Conference Agenda

Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).

 
Session Overview
Session
MS146, part 4: Random geometry and topology
Time:
Saturday, 13/Jul/2019:
10:00am - 12:00pm

Location: Unitobler, F006
30 seats, 57m^2

Presentations
10:00am - 12:00pm

Random geometry and topology

Chair(s): Paul Breiding (Max-Planck Institute for Mathematics in the Sciences, Germany), Lerario Antonio (SISSA), Lundberg Erik (Florida Atlantic University), Kozhasov Khazhgali (Max-Planck Institute for Mathematics in the Sciences, Germany)

This minisymposium is meant to report on the recent activity in the field of random geometry and topology. The idea behind the field is summarized as follows: take a geometric or topological quantity associated to a set of instances, endow the space of instances with a probability distribution and compute the expected value, the variance or deviation inequalities of the quantity. The most prominent example of this is probably Kostlan, Shub and Smales celebrated result on the expected number of real zeros of a real polynomial. Random geometry and topology offers a fresh view on classical mathematical problems. At the same time, since randomness is inherent to models of the physical, biological, and social world, the field comes with a direct link to applications.

More infos at: https://personal-homepages.mis.mpg.de/breiding/siam_ag_2019_RAG.html

 

(25 minutes for each presentation, including questions, followed by a 5-minute break; in case of x<4 talks, the first x slots are used unless indicated otherwise)

 

Geometric limit theorems in topological data analysis

Christian Lehn
Universität Chemnitz

In a joint work with V. Limic and S. Kalisnik Verosek we generalize the notion of barcodes in topological data analysis in order to prove limit theorems for point clouds sampled from an unknown distribution as the number of points goes to infinity. We also investigate rate of convergence questions for these limiting processes.

 

Homological Connectivity in Random Čech Complexes

Omer Bobrowski
Technion

A well-known phenomenon in random graphs is the phase-transition for connectivity, proved first by Erdős Rényi in 1959. In this talk we will discuss a high-dimensional analogue of this phenomenon known as "homological connectivity". A simplicial complex is a structure consisting of vertices, edges, triangle, tetrahedra and higher dimensional simplexes. Homological connectivity refers to the vanishing of "holes" in various dimensions. We will discuss the phase transitions for homological connectivity in a random Čech complex - a simplicial complex generated by a spatial Poisson process. We will see how the well-known results for graphs are generalized in higher dimensions. In particular, we will discuss the analogue of isolated vertices in higher-dimensions, and its effect on homological connectivity.