Undergraduate, graduate, postgraduate students,
and everybody interested in geometry
are welcome to the
AMOEBAS of ALGEBRAIC VARIETIES
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
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,
determinants and arrangements of hyperplane amoebas. Adv. Math.
no. 1, 45--70.
I. M. Gelfand, M. M. Kapranov, and A. V. Zelevinski,
Discriminants, resultants and multidimensional
Birkhauser, Boston, 1994.
Real algebraic curves, the moment map and amoebas,
Ann. of Math. (2) 151 (2000), no. 1, 309--326.
Amoebas of algebraic varieties,
preprint at http://www.arxiv:math.ag/0108225, 2001.
G. Mikhalkin and H. Rullgard, Amoebas of maximal area, IMRN 9
M. Passare and H. Rullgard,
Amoebas, Monge-Ampere measures
and triangulations of the Newton polytope,
Research report in Math. no. 10, 2000, Stockholm University.
TIME and PLACE:
Wednesday, 10:30-12.00, Schreiber 209. The first meeting on April 24.