You are cordially invited to our next Monday Lecture. Next
Monday, there will be the hearing of the next PhD candidates.
We will have three talks. Talks will be 30 min. 15 min
discussions, 15 min break.
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 December 14th 2020 at 14:00 h, 15:00,
16:00.
Online via:
Zoom - Invitation
Time: Monday, December 14th - 14:00 h
Lecture: Matthias Himmelmann
Title: Generalized Principal Component Analysis for
Algebraic Varieties
Abstract:
The Buchberger-Möller algorithm is a famous symbolic method for
finding all polynomials that vanish on a point cloud. It has even
been extended to noisy samples. However, the resulting variety does
not necessarily represent the topological or geometric structure of
the data well. By making use of the Vandermonde matrix, it is
possible to find polynomials of a prescribed degree vanishing on the
samples. As this matrix is severely ill-conditioned, modifications
are necessary. By making use of statistical and algebro-geometric
techniques, an algorithm for learning a vanishing ideal that
represents the data points‘ geometric properties well is presented.
It is investigated that this method -- among various other desirable
properties -- is more robust against perturbations in the data than
the original algorithm.
Time: Monday, December 14th - 15:00 h
Lecture: Dante Luber
Title: Boundary Complexes for Moduli Spaces of Curves
Abstract:
In 2016, Noah Giansiracua showed that a collection of boundary
divisors in the moduli space of genus-0 n-pointed curves has
nonempty intersection if and only if all pairwise intersections are
nonempty. This result is equivalent to showing that the boundary
complex associated to such a moduli space is a flag complex. Kyla
Quillin extended Giansiracusa's result to most moduli spaces of
genus-g n-pointed curves. We give a complete classification of all
(g,n) pairs for which the boundary complex is a flag complex.
Time: Monday, December 14th - 16:00 h
Lecture: Jannik Peters
Title: Efficiency and Stability in Euclidean Network
Design
Abstract:
We study the recently proposed Euclidean Generalized Network
Creation Game by Bilò et al.[SPAA 2019] and investigate the creation
of (beta,gamma)-networks, which are in beta-approximate Nash
equilibrium and have a total cost of at most gamma times the optimal
cost. In our model we have n agents corresponding to points in
Euclidean space create costly edges among themselves to optimize
their centrality in the created network. Our main result is a simple
O(n^2)-time algorithm that computes a (beta,beta)-network with low
beta for any given set of points. Along the way, we significantly
improve several results from Bilò et al. and we asymptotically
resolve a conjecture about the Price of Anarchy.
