[Facets-of-complexity] Invitation to Monday Lecture & Colloquium - TODAY January 6 2020

[Günter Rote <rote@inf.fu-berlin.de>]

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