Location: Room 005 - Ground Floor Freie Universität Berlin Institut für Informatik, Takustr. 9 14195 Berlin Time: Monday, Jan 6 - 14:15 h Lecturer: Frank Sottile (Texas University) Title: *Irrational toric varieties and the secondary polytope* Abstract: The secondary fan of a point configuration A in R^n encodes all regular subdivisions of A. These subdivisions also record all limiting objects obtained by weight degenerations of the irrational toric variety X_A parameterized by A. The secondary fan is the normal fan of the secondary polytope. We explain a functorial construction of R^n-equivariant cell complexes from fans that, when applied to the secondary fan, realizes the secondary polytope as the moduli space of translations and degenerations of X_A. This extends the work of Kapranov, Sturmfels and Zelevinsky (who established this for complex toric varieties when A is integral) to all real configurations A. Coffee & Tea Break: Room 134 Time: Monday, Jan 6 - 16:00 h s.t.* Colloquium: Lukas Kühne (Hebrew University of Jerusalem) Title: *Matroid representations by c-arrangements are undecidable* Abstract: A matroid is a combinatorial object based on an abstraction of linear independence in vector spaces and forests in graphs. It is a classical question to determine whether a given matroid is representable as a vector configuration over a field. Such a matroid is called linear. This talk is about a generalization of that question from vector configurations to c-arrangements. A c-arrangement for a fixed c is an arrangement of dimension c subspaces such that the dimensions of their sums are multiples of c. Matroids representable as c-arrangements are called multilinear matroids. We prove that it is algorithmically undecidable whether there exists a c such that a given matroid has a c-arrangement representation. In the proof, we introduce a non-commutative von Staudt construction to encode an instance of the uniform word problem for finite groups in matroids of rank three. The talk is based on joint work with Geva Yashfe. -- G"unter Rote (Germany=49)30-838-75150 (office) Freie Universit"at Berlin -75103 (secretary) Institut f"ur Informatik FAX (49)30-838-4-75150 Takustrase 9, D-14195 Berlin, GERMANY