristóbal Rojas, José Zamora

UAI: Marcos Goycolea, Eric Goles, Eduardo Moreno, Karol Suchan

## About the research group

Discrete mathematics (DM) is the branch of mathematics dealing with objects that can assume only distinct, separated values. Most of the objects studied in DM are countable sets, finite graphs, lattices, and finitely described procedures. DM has become popular in recent decades of its applications to computer science.

What distinguishes the DM group at the CMM is a common interest to study the mathematical and computational properties of discrete structures such as networks. These structures appear in diverse areas of current scientific and technological endeavor. For example, real-world phenomena involving networks include urban traffic, the flow of electronic mail through the Internet, the spread of contagious diseases, the distribution of goods from warehouses to retail outlets and the self regulation of cells.

Computer and communications networks will continue to play a major role in society, and new applications will continue to appear at a blinding pace. This situation gives rise to many fascinating scientific challenge, beginning with foundations for designing, evaluating, and managing these networks; encompassing new algorithms and models that can help understand the behavior and evaluation of existing networks; concerning abstract and combinatorial questions such as the theory of graph minors; etc. All of the latter are topics of general interest to the DM group at CMM.

Speaking in more technical and precise terms the main research areas of interest of our group are:

- Combinatorial optimization
- Graph theory & algorithmic graph theory
- Automata theory
- Computational complexity
- Cryptography
- Distributed Computing