3. Postdoctoral Program - MSRI

Connections for Women – Tropical Geometry
MSRI Berkeley, August 22 & 23, 2009
Organizers: Alicia Dickenstein, Eva-Maria Feichtner
The 2-days Connections for Women workshop was the very first event of the then upcoming
fall program on Tropical Geometry at MSRI. It was organized back to back with the 5-days
Introductory Workshop of the program. Both events being of an introductory nature, close
collaboration of the organizing teams resulted in complementary programs of both mini-courses
and research talks and brought the financial resources for both events to an optimal use. We
were able to support a high number of young, female participants, enabling them to familiarize
themselves with tropical geometry and providing them with manifold networking opportunities
both with women mathematicians and throughout the tropical community as a whole.
Scientific description
Recent years have seen a tremendous development in Tropical Geometry that both established
the field as an area of its own right and unveiled its deep connections to numerous branches of
pure and applied mathematics. Formally speaking, Tropical Geometry is the algebraic geometry
over the tropical semiring R∪{∞} with arithmetic operations x⊕y := min{x,y} and x⊙y := x+y.
From an algebraic geometric point of view, algebraic varieties over a field with non-archimedean
valuation are replaced by polyhedral complexes, thereby retaining much of the information about
the original varieties. From the point of view of complex geometry, the geometric combinatorial
structure of tropical varieties is a maximal degeneration of a complex structure on a manifold.
The tropical transition from the objects of algebraic geometry to the polyhedral realm is an
extension of the familiar theory of toric varieties. It opens classical problems to a completely new
set of techniques, and has already led to remarkable results in Enumerative Algebraic Geometry,
Symplectic Geometry, Dynamical Systems and Computational Commutative Algebra, among
other fields, and to applications in Algebraic Statistics, Mathematical Biology, and Statistical
Physics.
Mini-courses and talks
The Connections for Women event featured two mini-courses of two 1-hour lectures each.
The mini-courses were addressed to newcomers to the field of Tropical Geometry and provided
accessible as well as intriguing introductions from different viewpoints. For both mini-courses,
selected exercises were provided and the lecturers were available for discussions of the problems
during the workshop.
Federico Ardila (San Francisco State University): Linearity in the tropics
Abstract: Tropical geometry studies an algebraic variety X by ‘tropicalizing’ it into a polyhedral
complex Trop(X) which retains some information about X. Tropical varieties may be simpler
than algebraic varieties, but they are by no means well understood. In fact, tropical linear
spaces already feature a surprisingly rich and beautiful combinatorial structure, and interesting
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