Tropical geometry is a young and rapidly growing area in mathematics, rooted in algebraic geometry, complex analysis, commutative algebra, and combinatorics, with successful applications in computer science, biology and statistical physics, in addition to other areas of mathematics. Tropical geometry is a polyhedral analogue of algebraic geometry. Algebraic varieties over a valued field are replaced by polyhedral complexes, retaining some invariants of the original algebraic varieties. Tropical geometry provides a framework for solving algebro-geometric problems using concrete combinatorial tools. Recent years have seen tremendous development in tropical geometry that both established the field as an area in its own right and unveiled its deep connections to numerous branches of pure and applied mathematics.
A workshop on Tropical Geometry will be held at International Centre for Mathematical meetings (CIEM) in Castro Urdiales, Cantabria, Spain, on December 12-16, 2011. It will be the first major international event in tropical geometry in two years and will as such serve to display the most recent developments, to foster interaction within a geographically wide-spread community, to initiate new collaborations, and to sustain and broaden the mentoring network within the field. The workshop will have 22 invited talks, a poster session, a software presentation, and a special discussion session devoted to open problems. The list of speakers includes senior as well as young promising researchers and all leading female mathematicians in the field. Graduate students and early career researchers will be able to showcase their work and get feedback from leading experts at the poster session. Around 60 participants, including around 30% from under-represented groups, are expected. To disseminate the results of the workshop to a wider audience, slides and notes from the presentations and discussions will be placed on the web. Conference proceedings of refereed articles on tropical geometry will also be published.
Tropical geometry is a young and rapidly growing area in mathematics, rooted in algebraic geometry, complex analysis and commutative algebra, with successful applications in computer science, biology and statistical physics, in addition to other areas of mathematics. The workshop provided an opportunity to display the most recent developments, to foster interaction within a geographically wide-spread community, and to initiate and sustain mentoring of young researchers. The workshop took place at the International Centre for Mathematical Meetings (CIEM) in Castro Urdiales, Spain, during December 12-16, 2011. NSF funding was used to support travel expenses for 20 young researchers and graduate students. Seventeen countries were represented by the 82 attending participants. Intellectual merit: The workshop's goal was to familiarize researchers within the community and beyond with the most recent developments, to intensify existing and initiate new collaborations, and to sustain and broaden the existing mentoring network within the field. Another successful aspect, due to the location of the workshop, was promoting the interaction of related research groups in Spain, most notably in the areas of computer algebra, combinatorics, real algebraic geometry, and singularity theory, with the tropical geometry community. Broader impacts: The workshop had 21 invited talks, a poster session, a software presentation and a special discussion session devoted to open problems in the field. The list of speakers, selected by the organizers, included senior as well as young promising researchers and all leading female mathematicians working in the field. The workshop exposed students and young scholars to the latest developments in the field and encouraged them to share their work with the leading experts via poster presentations and informal discussions. The committee invited all leading female researchers in tropical geometry, and actively encouraged participation from female students and researchers. In addition, the organizing committee included a female representative from each career stage: a senior researcher, a young professor, and a postdoc.
