Polyhedral Complexes, Non-Archimedean Amoebas and Tropical Varieties: A First Glimpse on Tropical Geometry
 
 
Description:  Tropical geometry has been around for some time, with different names and in different contexts. In the last few years, a growing interest appeared on this subject, motivated by important applications of this theory to Algebraic Geometry: Tropical Geometry seems to be a strong tool on translating from the algebraic context to a more combinatorial one. The area is, however, still in its beginnings, and some basic results and definitions still lack consensus. We will first present a definition of tropical hyper-surface and its main properties; proceed to show two completely different characterizations of the same object; and finish by presenting a tentative basic theory of tropical algebraic varieties, as well as some results that support this choice. In the process, strong (and hopefully interesting) links with well known areas of algebra and geometry will be revealed.
Area(s):
Date:  2006-04-11
Start Time:   14:45
Speaker:  João Gouveia (CMUC, U. Coimbra)
Place:  5.5
Research Groups: -Algebra and Combinatorics
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