North American Workshop on Tropical Geometry (07w5055)

Arriving in Banff, Alberta Sunday, March 4 and departing Friday March 9, 2007


(University of Strasbourg)

Grigory Mikhalkin (University of Toronto)

(Kansas State University)


Tropical Geometry already proved to be useful in quite distinct areas of Mathematics. By now it has applications in Real Algebraic Geometry, Enumerative Geometry, Mirror Symmetry, Symplectic Geometry and Computational/Combinatorial Geometry. The list of its applications keeps growing. E.g. most recently, Tropical Geometry had a brand-new appearance in the Statistical Physic work of R. Kenyon and A. Okounkov where they studied mathematical model for dimers accumulation. Currently there are several research groups around the globe that are doing active research in Tropical Geometry from somewhat different points of view. One can also mention a conjectural relationship with the String Theory (e.g. topological vertex, Donaldson-Thomas invarians and melting crystal model).

Tropical Geometry is still a very young subject. It received its current name in March 2002 (when B. Sturmfels visited G. Mikhalkin in Salt Lake City). It went to the scope of the Bourbaki seminar in June 2003 (when I. Itenberg gave a talk at the Bourbaki seminar in Paris). The first conference on Tropical Geometry that helped to understand the state of the emerged subject and to outline some important directions of its development took place in the Fall of 2003 in the American Institute of Mathematics in Palo Alto (organized by Mikhalkin, Sturmfels and Viro). There is a number of young researchers, in particular, graduate students and post-docs who work in this area. In the Fall of 2004 Itenberg, Mikhalkin and Shustin organized an Oberwolfach Seminar on the subject (which was aimed, mainly, to the young researchers). The most recently there was a joint workshop of mathematicians and physicists in May 2005 in Strasbourg (organized by Itenberg and Turaev) where new connections with Physics
were discovered.

We propose to organize a workshop in Banff that would enable "Tropical" researchers in different areas
of Mathematics to communicate and to develop a more global point of view on the subject. We believe that the beginning of 2007 would be a perfect time to review the development of this young subject and to set up further directions of development. Also, one goal why we would particularly like to organize such a workshop in Banff (while all prior workshops only took place either in the United States
or Europe) would be to stimulate connections between Canadian and American research groups in Tropical Geometry (as well as connections of North American research groups to the rest of the world).