[Facets-of-complexity] Invitation and link to Monday Lecture - January 18th 2021 - online via zoom

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

You are cordially invited to our next Monday Lecture in the New Year. 

All Monday Lectures and Colloquia of winter term 2020/21 will be given online via zoom.

You may find valid Invitation for zoom throughout all winter term here:
http://www.facetsofcomplexity.de/monday/WS-2020-21/index.html

Invitation link:
https://tu-berlin.zoom.us/j/69716124232?pwd=dzFlcTFHMmFXRTE5QmZLaEV5N0FRUT09

Monday Lecture will be on January 18th 2021 at 14:15 h & 16:00.

Online via:
Zoom - Invitation

Time: Monday, January 18th - 14:15 h

Lecture: Florian Frick (Carnegie Mellon University)

Title: New applications of the Borsuk--Ulam theorem

Abstract:

The classical Borsuk--Ulam theorem states that any continuous map from the d-sphere to d-space identifies two antipodal points. Over the last 90 years numerous applications of this result across mathematics have been found. I will survey some recent progress, such as results about the structure of zeros of trigonometric polynomials, which are related to convexity properties of circle actions on Euclidean space, a proof of a 1971 conjecture that any closed spatial curve inscribes a parallelogram, and finding well-behaved smooth functions to the unit circle in any closed finite codimension subspace of square-intergrable complex functions.

Time: Monday, January 18th - 16:00 h

Lecture: Pavle Blagojević (Freie Universität Berlin)

Title: Ten years in one lecture

Abstract:

Ten years ago, in February 2011, I joined the group of Günter M. Ziegler at Freie Universität Berlin. Now, ten years later, I will show you some of the problems in Geometric and Topological Combinatorics that intrigued us, some of which we managed to solve, and sketch some of the crucial ideas, methods, and the tools we had to develop in order to answer them. 

We will see how 

-- work on the Bárány-Larman conjecture on colored point sets in the plane   gave birth to the Optimal colored Tverberg theorem, 

-- the constraint method collected all classical Tverberg type results under one roof    and opened a door towards counter-examples to the topological Tverberg conjecture.

Furthermore, we will illustrate how the search for convex partitions of a polygon into pieces of equal area and equal perimeter forced us to 

-- study the topology of the classical configuration spaces, 

-- construct equivariant cellular models for them, 

-- prove a new version of an equivariant Goresky-MacPherson formula for complements of arrangements, 

-- revisit a classical vanishing theorem of Frederick Cohen, and explain why these answers are related to the existence of highly regular embeddings and periodic billiard trajectories.

Finally, we will talk about 

-- equi-partitions of convex bodies by affine hyperplanes, and 

-- greedy convex partitions of many measures.

These results are joint work with, in chronological order, Günter M. Ziegler, Benjamin Matschke, Florian Frick, Albert Haase, Nevena Palić, Günter Rote, and Johanna K. Steinmeyer.