Tropical Methods in Real Algebraic Geometry (19w5100)


Lucia Lopez de Medrano (Universidad Nacional Autonoma de Mexico)

(Université de Nantes)

Kris Shaw (University of Oslo)


The Casa Matemática Oaxaca (CMO) will host the "Tropical Methods in Real Algebraic Geometry" workshop in Oaxaca, from September 8, 2019 to September 13, 2019.

Tropical methods provide an extremely powerful new set of tools in the study of complex and real algebraic geometry. Among the branches of real algebraic geometry that have benefited from these tools are the construction of real algebraic varieties with controlled topology, and also real enumerative geometry. One of the roots of tropical geometry lies in Viro's patchworking invented in the late seventies to construct real algebraic varieties with a rich topology. Applications of tropical methods to real and complex enumerative geometry were initiated by Mikhalkin's seminal Correspondence Theorem in the early 2000. In particular, it supplied at that time the first method to compute Welschinger invariants of del Pezzo real toric surfaces. In recent years, new real, complex, and tropical enumerative invariants have been discovered. Computing and relating all these invariants is one of the current leading research directions in this field.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). The research station in Oaxaca is funded by CONACYT