[Facets-of-complexity] Invitation to Monday Lecture & Colloquium - February 10th 2020 / Third 17:00 talk canceled

[Günter Rote <rote@inf.fu-berlin.de>]

You are invited to our last Monday Lecture & Colloquium for this term 
next Monday at 14:15 h and 16:00 h at FU Berlin.

The *second Colloquium* that was planned for *17:00* is CANCELED.

Location:

Room 005 - Ground Floor
Freie Universität Berlin
Institut für Informatik
Takustr. 9
14195 Berlin

Time: Monday, February 10th - 14:15 h

Lecture: Lionel Pournin (Université Paris 13)
Title: Recent results on the diameter of lattice polytopes

Abstract:
Several new results about the largest possible diameter of a lattice 
polytope contained in the hypercube [0,k]^d, a quantity related to the 
complexity of the simplex algorithm, will be presented. Upper bounds on 
this quantity have been known for a couple of decades and have been 
improved recently. In this lecture, conjecturally sharp lower bounds on 
this quantity will be presented for all d and k, as well as exact 
asymptotic estimates when d is fixed and k grows large. These lower 
bounds are obtained by computing the largest diameter a lattice zonotope 
contained in the hypercube [0,k]^d can have, answering a question by 
Günter Rote. This talk is based on joint work with Antoine Deza and 
Noriyoshi Sukegawa.


Coffee & Tea Break: Room 134

Time: 16:00 h s.t.

Colloquium: José Samper (Max-Planck-Institut Leipzig)
Title: Dual matroid polytopes and the independence complex of a matroid

Abstract:
A shelling order of a simplicial/polytopal complex is an ordering of the 
top dimensional faces that allows us to understand various properties of 
the underlying complex (when it exists). Empirically, some shelling 
orders are better than others in the sense that they are easier to 
analyze or come equipped with . This is especially notable for complexes 
that admit many shelling orders, like polytopes and and matroid 
independence complexes. We propose a strange connection, linking 
shelling orders of dual matroid polytopes to shelling orders of 
independence complexes. In particular, we show that several classical 
theorems about shellability of matroids have geometric interpretations. 
We use this to address to propose a new strategy for a 1977 conjecture 
of R. Stanley about face numbers of independence complexes: that the 
h-vector is a pure O-sequence. The talk is based on joint work with Alex 
Heaton.

The second colloquium that was planned at 17:00 h (by Zsolt Ádám Wagner 
from ETH Zürich, about recent developments in the container method)
is CANCELED.