[Facets-of-complexity] Invitation & Link to Monday Lecture & Colloquium - June 14th 2021 - changed times.

[Ita Brunke <i.brunke@inf.fu-berlin.de>]

You are cordially invited to our next Monday Lecture & Colloquium on June 14th.

Attention: Time is changed! Colloquium is at 14:45 h & Lecture is at 16:30 h.

Monday's Lecture & Colloquium will be online via Zoom, as used to.

Invitation link:
https://tu-berlin.zoom.us/j/69716124232?pwd=dzFlcTFHMmFXRTE5QmZLaEV5N0FRUT09
No password is required.

Online via:
Zoom - Invitation

Time: Monday, June 14th - 16:30 h !!!

Lecture: Alex Postnikov (MIT)

Title: Polypositroids

Abstract:

Polypositroids is a class of convex polytopes defined to be those polytopes that are simultaneously generalized permutohedra (or polymatroids) and alcoved polytopes. Whereas positroids are the matroids arising from the totally nonnegative Grassmannian,polypositroids are "positive" polymatroids. We parametrize polypositroids using Coxeter necklaces and balanced graphs, and describe the cone of polypositroids by extremal rays and facet inequalities. We generalize polypositroids to an arbitrary finite Weyl group W, and connect them to cluster algebras and to generalized associahedra. We also discuss membranes, which are certain triangulated surfaces. They extend the notion of plabic graphs from positroids to polypositroids. The talk is based on a joint work with Thomas Lam.

Coffee Break!

Time: Monday, June 14th - 14:45 h !!!

Colloquium: Davide Lofano (Technische Universität Berlin)

Title: Random Simple-Homotopy Theory

Abstract:

A standard task in topology is to simplify a given finite presentation of a topological space. Bistellar flips allow to search for vertex-minimal triangulations of surfaces or higher-dimensional manifolds, and elementary collapses are often used to reduce a simplicial complex in size and potentially in dimension. Simple-homotopy theory, as introduced by Whitehead in 1939, generalizes both concepts.

We take on a random approach to simple-homotopy theory and present a heuristic algorithm to combinatorially deform non-collapsible, but contractible complexes (such as triangulations of the dunce hat, Bing's house or non-collapsible balls that contain short knots) to a point.
The procedure also allows to find substructures in complexes, e.g., surfaces in higher-dimensional manifolds or subcomplexes with torsion in lens spaces.
(Joint work with Bruno Benedetti, Crystal Lai, and Frank Lutz.)