Undergraduate, graduate, postgraduate students, and everybody interested in geometry are welcome to the

Seminar on


Seminar outline:

Amoeba of an algebraic variety in the complex torus is the image of this variety under the logarithmic map into the real vector space. Introduced by Gelfand, Kapranov and Zelevinski in 1994, amoebas have revealed a number of interesting geometric properties and have found nice applications, for instance, in the real algebraic geometry. Amoebas are naturally linked with the geometry of Newton polytopes and, in particular, with the Viro construction based on the combinatorics of subdivisions of convex lattice polytopes. In turn, the idea of Viro has lead to the definition of non-Archimedean amoebas and related combinatorial objects which conjecturally (Kontsevich) count the number of rational curves passing through a given finite set. We plan to discuss this developing theory and related questions which may appear in our study.


Basic courses in linear algebra, differential geometry and topology.


M. Forsberg, M. Passare, and A. Tsikh, Laurent determinants and arrangements of hyperplane amoebas. Adv. Math. 151 (2000), no. 1, 45--70.
I. M. Gelfand, M. M. Kapranov, and A. V. Zelevinski, Discriminants, resultants and multidimensional determinants, Birkhauser, Boston, 1994.
G. Mikhalkin, Real algebraic curves, the moment map and amoebas, Ann. of Math. (2) 151 (2000), no. 1, 309--326.
G. Mikhalkin, Amoebas of algebraic varieties, preprint at http://www.arxiv:math.ag/0108225, 2001.
G. Mikhalkin and H. Rullgard, Amoebas of maximal area, IMRN 9 (2001), 441-451.
M. Passare and H. Rullgard, Amoebas, Monge-Ampere measures and triangulations of the Newton polytope, Research report in Math. no. 10, 2000, Stockholm University.


Wednesday, 10:30-12.00, Schreiber 209. The first meeting on April 24.