Soy profesor asistente en la Universidad de los Andes. Mi área de investigación es la geometría tropical y sus conexiones con la geometría enumerativa, la geometría algebráica real y la teoría de intersecciones. Mas generalmente, mi investigación está radicada en la geometría algebráica, la geometría simpléctica y la combinatoria. Si quieren saber más, miran abajo o escribenme un correo.
Email: j.rau (at) uniandes.edu.co
Estamos organizando quincenalmente el seminario Latino-Americano Geometría Algebráica Real y TrOpical. En caso de interesa a participar, esribennos por favor.
Construye tu curva algebráica personal con esta pequena aplicación de browser ;)
Estoy preperando un libro sobre la geometría tropical en colaboración con Grigory Mikhalkin. El siguiente enlace dirige al borrador (más o menos) actual. Me alegro mucho recibir sus correciones y sugerencias.
(hasta ahora, solo en inglés)
My research area is tropical geometry (the fancy adjective tropical was originally used in the context of the max-plus algebra to honour earlier work of the Brazilian (Hungarian-born) mathematician Imre Simon). Even though the origins of the field are much older, tropical geometry emerged as an new trend in algebraic and symplectic geometry around 2000. Here is a list of keywords describing my research interests.
Tropical mathematics can be compared to the world of dinosaurs. When paleontologists want to learn more about these animals, they can't just watch them them in the zoo or the jungle, because unfortunately the poor things became extinct a long time ago. Instead, they work more like archeologists. They go digging for their bones, try to reassemble their skeletons, and from that draw conclusions about how these animals looked like, what they ate, how they hunted etc. In tropical geometry, we do exactly the same!
In our setting, the dinosaurs are called algebraic varieties. These are complicated geometrical shapes given by polynomial equations. Such algebraic varieties show up all the time in mathematics, science and real life, and therefore their study forms one of the oldest and most sophisticated fields in mathematics (called algebraic geometry). Algebraic varieties are often so complicated that it is impossible to get our hands on them directly – like the extinct dinosaurs. However, in some cases mathematicians found a way to get hands on the skeletons of these mathematical dinosaurs. Technically, you first have to turn the dinosaurs into amoebas and then starve them out until only the skeletons are left – this is where the analogy gets a little violent ;).
The mathematical skeletons are called tropical varieties, and in tropical geometry we play paleontologist and try to find out more about the original geometrical objects by studying their tropical skeletons (you can find some pictures on this page). The nice thing is that tropical varieties are much simpler objects than the original ones and can be studied in much more down-to-earh terms. Of course, we cannot work wonders and find answer all questions (it is easy to estimate the size of the real-life dinosaur from its skeleton, but did it have furry or smooth skin?), but by now some remarkable facts about algebraic varieties were deduced from the study of their tropical skeletons, and that is why tropical geometry is nowadays such an exciting and rapidly growing field.
You are bachelor/master student in mathematics (or a researcher from a different field) and want to embark on a first expedition to the tropics? Then have a look at these lecture notes.
One of the origins of tropical geometry is Viro's patchworking method. The link below leads to a small browser app which allows you to do some experiments with this method.
Seminarios de Estudiantes
Seminarios de Investigación
j.rau (at) uniandes.edu.co
Departamento de Matemáticas
Fon: +57 1 3394949